Robert Gilmore

Robert Gilmore Alice in the Country of Quantum Quantum physics for everyone

http://groups-beta.google.com/group/digitalsource SUMMARY Preface In the Country of Quantum The Bank Heisenberg The Institute of Mechanical The School of Copenhagen The Academy Fermi-Bose Virtual Reality Atoms in the Vacuum The Rutherford Castle The dance of the particles Massacarados The Piteira Phantástica of Experimental Physics Preface In the first half of the twentieth century, our understanding of the universe was turned upside down. The old theories of classical physics were replaced by a new way of seeing the world - the quantum mechanics. This was at odds, in many ways with the ideas of the old Newtonian mechanics, in fact, in many ways, was at odds with our common sense. However, the strange thing about these theories is its extraordinary success in predicting the observed behavior of physical systems. For more absurd that quantum mechanics may seem, this seems to be the way that Nature chose - once, we have to comply. This book is an allegory of quantum physics in order dicionarizado of "a narrative that describes a subject under the guise of another." The way in which things are behaving in quantum mechanics seems very strange to our habitual way of thinking and becomes more acceptable when we analogies with situations with which we are familiar, even when such analogies may be inaccurate. Such analogies can never be a true representation of reality, to the extent that quantum processes are in fact quite different from our ordinary experience. An allegory is an extended analogy, or a series of analogies. As such, this book follows the further steps of the Pilgrim s Progress or travel Gulliver than Alice in Wonderland. Alice seems the most appropriate model, however, when considering the world we inhabit. The Country of the quantum by which Alice travels is looks more like a theme park in which Alice is sometimes an observer, while sometimes it behaves like a particle with electric charge may vary. The Country of the Quantum shows the essential features of quantum world: the world we all inhabit. Much of the story is pure fiction and the characters are imaginary but the notes that describe the "real world" are true. Through the narrative you will find many statements obviously absurd and very different from common sense. For the most part, they are true. Niels Bohr, the father of quantum mechanics emseus beginning, is known to have observed that anyone who has not been stunned to think of quantum theory does not understand.

Seriously, though ... The description of the world proposed by quantum mechanics is certainly interesting and remarkable, but we seriously prepared to believe that is true? (Interestingly we find that. To emphasize this statement, throughout this book you will find brief notes that emphasize the importance of quantum mechanics in the real world. The notes are more or less like this: These notes summarize the importance to our world, quantum of topics encountered by Alice in each chapter. They want to be sufficiently nonintrusive, so you can ignore them while reading the story of the adventures of Alice, but if you want to discover the real meaning of these adventures, the notes are conveniently close. There are also some long notes at the end of chapter. They explain some of the key points in the text and are well characterized: See Note 1 at the end of Chapter Various aspects by which the quantum theory describes the world may seem absurd at first sight - and thus may possibly opinion of the second, third and twenty-fifth time. And yet, the only game in town. The old classical mechanics of Newton and his followers are unable to give any explanation for ripo of atoms and other microsystems. Quantum mechanics agrees well with observation. The calculations are often difficult and boring, but they were made, is perfectly suited to what was actually observed. It is impossible to emphasize enough the remarkable practical success of quantum mechanics. Although the result of a measure can be random and unpredictable, the predictions of quantum theory consistently fit the average results obtained from many measures. Any macroscopic observation involve many atoms and therefore many comments atômica.De new scale we see that the quantum mechanics is successful in that it automatically fits the results of classical mechanics for macroscopic objects the reverse is not true. The quantum theory was developed to explain observations made in atoms. Since its conception, was successfully applied to the core atom, the strong interaction of particles that come from the core and the behavior of which are composed of quarks. The application of the theory was extended by a factor of something like one hundred billion. The systems considered both decreased in size and increased in energy by this factor. And a long way of extrapolation of a theory from its original design, but even here the quantum mechanics seems to be able to deal with these extreme systems. Until the point where it was investigated, quantum mechanics seems to know of universal applicability. On a macroscopic scale, the predictions of quantum theory lose their random appearance and fit those of classical mechanics, which works very well with large objects. On a microscopic scale, however, the predictions of quantum theory are consistently confirmed in experiments. Even these forecasts, which seem to involve an absurd picture of the world, are supported by experimental evidence. Intriguing mind, as discussed in Chapter 4, the quantum mechanics appears to be in a strange position to fit all the observations, although we discuss which observations can actually be made. It seems that the world is more strange than imagined and perhaps more strange than we can imagine. Meanwhile, however, we follow Alice in the beginning of his journey by Country of Quantum. Robert Gilmore

Alice was bored. All his friends were on vacation, visiting relatives and she, because of rain, was locked in the house, watching television. That

afternoon had seen the fifth episode of an introductory course in Esperanto, a program of political propaganda and a garden. Alice was really bored. He looked at the book that was on the floor beside the chair. It was an edition of Alice in Wonderland it, earlier that day, had left there to finish reading. "I do not know that there can be more interesting designs and programs on television," wanders. "I wanted to be like the other Alice. She was bored and found the path to a land full of strange beings and interesting events. If there was any way to shrink to float through the screen of television, maybe I could find many things fascinating." Frustrated, she looked to the screen, which at that moment an image of the Prime Minister said that made all the, things were better than three years before, although not always seemed so. It was a little surprised to see the image of the face of the prime minister was cutting up and slowly becoming a blur of bright dots that danced and seemed to flow into the TV, as if they were calling it. "Wow," said Alice, "I think they want me to follow!" He is a heel and was toward the television, but stumbled in the book that was displeasing dropped on the floor, and fell head. As it fell, was amazed to see the screen is huge, and was surprised surrounded by dancing dots that fluíam into the picture. "I can not see anything with these points turns giving around me," he thought. "And be lost in a snowstorm. I can not even see my feet. I just see a little. It is not to know where I am." At that time, Alice felt pull your feet into something solid and was on a level hard surface. His back began to disappear the dots and realized that she was surrounded by undefined ways. Looked more closely to what was nearest and observed a small figure, the height of your waist, max. It was very difficult to define it, as was leaping from one side to another and are moving so fast you barely had to see right. The form seemed to be carrying some kind of cane, or perhaps an umbrella closed, it was pointed upwards. "Hello, Alice is presented politely. "I am Alice. I know who you are?" "I'm an electron," said the form. "I'm an electron spin-up. It is easy to distinguish me from my friend there, the electron spin-down, which is obviously very different from me." And he said to himself, in a low tone, something that sounded like "Vive la différence". So that Alice could see, the other electron is nearly equal, unless the umbrella, or whatever it was that pointed down toward the floor. It was difficult to be sure, since the dig is also leaping from one side to another as soon as the first. "Please," said Alice to his younger acquaintance. "It could make a nice stop for a moment so I can see it more clearly?" "I am very gentle," said the electron, "but I fear that there is enough space. But I will try anyway." So saying, he began to reduce its rate of agitation. But the more slowly moved, the more it expanded to the sides and would become more diffuse. At that time, although not to move quickly, he was so vague and out of focus so that Alice could not see it more clearly than before. "This is the best I can do," puff the electron. "I fear that the more slowly I move, I am more widespread. Things are well here in the country of Quantum: the less space you occupy, the faster you have to move, h. a rule, and there is nothing that I can do. " "Indeed there is no room to reduce the speed here," continued the companion of Alice as a start to jump quickly from one side to another. "The season is getting so crowded, it must be more comp.u it." In fact, the area where Alice was manned by the figures was that squeeze side by side, dancing and moving feverishly.

Atomic particles at different objects in a macroscopic scale. Electrons are very small and do not have particular characteristics, being completely identical to each other. In fact, they have some kind of rotation, although not possible to say exactly what's in rotation. A peculiar feature is that all the electrons rotate the rate itself, no matter in which direction the rotation is measured. The only difference is that each turn in one direction and rotate in another direction. Depending on its direction of rotation, the electrons are known as spin-up or spin-down. "What strange beings," Alice thought. "I never see that they are really quiet because it does not stop and nothing indicates that he will stop." Why not seemed possible to make them move more slowly she decided to try another topic. "You could tell me please what kind of season this is where we are?" She asked. "In a train station, of course," replied happily one of electrons (Alice was very difficult to say which of them had spoken since they were all very similar). "Let's take the train of waves to that screen that you see. You will then get the express photon, I believe, if you want to go further." "You are talking about the television screen?" Alice asked. "Now this, of course," said a high of electrons. Alice could have sworn that was not the same to answer the first question, but it was very difficult to be sure. "Come! The train is here and we must embark." In fact, Alice could see a row of small wagons lined up at the station. They were all very small. Some were empty, some were occupied by one electron, and two electrons. Wagons filled up quickly - in fact, seemed no more than left empty - but Alice realized that none of the wagons carrying more than two electrons. When they passed near the wagons, the two occupants shouting "Lotado! Lotado." "You could not squeeze more than two in a wagon, the train is so full?", Alice said to his companions. "Oh, no! Never addition of two electrons together, this is the rule." "I think then we will have to occupy different wagons," said Alice a little inconsistent, but the electron reassured. 0 the uncertainty principle of Heisenberg states that no particle can have well defined values for position and velocity at the same time. This means that a particle can not remain stationary at a given position, as a particle state has a well defined velocity: the speed of zero. "You is not a problem, you can enter the car you want, of course!" "I do not see how this is possible," replied Alice. "If a car is too full for you, certainly no room for me too." "No way! Wagons can only accommodate two electrons, so the places for nearly all electrons must be taken, but you are not Élet IOH! There is no other train in Alice, then there is more than enough space Paia a Alice in any of the wagons. " Alice did not understand everything he said, but, fearing that the train broke soon, began to seek a post that could accommodate one more electron. "And this here", said to his companion. "Here is a wagon with only one electron. Can you come here?" "Of course not!" shot him, horrified. "This is an electron spin-up. I can share a car with another electron spin-up, that suggestion, it is totally against my principle." "Against its principles, is what I mean?" Alice asked. "I mean what I said. Against my principle, or rather, against the principle of Pauli, which prohibits two of us, electrons, do the same thing

at the same time, including occupying the same space f have the same spin "he replied, offended. Alice could not understand what was left so hurt, but gave a quick look around you to see was another car that was more appropriate for him. You find one that housed a beckers electron-type spin-down, and the companion of Alice promptly jumped inside. Alice was surprised to see that, although now it seems the little wagon full of some form had space enough for her. Once we took their seats, the train began to move. The trip was monotonous and uninteresting landscape. So Alice was happy to see that the train speed decreased. "This must be the screen, I suppose," thought Alice. "I am anxious to know what will happen now." While the electrons will jump from the screen Paia, a J; Iaiulc stirring account of loniDii place. "What's happening?", Alice asked high. "Why is everyone so excited?" Their questions were answered by a warning that the air that seemed to come about. "The match of the screen is now being excited by electrons coming, so we will soon have the emission of photons. Soon the departure of the photon Express." Alice looked around them to try to see the arrival of the Express, where forms and bright light went running through the platform. Alice was a surprise catch in the crowd and carried along with it while everyone gathered in the same wagon. "They do not seem concerned with any principle, Pauli or any other", while Alice thought the pictures would be squeezing into rorno it. "These here are certainly not bother to be in the same place. I think the Express is just starting. ... I wonder where you will stop that," concluded the fall in the other platform. "Wow! It was a quick trip, for sure." (Alice was corretíssima here. The journey lasted no some time, because time is effectively frozen for anything that travels with the speed of light.) Again it was surrounded by a crowd of electrons, all running away from the platform. "Come!", One shouted at her to land. "We must leave the station now if we go somewhere." "Sorry," Alice asked, hesitantly, "you are the same electron with whom I was talking about before?" "I am", replied, as triggered by a side passage. Alice was dragged by the crowd of electrons and conducted through the main entrance of the platform. "Damn, that annoying thing", said Alice. "I lost sight of the only person I know in this strange place and not have anyone explain to me what is happening." "Do not worry, Alice," said a voice at the height of your knee. "I'll show you where to go." It was one of the electrons. "You know my name?" Alice asked with amazement. "Simple. I am the same electron that was talking to you before." "No way!", She exclaimed. "I saw one electron going in another direction. Maybe not the same with whom I was talking about before." "Certainly it was." "So you can not be the same," said Alice, of course. "You can not be the same electron, you know?" "Oh, yes we can", replied the electron. "He is the same. I am the same. We are all the same, you know? Exactly the same!" "This is ridiculous!," Alice argued. "Are you here by my side while the other was for somewhere in that direction, so you two can not be the same person. One of you has to be different."

"No way," shouted the electron, jumping from one side to another, even faster because of its excitement. "We are all identical. There is no way to differentiate. So you see, it must be the same and I should be the same too." At that point, the crowd of electrons surrounding Alice began to shout: "I am the same," "I am the same too," I am the same as you, "" I am the same as you. " The uproar was terrible. Alice closed his eyes and put your hands in the ears until the noise stop. When everything was quiet again, Alice opened his eyes and lowered his hands. Saw that there was no sign of the crowd of more electrons and that she was alone, leaving the entrance of the station. Looking around, he was a street that, at first sight, and seemed normal. Turned left and began walking by the sidewalk. Before it was too far, crossed with a picture in front of a passage gloomily looking for something in their pockets. Was low and very pale. It was hard to see your face clearly, as was the case with everyone that Alice had met recently. But he seemed quite a rabbit, Alice thought. "My God, my God! I'm late and I can not ontrar in my keys. I have to enter directly! So saying, he moved away a bit and running again directed to the port. Went so fast that Alice could not see him in any position. Instead, he saw a series of pictures of him in different positions held throughout its path. The images were from the point of departure to the port where, instead of to Alice as expected, remained at home, falling increasingly to become too small to be seen. Alice barely had time to record this strange series of images where the figure rebound back at the same speed, leaving again a series of images. This time it ended abruptly with the unfortunate character of fallen back on top of a culvert. Also decided, he stood up and fired again toward the door. Again came the series of images that shrink into the door, and again it bounce and then falling back. While Alice ran in his direction, he repeated the movement several times, throwing himself against the door and fell back again. "Stop, stop!", Shouted Alice. "Do not do it. You end up getting hurt." The person stopped running and looked at Alice. "Hello, my dear. I fear that I should do this. I locked on the outside and must come soon, so I have no choice but tunelanitvavés of the barrier." Alice looked at the door, which was big and strong. "I do not think has much chance of running through it and throwing it against her," he said. "You are trying to shoot it down?" "Oh, no, certainly not! I do not want to destroy my beautiful door. I just want to cross it. Moreover, I fear that what I said is true. The probability of achieving cross it is not great, really, but I try . I Hzendo it, threw it back against the door. Alice the left, thinking that would be waste of time, and moved away when he returned tottery again. After some steps, Alice could not resist and took a look back to see if, by chance, he had abandoned. He saw once more the series of images that went toward the door and cm shrink to get it there. She waited for the rebound. Of <> ut the 1st time is was immediate, but this time nothing happened. The door was there, solid 6 alone, and there was no sign of his acquaintance. After a few seconds where nothing iii onteceu, Alice heard the noise of chains and locks from behind the door, which opened. His known reappeared and waved to her. "What my luck!", He said "The probability of penetrating a thick barrier like this is really very small. And a stunning lucky I have got through it in such a short time." Cm then closed the door with a solid beat that indicated the end of that meeting. Alice continued to walk. A little ahead she reached a spot next to the empty street, where a group of workers was assembled around a pile of bricks. Alice concluded that

workers were therefore more bricks were downloading from inside a car. "Well, at least these people are behaving summer of sensible way," I thought it. At that time, another group doubled the corner running, carrying something that resembles a huge carpet rolled up, and started to take it on the ground. Alice then realized it was some kind of floor of a building. The plan seemed to be quite large, since it covered most of the available space. "Oh I think that should be the same size of the building they will build," said Alice, "but will build anything if the plant now occupies the space?" Workers have just put the plant in position and returned to the pile of bricks. Began to get the bricks and play them apparently at random on top of the plant. Everything was confusing - the bricks catamaran now a place, sometimes in another - and Alice did not see any purpose that. "What are you doing?" asked a man who was away to the side. As he seemed not to be doing nothing, it was inferred that the master-of-works. "You are just piling the bricks disorganized. There should be building a building?" "Sure, honey. And we," replied the master-of-works. "It is true that the random fluctuations are still large enough to hide the default, but once we have established the distribution of probabilities for the result we need, we are getting, there is the fear." Alice felt that demonstration of optimism not very convincing, but was quiet and noted that the rain of bricks continued to fall on the ground. Little by little, to his surprise, noticed that some bricks were falling in some regions more than others and that it was possible to distinguish between walls and doors. She looked fascinated as the recognized forms of comfortable chaos that would arise from that original. "Wow, that amazing!" He said. "How to do this?"

"It has not said to you", smiled the master-of-works. "You saw us establish the distribution of probabilities before we start. It specifies that it should be the places where bricks and which should not. We need entertainment that before starting to throw the bricks because they do not know where they will stop when the play means ", continued. "I see why!," Interrupted Alice. "I used to see the bricks are placed one after the other, in certain lines." "Well, is not that we do here at Quantum. Here we can not control where each brick goes, only the probability of that will go to a place or another. This means that when a few bricks, they can fall in almost all places and then not appear to have any kind of pattern. When their number increases, however, you discover that there are only bricks where there is some possibility that they exist and where the probability is greater, where there is more bricks. When dealing with large quantities of bricks, all just work very well, true. " Alice found it very funny, although the master-to-talk works so precisely that it seemed to make some sense. Not asked anything, because the answers just to confuse him more. Thanked for the information and then continued walking down the street. Not long after, she spotted a window where a large sign saying: "I'm sure it must be something very exciting, but I have no idea what it is, and if someone were to ask, I am sure that I would answer more lost than I am now," exclaimed Alice desperate. "Do not understand anything of what I have seen so far. I find someone I give a good explanation about what is happening around me."

I had noticed that had spoken up high to hear the answer for a pass. "If you want to understand the country of Quantum, will need someone to explain quantum mechanics. Therefore, you should go to the Institute of Mechanics," it advised.

"Oh, they will be able to explain me what is happening here", shouted Alice delighted. "And I will be able to explain all the things I saw, so (orno 0 poster in that window and that means that 'eV'?" "I think the mechanics can explain most of you," replied his informant, "but as" eV are units of energy, you probably should start asking about them in the Bank Heisenberg, mainly because there is across the street. " Alice looked at where he pointed and saw a large building with a facade very pompous, obviously built to impress. Had an entry with pilasters of stone and, at the top, in letters bottle was engraved with the name BANK Heisenberg. Alice through the street, climbed a long stairway that led to the great door and entered. Through the door, Alice was in a room with tall columns and walls of marble. It was like that of other banking houses that she had known, but this looks more like a bank. There was a row of boxes along the wall, and large hall was divided by barriers of tape so that clienres were already forming queues while waiting to be served. Currently, however, there was a customer. In addition to the boxes behind the counter and the guard standing next to the door, Alice did not see anyone else. How were you advised to inquire at the Bank, she started walking with determination toward the row of boxes. "One moment", said the guard. "Where do you think you're going, missy? Not see that there is a queue?" "Sorry," replied Alice, "but I am not seeing the same line. There is nobody here." "Of course there is, and many", emphasized the guard. "We received many 'ninguéns' today. Usually we refer to them as virtual. Rarely seen many particles virtual waiting for their loans of energy." Alice noticed - and this was becoming common - that nothing would be quickly cleared. He looked at the window of the box and saw that although the Bank seems to be empty, the boxes were very busy. Glossy pictures would appear one at a time in front of a window or another, and then left at the Bank. In a moment, she saw a couple of pictures together to materialize in front of the box. Realized that one was an electron, the other was very similar, but was half as the negative of a photograph of the first, the opposite in every detail of electrons that she had seen before. "He is a positron, a antielétron," muttered a voice heard in the Alice. She turned and saw a young woman to look hard and very well dressed. "Who are you?", Asked Alice. "I am the Manager of the Bank," replied the young. "I am in charge of the distribution of loans to energy virtual particles. Lótons The majority is, as you can see, but sometimes serve pairs of particle and antiparticle, coming together to ask for a loan, as one pair of electron and positron you saw earlier. " "Why need loans of energy", said Alice. "Why not see them even before they get the loan?" "Well, see," replied the manager, "so that a particle exists properly, to be free, and can be seen moving normally and everything else, it must have at least a specific minimum energy that we call energy mass at rest. These

poor virtual particles do not even have the energy. The majority has no power and there is so not true. lucky for them, can make a loan in the Bank of energy here and there that allows for some time . She pointed to a poster on the wall that said: TERMS OF LOAN ? • t =? / 2 is given preference to immediate payment. "This is what we call the Heisenberg relation. It governs all our transactions. The" is called the Planck constant, reduced the value correctly, of course. The? Gives the exchange rate for our loans for energy. The quantity? is the amount of energy and loaned? t is the time for which the loan is worth. " "I mean," said Alice, trying to follow what the manager said, "that is how the exchange rate between two currencies, so the more time there, more energy can be borrowed? "Oh, no! It's just the opposite! The energy and time is multiplied together to give a constant value. The higher the energy, the shorter is the period of time that the loan is worth. To understand properly, take a look at that particle and antiparticle alien who came to make a loan in Box 7. " Alice looked at where the manager indicated and was impressed. In front of the box was a pair of pictures, one was the opposite of the other, just as the electron and positron that she had seen before. This pair, however, was bright and flashy figures whose presence had so much space that almost hide the box behind them. Alice was impressed with the extravagance of the two, as could not fail to be, but when I would open the mouth to make a comment, they disappeared and disappeared completely. "Here is an example of what I was saying," continued the manager calmly. "He even got a huge amount of energy to sustain the huge mass of rest necessary for the style of their life. But because the loan was too high, the deadline for payment was so short, but very short, they managed to not leave the counter before paying the loan back. Because these heavy particles can not go very far before you pay your loans for energy, they are known in our industry as short-range particles, the manager added. "The relationship between time and energy is the same for all, then?", Alice asked, feeling that it might have finally managed to find anything definitive. Most of the particles have a mass at rest, and that is the equivalent B joined large amount of energy. Without initial energy virtual particles can exist for a short time "getting loaned" the power of that $ precl am for your rest and united mass of quantum fluctuations. "Exactly! The Planck constant is always the same, regardless of time and the place where it is implemented. And the so-called universal constant, which means simply that it is the same anywhere. "We work with energy here at the Bank," continued the manager, "because here in the country of Quantum, energy acts as if it were money. As you give real names or dollars to your money, we call the unit of energy used more eV from here. The amount of energy of a particle is what determines what it is capable of doing. The speed at which you can go, that the state can take, how will it affect other systems, it all depends on the energy that particle has. "Not all particles are completely devoid of energy, as they are in the queue. Many of them have enough energy itself and, if so, to keep it as

long as you want. They must have seen you walking outside. All particle that needs a body, must have enough energy to sustain its existence. " She pointed to another framed notice on the wall that said: Mass is Energy. Energy is mass "If you want a particle has mass, it must find energy to sustain that weight. If over some energy, it can be used for other things. Not all particles with mass mind. There are some" free-and-easy, "Particle bohemian who have no rest mass. They are not limited as the majority, who need to turn to get their mass and therefore can make use of even small amounts of energy. photons is a good example. A photon has no mass rest. Therefore, a photon at rest does not weigh anything. But look well, photons are not found at rest, usually, they are always running around, the speed of light because it is them that the light is made, it • The light is not a constant and smooth flow. It is a lot of quanta, small packets of energy, so that the flow is granular. These quanta, or particles of light are called photons. Almost everything is made of how much of any size. It is this that is the name of quantum physics. See all the photons leaving the bank now. The photons are all basically the same, just like the other one, as the electrons are the same, but you may notice that many of them are quite different. This is because they have different amounts of energy. Some have very little energy, like those of radio frequency photons that are coming out now. " Alice looked at a crowd of photons that was in her, flowing around your feet and out the door. While leaving, she heard snippets of music, voices empostadas and something about "a lunch Thursday." "I did not know that radio waves were made of photons," said Alice. "Oh, yes. They are. They are photons with a wavelength and large, low frequency and very little energy. They go in groups, because to have noticeable effects need a lot of time. They are very nice figures, are not ", smiled the partner of Alice. "But the visible photons, those who are the light that people use to see, have a higher frequency and more energy. The effect of one can be quite noticeable. The most wealthy, the big spending, are the waves of X-ray and gamma photons. Each one carries a lot of energy and can make your presence is noticed in the environment, if they decide interact. " "This is all very interesting," said Alice, most sincere, "but I am still confused about the very idea of energy. Could I say the real power?" "Very wise for his question," replied the manager, met. "Unfortunately, it is not easy to answer it. Come to my office and I try to give you an explanation." The manager crossed the hall, Alice quickly pulling up a slight but intimidating door in the corner opposite, leading to a large and modern office. Making a signal to Alice sits in a comfortable armchair in front of a large table, the manager gave it back and sat in a chair, across the table. "Well," she began, "energy is a bit like the money in his world, and it is not easy to explain exactly." "I thought it was easy," replied Alice. "Money is made of coins, and my change, or may be cash, too." "That's paper-money, which certainly is a form of money. But the money does not need to be in coins and notes. It can also be a savings account, for example, or in shares of companies, or invested in construction. E as energy, which can take several forms, very different from each other. "The most obvious is the kinetic energy," said the manager, while in the swing chair. His voice had the tone of complacent who is preparing to make a long speech to a captive audience. "A particle, or any object will have kinetic energy when moving. Cinética means movement. There are other forms of energy, too. There is the potential energy as the gravitational energy of a rock that is on top of a hill and that so you can scroll down. There is also the energy, or chemical

energy, which is the potential energy that the electrons have when they are within atoms. There is, as I said, the rest mass energy, many particles need only have to exist, so we have some mass. A form of energy can be converted into another, as you deposit money in your paper-notebook. I can give an example, if you look through the window. " She bent and pressed a button on your desk, and a round window was opened on the wall in front of Alice. Through her, Alice could see a mountain-Russian. While watching, a cart arrived at the top of a rise, making a break before descending the other side. "That cart, as you see, is not moving now and so it has zero kinetic energy. But he is on top, and its position gives it potential energy. When you start to fall, he loses time and therefore also loses a little of its energy potential, which is converted into kinetic energy. And what does go further and faster while descending. " Alice could barely hear the excited shouts of joy of shooting passengers on the cart paths.

Energy exists in many forms. It can manifest as, rest mass energy of a particle, such as kinetic energy that is involved in the movement of any object and how the various types of potential energy. One form of potential energy is gravitational potential energy of an object, which decreases as the object falls. "If the trails were smooth and well-wheel racing without friction," continued the speaker disinterested, "the cart back to sleep only when you were exactly the same time that he left." She bent back to tinker with something on the table. The figures in the distant mountain-Russian shouted by surprise when they saw that the next rise before them suddenly acquired a much greater height. The trolley speed dropped to stop completely before reaching the top. "How did you do that?" Alice exclaimed, astonished. "Never underestimate the influence of a Bank," muttered his companion. "Let's see what happens now." The cart began to move backwards on the rails amid cries still excited but not so happy about the last time. The speed was increased to the cart to move triggered by the lowest point and start to climb the other side, less speed. He did precisely where Alice had seen first and then started to decline again. "So he continued indefinitely, with the energy of the moving cart of potential energy to kinetic energy, and vice versa, but I think you understand." The manager pressed another button on the table and the window is closed. "This is the kind of look obvious that they see the energy in the World Classic. It changes the form of a continuous and smooth. You saw the car speed increased progressively as descended without large jumps. And there is no obvious restriction on the amount of energy that any object can have. Here in the country of Quantum, is not often that happens. In many situations, a particle can have only a limited set of values of energy and can only accept or reject energy in packages, that we call quanta. In the World Classic, all payments are made to power supply, with many plots and too frequent and pequenininhas same infinitesimal, but here it is normal to be made in installments with certain value. In quantum theory, consider energy and momentum is considered as important as position and time. More important, in fact, it is easier to measure the energy of an atom to determine where he is. Energy is in a sense, the equivalent of money in the physical world. Energy is classically defined as "the ability to perform work." It is necessary to have energy particles,

if they want to do something, that is, make transitions from one state to another. Momentum is a quantity more like speed. It is going in a certain direction, while energy is only a direction associated with greatness. When we say how much energy there is not anything left to say. Electrons, moving from right to left and from left to right at the same speed, have the 'same kinetic energy, but momenta1 opposites. "As you saw, the kinetic energy is a kind of theatrical energy and spectacular - something that the bodies only when they are in motion. The more body mass you have, the more kinetic energy it has and the faster moving, more energy kinetics will no quantity depends on the way the direction in which the body moves, just the speed. In this sense, there is a difference with the other important quantity that tells us how a particle moves. This is something that call momentum or momentum. The momentum is such as measure of the obstinacy of a particle. Every particle is determined to continue to move in exactly the same way moved before, without any changes. If something moves quickly, is need a certain strength to make it slower. A force is also necessary to change the direction of motion, even if the speed of the particles remain the same. A change only in the direction of movement is not such that the particle loses its precious energy kinetics, since it only depends on the speed of movement and not its direction. Still, the particle to resist this change because it involves the change of its momentum. Particulates are very conservative in that sense. "It's all a matter of what we call the switch," continued the enthusiastic manager. "When you describe a particle, we must use the correct parameters. If you want to say where she is, you should talk to their position and time, for example. " "I thought it was only necessary to say in which position it is," objetou Alice. "This is where she will not tell?" "Certainly not. You need the time, as the position. If you want to know where an object is now or where it is tomorrow, not advance nothing I tell you if your position is where he was a week ago. You must know the time and position, because things tend to move, you know? " Like if you want to know what a particle is doing, you must describe it in terms of its momentum and energy. Generally, we have the position and time if you want to know where a particle is. " "Here in the country of Quantum, the parameters tend to be related. When you try to see where something is, it affects the momentum of this object, how fast it is moving. It is another form of Heisenberg's relation that I showed you at the Bank . There are many types of energy. The kinetic energy is due directly to the movement. A cannon ball in motion has an energy that does not stop a bullet. Rest mass energy is another type. The rest mass energy of any object is large. In Newtonian mechanics did not need to consider the rest mass energy which, by not changing, not affecting the transfer of energy. Quantum processes in the masses of the particles change frequently and the variation in energy, rest mass can be released for other forms. A conversion of less than one percent of the body at rest to a small part of the material occurs in nuclear weapons, for example. Not a very large variation in energy compared with other cases investigated in the physics of particles, but it is devastating when released by a significant number of particles within our everyday world. "That is why, then," said Alice, remembering is a previous meeting, "that the electron with whom I earlier could not stop so I could see it all without being diffuse?

"Without doubt. The relationship of uncertainty affect all particles in this way. They always seem somewhat vague and it is impossible to locate them with precision. "I know what I do! Call the Counter Uncertainty to explain that," exclaimed the Manager. "His work is to balance the accounts. So he has to worry all the time with the quantum fluctuations." She has an elegant finger to push a button more among the many who trimmed his desk. There was a brief pause, then one of the ports scattered along the wall of the room is opened and a figure entered. It seemed a very design of the millionaire miser of an illustrated edition of "A Tale of Christmas," not to be entertained by his words and an uncontrollable nervous tic. Carrying a huge book that seemed to swell-box, shaking as if its contents were in constant motion. "I think it," he cried, triumphant, trembling so much that almost left the book drop. "Close the balance of the accounts! Residual quantum fluctuations Except, of course," he added, less enthusiastic. "Very good," the manager replied, distracted. "Now I want you to take this girl here, Alice, telling him the uncertainties and fluctuations in quantum energy of a system, those things." With a wave goodbye to Alice, the manager returned to his desk and started to do something especially complicated with all the buttons that were there. The Count took Alice out soon, before anything else happened. It is appropriate to speak of relations of the Heisenberg uncertainty is to describe the strange mixture of energy and time, position and momentum, which occurs in quantum systems. 0 of this problem description is that it promotes the belief that Nature is, in fact, uncertain, that nothing can be reliably predicted and that, in fact, worth anything. This is not true! They reached a much smaller office and more stodgy, with a high desk and old, covered with books, boxes and pieces of paper stacked on the floor. Alice looked at a box of books-that was open. The page was filled with columns of numbers, as well as other books, box that she had seen, except for the fact that these books were the numbers changing, but in small quantities without stop, when she looked for them. "Okay", said the figure Victorian middle in front of Alice. "You know about the uncertainty, is not it, young lady?" "Please, if not quite work," Alice said politely. "Well," he began, sitting at the table and crossing your fingers as the judges are to increase the dignity of their appearance. What was not a good idea, because this time he began to tremble so violently that the fingers were stuck in one another and he had to stop through to them. "Well," repeated, putting the hand in the pockets by force, by security. You should not ever forget that energy is preserved, which means there's always the same amount of energy. It can be converted from one form to another, but the total is always the same. At least when you think the long term, "he added gloomily and sighed, looking away with regret. "It is not true in the short term, then", said Alice, feeling that it should say something to continue the conversation. "No. Not completely. In fact, not even if the period is well short. You saw the relation of Heisenberg on the poster outside the Bank, did not see?" "Ah, yes, I said it ditava the terms of loans for energy." "In a way, is what she does. But where do you think has the energy for the loans?" "The Bank, of course."

"Oh, my God, no!", Said the meter, slightly horrified. "With all certainty, no! It would be good if the banks started to lend energy to your own stock! "No," continued in a tone of conspiracy, looking around carefully, "Not everyone knows that, but the energy is not the Bank. Actually, it does not come from anywhere. It is a quantum fluctuation. The amount of energy that a system has not fully defined, but varies for more and less, and the shorter the time period in which we examined, the greater will be its variations. "In this sense, energy is not like the money. The money keeps it well in the short term. If you want money for something, you must get it somewhere, right? You can get a bank account or borrow to someone, or even steal! " "I do not do that", shouted Alice outraged, but the counter continued, undisturbed. "No matter where it, he has to come from somewhere. If you get more is because someone else has less. This is what happens in the short term immediately, at any rate. "The long term is different, it is possible that there is inflation and you discover that much money circulating. We have more, but the money does not seem to buy as much as before. Energy is the opposite. In the long run it keeps the quantity total remains the same, and nothing like the economic inflation. Every year you will need on average the same amount of energy to transfer from one state to another in an atom. In the short term, on the other hand, energy is not well preserved. A particle can harvest the energy they need without it having to come from somewhere, it simply appears as a quantum fluctuation. These fluctuations are the result of the relationship of uncertainty: the amount of energy that is to uncertain and the shorter the time that you have, the more uncertain the amount will be. " "That seems terribly confusing," said Alice. "Suffice to say", replied emphatically his companion. "Really, you would like to counter when the numbers in your books are floating without stopping?" "It must be horrible," she said in solidarity. "How do you get?" "Usually, I try to take as much as possible when I'm doing the balance of accounts. It helps a little. The greater the time I spent, minor fluctuations waste, right? Unfortunately, people get impatient and come ask me if I am planning is calculating the balance forever. This is the only way to do that, "he continued, with honesty. "The longer I take, will be minor fluctuations in energy. If I was doing this forever, there would be no fluctuation and my accounts have a perfect balance," he said, triumphant. "Unfortunately, I do not leave in peace. All are impatient and eager to make transitions from one state to another, all the time." "There is one more question I want to do," Alice pointed out. "What are these states so that I hear talking? Could explain them to me, please?" "I am a better person for it. How is all part of Quantum Mechanics, you should go to the Institute of Mechanics and ask there." "It was what I said before," said Alice. "Since this is where I ask, could you tell me how to get there?" Energy can be transferred from one form to another, but the total energy of a system is constant (provided that there is no exchange of energy in the neighborhood). This is an absolute truth in classical mechanics. True long-term quantum systems, but in the short term, the value of energy is subject to fluctuations. The floating floor is better than the word uncertainty, since there are real physical consequences. The penetration into

the barriers during alpha decay of nuclei is one of the cases, talk to alpha decay in Chapter 8 and we have seen the penetration barriers in Chapter 1. "I can not really tell you how to get there. This is not how we do things here. But I can get is very likely that you'll get there." He turned and went to the other side of his office, before a wall covered with a dusty curtain. When you suddenly pull it revealed to Alice a row of doors along the wall. "What brings each of them?" She asked. "Some of them leads to the Office that you were talking about?" "Each one could take it to almost anywhere, including, of course, the Office. But the question is they all are likely to lead to the door of the Institute." "I do not understand," demanded Alice, with a growing sense of confusion that was already becoming familiar. "What is the difference? Say that each of them leads to almost anywhere is the same as saying that all they can take almost anywhere." "No way! Is completely different. If you go through any of them, you will end up almost anywhere, but if you go through all the same time, probably get my point, at the peak of the pattern of interference." "What nonsense!" She exclaimed. "We can not go through all doors at once. You can only go through a door at a time." "Ah, this is different! Of course, if I see you going through a door, then you will have this port, but if I do not see it is quite possible that you have gone through any of the doors. In this case, the rule generally applies. " With a gesture, he indicated a large poster and fascinating, nailed to the wall opposite the table, where it was impossible not to be seen. The poster said: What is not forbidden is COMPULSORY! "This is one of the most basic rules that we have here. If you can do many things together, you is not only a must do them all. So, you avoid having to make decisions all the time. So go, go by all the doors and in so doing leaving in all directions at once. You will see that it is very easy and then come to the right place. " "This is ridiculous!," Alice protested. "There is no way to go through several doors at the same time!" "How can you say that before you try? Never did two things at once?" "Sure," she replied. "I watched TV while the house was my duty, but this is not the same thing. I never went in two directions at once." "I suggest you try," replied the Count, irritated. "You will never know if you can not do anything if you try. This is the kind of pessimism that always hinder progress. If you want to go somewhere here, you have to do all that is possible, and all at the same time. No need to worry about where you will stop. The interference takes care of this! " "What? What is interference?" She asked. "No time to explain. In the Institute of Mechanics will tell you that. Now go, and they explain it when you arrive." "This is horrible!", Alice thought with itself. "All the people who told me I hurried to another place, promising explanations when I get there. I wish that someone explain me all right, once and for all! I am sure you do not know how I can go in several directions at once . It seems impossible, but he is so sure that we have, which I think is best to try. " Alice opened a door and entered. THE MANY WAYS OF ALICE: Alice entered the door and the left was a small square of parallelepiped with three narrow alleys that left her. Chose the left alley. Before he could go very far, it is a wide paved area. In the center it built up a high, dark building, without windows on lower floors. Was threatening.

*** Alice entered the door and the left was a small square of parallelepiped with three narrow alleys that left her. Chose the right lane. Before he could go very far, it is a park with paths of stone covered with herbs, followed by that between trees that hung melancholy. High iron fences around the park and a wet mist darkened the picture of the inside. *** Alice entered the door and the left was a small square of parallelepiped with three narrow alleys that left her. Chose the middle lane. Before he could go very far, it is another square, in front of a building, looking very poor. *** Alice entered the door from the right and was in a narrow alley where the other two left. Chose the left alley. Before he could go very far, it is a wide paved area. In the center it built up a high, dark building, without windows on lower floors. Was threatening and she had the clear impression that should not be there. *** Alice entered the door from the right and was in a narrow alley where the other two left. Chose the right lane. Before he could go very far, it is a park with paths of stone covered with herbs, followed by that between trees that hung melancholy. High iron fences around the park and a wet mist darkened the picture of the inside. She had the clear impression that should not be there. *** Alice entered the door from the right and was in a narrow alley where the other two left. Chose the middle. Before he could go very far, it is another square, in front of a building, looking very poor. In a way, it seemed to him that this was the right place for her to be. *** ****** *** Alice entered the door of the middle and was facing a wall with three passages in arc alleys that led to a little further. Chose the left alley. Before he could go very far, it is a wide paved area. In the center it built up a high, dark building, without windows on lower floors. Was threatening and this time the feeling that should not be there was very strong. *** Alice entered the door of the middle and was facing a wall with three passages in arc alleys that led to a little further. She followed the alley on the right, because this way somehow seemed to be completely wrong. *** Alice entered the door of the middle and was facing a wall with three passages in arc alleys that led to a little further. Chose the middle lane. Before he could go very far, it is another square, in front of a building, looking very poor. She was sure now that this was the place where it should be. *** Alice noted the building more closely. A poster near the door foxy she read the words "Institute of Mechanics." It was there that she wanted to come! Particles that can take different paths exist as a superposition (sum) of amplitudes. Each path contributes with a possible range, or option, for the behavior of the particle and all amplitudes are present, together. The different amplitudes can interfere, combining it and focusing on certain areas to increase the likelihood of there being particles. In

other places, can cancel each other to reduce probability of finding particles. Amplitude and interference will be discussed in the next chapter.

Alice considered the building that was ahead. It was a modest structure of bricks, already punished by the media time. In front, there was a poster that said "the Institute of Mechanics." Beside the door was a poster in which someone had nailed a warning: "Do not knock. Only from." Alice tried and saw that the door was not locked. Opened it and entered. Across the room door had a large and dark. In the middle of the room was bright and clear an area. Within this limited region was possible to distinguish anything with reasonable sharpness. More to beyond, lay an apparently limitless extension of darkness in which nothing substantial could be discerned. In the spot light she saw a billiard table with two figures moving around. Alice walked in his direction and when approached, they turned to look at it. It was a strange double well. One was tall and angular and was wearing a white shirt with collar pressing too hard and high, narrow and a tie, to the surprise of Alice, an overalls. His face was aquiline, and he had sideburns tired. He looked at her with such intensity that Alice felt that he could see even the smallest detail what they observed. His companion was smaller and younger. His round face was decorated with a few large glasses of a metal frame, it was difficult to understand where he was, looking, or even where exactly were his eyes. He wore a white laboratory coat under which appeared a shirt with the design of something vaguely atomic ahead. It was not easy to say with certainty what it was, because the colors were faded. "Excuse me, this is the Institute for Mechanics? Alice asked, more to pull conversation. For the poster, she knew it was. "Yes, my dear," said the chief and impressive of the two. "I am a classical mechanics of the World Classic, and I am visiting my colleague here, which is a quantum mechanics. Whatever your problem, I am sure that one of us can help it. Just wait until we finish our shots. " Both have turned to the billiard table. The classical mechanics mirou carefully, considering the minimal Panesar of all angles involved. Finally, the shot was well at ease. The ball came back and hit a series of impressive rebound and eventually come into collision with the red ball, which was precisely to within one of Caçapa. "There is," exclaimed with satisfaction when taking the ball from inside the hole. "It's the way it is, you see? Careful and accurate observation, then action needs. Proceeding thus, you get the result we choose." His companion did not reply, took his place on the table and made a vague motion with his putter. After their previous experience, Alice was not surprised to see the ball shoot in all directions at the same time, there was no place on the table where she could say with certainty that the ball had not been, but also could not tell where the ball was state. After a break, the player looked inside one of Caçapa, stuck his hand and took a red ball. "If you do not mind if I make an observation," said Alice, "it seems that you play so much different." "That's right," replied the classical mechanics. "I hate when he makes shots like that. I like that everything is done with great care and precision and that all details are planned in advance. However," he added, "imagine that you have not been here to see us play pool, so can tell us what you know. "

Alice brought back all his experiences since he had come to the country and explained how the quantum had found everything very confusing and everything seemed strange and undefined. "I do not know how I found this building," he concluded. "I said that I would probably interference to the right place, but could not understand what happened." "Well," said the classical mechanics, which seemed to have chosen itself to be the spokesman of the double. I can not say I understood everything well. As I said, taste of things clear, the question is followed by the end, it all very clear and predictable. In fact, many things that happen here do not make sense to me, "he muttered, in a confidential tone." I left the world only to give a classical spin. There is a splendid place, where everything happens with mechanical precision. The question then is the effect in a wonderfully predictable, so that everything makes sense and you know what will happen. There's more: the trains are always on time, "he added. See Note 1 at the end of the chapter. "Sounds impressive," said Alice with education. "To be so organized, everything must be controlled by computers." "No," replied the classical mechanics. "We do not use a computer. In fact, things do not work in the world electronic classic. We are better machines with steam. I do not feel very at ease here in the country of Quantum. My friend here is much more familiar with the quantum conditions . "However," he continued, more sure of himself, "I can tell you what is interference. This is also in classical mechanics. Follow me and show how it works." He took Alice through a door after a long hallway and into another room. This room was well lit, with bright lights that illuminated every corner of the room and it did not seem to come from any particular source. They were standing in a narrow wooden bridge, which was in the back room, held on the walls. The floor in the middle of the room was covered with a kind of substance that did not seem bright gray solid. Random flashes of light through this material, as well as a TV channel with the outside air. The guide explained to Alice, "This is the room in Gedanken, which means' room to think." You should know that in some clubs there are rooms and rooms to write to read. Well, we have a room to think. Here, the thoughts of people take shape, so that everyone can see them. You can do experiments of thought that allow us to discover what would happen in various physical situations, and much cheaper than the experiments of truth, of course. "How does it work?", Asked Alice. "Just think of something and it appears?" "Correct, in essence, is just what you need to do." "Oh, please, can I try?" Alice asked. "Certainly, if you want." Alice thought the substance moving with intensity and bright. To his surprise and joy, where before there was nothing, she saw a group of furry bunny jumping here and there. "Yes, very beautiful," said Mechanic, very impatient. "But that does not help to explain the interference." He made a gesture and all the birds disappeared, except for a pequenininho it is without being noticed, in one corner of the area. "Interference," he began, with authority, "is something that happens to the waves. There are several types of waves in physical systems, but is simpler to think of water waves." He looked hard to the floor, which, right in front of the eyes of Alice, became a sheet of water with small waves through the surface. In one corner, the rabbit sank with a "plop" when the floor beneath it became water. He tried to leave and looked for them. Then he shook it, looked with sympathy for his hair soaked, and disappeared.

"Now, a little wave," continued the classical mechanics, without paying attention to the unfortunate rabbit. Alice looked unwilling to ground and a wave came up to blow across the surface dramatically break on a beach, on one side of the floor. "No, not this kind of wave you want. These big waves that overflow are complicated enough. We want that sort of softer wave, which spreads when you throw a stone in water." As he spoke, a series of circular waves began to spread, from the center of the water. "But we believe in what we call the plane waves, all moving in the same direction." The circular ripples become a series of long parallel furrows, like a wet field and plow, all moving through the ground, on one side to another. "Now, we a barrier in the middle." One obstacle appeared low in the center, dividing the floor into two. The waves were up to the barrier and collided against her, but there was no way to move to the other side, which was now quiet and still. "We make a hole in the fence now, so that the waves can pass through it." A small cleft, very well-made, appeared a little left of center point of the barrier. To pass through this gap, the waves are scattered by the quiet region circumferentially opposite the barrier. "Now see what happens when we have two cracks in the barrier," exclaimed the Mechanic. Instantly there was a crack on the left and one on the right of the central point. Circular ripples spread out from both. Where they were, Alice could see that the water rose and descended more than when there was only a crack in the barrier, while in other places it barely moved. "You'll understand when you freeze the motion. It is clear that we can do this in a thought experiment." The movement was stopped in water and the ripples were frozen in place where they were, as if the whole area was suddenly transformed into ice. "We will now mark the regions of maximum amplitude and minimum", he continued, given the classical mechanics. "The scale measures how much water went from the level it had when it was stopped." Two fluorescent arrows appeared, floating in space by the surface. One was the color of green apples and was pointing to a location where a disturbance in the area had been increased. The other was a red arrow means pale and showed the place where the surface was hardly disturbed. "You can see what is happening if we see the effect of only one slot at a time," he said, with a growing enthusiasm. One of the cracks in the barrier disappeared and only the circular waves that left the other slot, still frozen in their positions as if they were made of glass. "Now, we move to another slot." Alice noticed that the difference between a very small place and another. The position of the crack had been altered and the circular pattern of ripples that it was moved a little, but in general appearance seemed the same. "We can not understand what you are trying to show me," she said. "The two cases seem the same to me." "It will be easier to see the difference if I move quickly from one event to another." A crack in the barrier began to jump from one side to another, first to right and then left. Until that happens, the pattern of ripples Forward and Back, first to right, then left. "See the pattern of waves below the green arrow," said Mechanic, who in the eyes of Alice, was more excited about it than it should. She, however, did what he asked and realized that the place indicated by the arrow was an increase in water, in both cases. "Every crack in the barrier produced a wave that brings this particular point. When both slits are open, the wave is twice as high here and the total elevation and depression are much higher than when only one slot. The so called constructive interference.

"Now we see the pattern of waves below the red arrow." Ali Alice saw that as a crack caused an increase in point, the other produced a depression. "See that in this position the wave of a crack up as the wave of the other down. When the two meet, they cancel each other and in total the disturbance disappears. The so called destructive interference. "This is, indeed, all that is to know about the interference of waves. When two waves are crossing and are combined, their amplitudes, the quantities that measure how much rise or fall, also match. In some places, the waves participating are all going in the same direction, then the disturbances are added and the final result is considerable. In other places, they go in opposite directions and cancel each other is. " "I think I understand," she said. "It means that the doors of the Bank functioned as the cracks in the barrier, causing a great effect in places where I needed to go and cancel each other in other positions. But I do not see how this applies to my case. With its waves of water, you say that most of the wave in one place and less in another because of this interference, but the wave is scattered throughout the region, while I'm in one place at a time. " "Exactly!" cried the triumphant classical mechanics. "That is the problem. As you said, you are in one place. You are more like a particle than a wave, and the particles are behaving in ways quite different sense in the classical world. A wave spreads by a wide area and we only see a small portion of it in any position. Because of the interference, you may have more or less of it in different positions, but still, you are looking for only a small part of the wave. A particle, for other hand, is located at some point. Looking at different positions, you see the particle, or it simply is not there. In classical mechanics particles do not exhibit effects of interference as evidence. " He turned to the floor of the room and looked Gedanken it with firmness. A mirror of water, the area turned into an area shielded with strengthened barriers along the perimeter, high enough for them to protect themselves behind them. From one side to another, in the middle of the floor, where before there was a barrier to wave, built up a wall with a narrow opening screened a little left of center. "We can now see the same arrangement, but I did some changes so that we can observe particles fast. They are more or less as the bullets of a gun, and that is why we use that one." Interference is, classically, a property of waves. It occurs when amplitudes, or disturbances, are from different sources and are combined in some places and adding or subtracting cancel in others. This results in regions of intense activity or low, respectively. You can see this effect in the pattern produced when the ripples left by two boats cross each other. The effects of interference can also cause poor reception of a TV when the waves reflected by a building near interfere with the direct signal. Interference requires extensive and overlapping distributions. In classical physics, particles occupy a certain position and do not produce interference. He made a gesture toward one of the ends of the room where a machine gun appeared to unpleasant appearance, with many boxes of ammunition stacked to the side. "This weapon is not very well supported and therefore not always shoot in the same direction. Some bullets reach the crack in the wall and go to the other side as part of the wave was in our last thought experiment. Most of them, of course, reach the wall and ricochet. Oh, that reminds me, "he said, suddenly. "We must use it, if any bullet strikes on the rebound." Getting a pair of steel helmets, he has one for Alice. "Is it really necessary?" She asked. "If the experiment is only thought, these bullets are designed and can not cause us any harm."

"Perhaps, but you may think that was hit by a bullet and it would not be very nice." Alice put the helmet. She felt the weight of it on his head, and thought he matter for anything, but continue talking too much would not be useful. The Mechanical stretch your body, waved like an emperor and machine gun fire began, making much noise. The bullets left in irregular flow. The majority agrees with the wall and zoom away in all directions, but some pass through openings in the barrier wall and came to the other side. Alice was intrigued to see that when a bullet was the wall on the other side of the barrier, she immediately stopped and stood slowly to be floating in the air well above the point where they reached the wall. "You see, while the wave of water spread across the wall above the slit, a bullet to reach in only one position. In this experiment, however, there is a greater likelihood of the bullet passed right by the sliding of the crack in the edge the opening and go up to the very end. If we wait a little longer, we will see how the probability varies for different points along the wall. " As time passed and the air was getting filled with bullets flying, the number of those floating near the wall with growing regularity. As noted, Alice began to distinguish a pattern that would be formed. "See, now you can see how the bullets that passed through the slit is spread by the wall," said the mechanic when the gun stopped. "Most did directly toward the opening, and the number is decreasing as much to one side to another. Now see what happens when the gap is shifted slightly to the right." In another gesture of his, the bullets fell on the floor and floating gun again. Although the demonstration and be loud and disruptive, Alice noticed that the end result was the same as the previous time. Frankly, it was disappointing. "As you can see," said a mechanic with undue confidence, "the distribution is similar to earlier, but slightly shifted to the right, because the center is now across the opening." Alice does not understand any difference, but was ready to accept what he said. "Now," said the Mechanic Theater in tone, "let's see what happens when both slits are present." So where Alice could see, was not the slightest difference. Except that with the two slits, and more bullets would reach the wall. This time, she decided to make a comment. "I fear for me, all times are equal," she said, apologizing up. "Exactly", replied the delighted Mechanic. "But, as you may have noticed, the center of distribution is now in the middle, between the cracks. We had a distribution for the probability of the bullets passing by the left slot and other distribution for that pass by the right slot. With the two slits, the bullets can go through any of them. The total distribution, then, is the sum of the probabilities obtained for each of the slits, since the bullets should go through one or the other. They can not pass through both the same time, "he added, turning to the quantum mechanics that had just entered the room. "It's what you say," replied the fellow, but how can you be so sure? Look what happens when we repeat the Gedanken experiment with electrons. " This time, it made a gesture toward the floor of the room was the quantum mechanics. His gestures were not as determined as those of his colleague, but seems to work the same way. The gun and the armored walls disappeared. The floor has to be shiny material that Alice had seen at first, but the wall that it had been used was still there, across the floor side by side with the two slits in the middle. Across the room was a large screen with a bright green. "This is a fluorescent screen," muttered the mechanism for Alice. "She emits a flash of light every time an electron to reach, so we can use it to detect where they are."

On the other side, where the gun was before there was another gun. This was pequenininha, like a small version of where those guns are fired bullet in the man-shows of circus. "What is it?", Alice asked. "And an electron gun, of course." Looking more carefully, Alice saw a escadinha which led to the mouth of the cannon, with a row of electrons waiting his turn to be fired. They were much smaller since the last time in the turns. "But of course," she said to herself, "these are just electrons thought." Looking at them, she was surprised to see them waving to her. "How will they know me", she asked. "They should all be the same electron that I knew before!" "Start shooting!", Commanded the quantum mechanics, and the electrons quickly risen the ladder, and entered the cannon were fired in a regular flow. Alice could not see them cross the room, but via a glint in the place where each one of them reached the screen. The ClaroI to erase it, leaving a bright star that was marking the place where the electrons were landing. As the first gun of the electron gun continued to fire a stream of electrons and a lot of star began to regroup, starting to show a distribution recognizable. At first, Alice was not sure what was seeing, but when the number of star began to rise, it became clear that their distribution was quite different from that obtained with piles of bullets from previous experience. Instead of a slow and gradual decline from a maximum in the center, toward the side, the stars were distributed in bands, with black spaces between them, where there was little or no star. Alice noticed that in some ways, this case was similar to the wave of water, where there are regions of high activity interspersed with quiet areas. Now, there were many regions where electrons were detected, with very few of them in intermediate areas. Because of this, Alice was not surprised when the quantum mechanical said, "What you're seeing there is the clear effect of interference. With the waves of water, had higher and lower regions of the surface motion. Here, each electron will be detected in only one position, but a. probability of detecting an electron varies from one position to another. The distribution of different intensities of the wave you saw before was replaced by a distribution of probabilities. With one or two electrons such distribution is not obvious, but using a bunch of electrons, you will find more of them in regions of high probability. With only one opening, we would see that the distribution to fall toward the low side, and the bullets and the waves of water they behaved when there was only one slot. Here we see that when there are two slits, the amplitudes of the two interfering in each other, with obvious peaks and dips in the distribution of probability. The behavior of electrons is very different from the bullets of my friend. " "I do not understand," said Alice, and this seemed the only thing that was in life. "It means that there are so many electrons that in some way, the electrons pass through a hole that are interfering with those who cross the other hole?" "No. That is not what I mean. No way. You will now see what happens when you shoot a single electron." He slapped palms and said "Okay, let's do it again, but slowly this time." The electrons into action, or to be more precise, one into the gun and was shot. The others remained where they were seated. Shortly after, another electron went through the mouth and the gun was fired too. Continued so for some time, until Alice began to realize the same pattern of clusters and voids appearing intervals. These groups and intervals were not as clear as before because the low intensity with which the electrons were getting was that there were not many of them in groups, yet the pattern was clear. "There it is. You see that the effect of interference works even when there is only this one electron at a time? An

electron alone can display interference. He can pass through both openings and interfere with itself, so to speak." The strongest experimental evidence of quantum behavior is provided by the phenomenon of interference. When a result can be obtained by a number of ways, there is an amplitude for each possible way. Then, if these amplitudes are joined with each other, can add or subtract and distribution of total probabilities show distinct maximum and minimum: intense bands and bands that alternate empty. In practice, this effect has been observed which is expected to find it. It is a form of interference that produces the various combinations of states of energy that occur in atoms. Only those states that "fit perfectly" will affect positively the potential to reach a maximum in high probability. Other states if you cancel one another, and therefore do not exist. "This is bullshit!", Exclaimed Alice. "An electron can not pass through the two openings. As the classical mechanics, makes no sense." She went to the fence and looked more closely to try to see where the electrons passing through the barrier. Unfortunately, the light was very weak and the electrons moved with such speed that she never could distinguish that they began opening. "This is ridiculous," she thought. "I need more light." Alice had forgotten it was a "fourth thinking" and was surprised when a beam supported by a strong tripod appeared alongside his elbow. She quickly sent the torch of light for the two openings and was pleased to see that there was a flash of visible near one or other opening when the electron was. "I did it!" She screamed. "I can see the electrons are passed through cracks and is exactly as I said. Each of them goes through only one opening." "Aha!", Replied the excited quantum mechanics. "But you saw what happened with the pattern of interference?" Alice turned to look at the wall behind the barrier and was amazed to see that now the distribution of star is the most concentrated in the center and would gently fell to the sides, just as the classical distribution of bullets. It was not fair. "It's always so and there is nothing we can do," said Quantum Mechanics, consoling her. "When there is to learn by observing which slit the electrons pass, the interference occurs between the effects of the two slits. If you watch the electrons, you see that, in fact, they are in one place or another and not in both, but this case, they behave as expected, ie as if they had passed through only one slit, not causing interference. The problem is that there is no way to observe the electrons without disturbing them, as when you put the light on them. The simple act of observing force the electrons to choose a route. Whether you notes for which hole each electron passed. Whether or not you pay attention in the holes. Any comments that would tell you this, disturbs the electrons and interference stops. The effects of interference only happen when there is no way of knowing by which slit the electron passed. If you know or not, it does not matter. "It is this: when there is interference, it seems that each electron is passing through both slits. If you try out, you will see that each electron only goes through one slit, but then the effect of interference disappears. We can not escape it!" Alice gave a little thought to the matter. "This is absolutely ridiculous!" He concluded. "Certainly," replied the quantum mechanics with a satisfied smile. "Totally ridiculous, I agree, but that is how nature works and we must follow it and mean complementarity", Alice asked. "Sure. Complementarity means that there are certain things you can not know. Not the same time at least." "It is this complementarity that mean," she protested.

"When I say, this is what you mean," said the Mechanic. "The words mean something, which I like. It's all a matter of who is the master. Complementarity is what I say." "You said that," said Alice, without fail completely convinced by the last statement of the facility. "No, you did not," said the Mechanic. "This time I mean that there are questions that can not be a particle, such as where it is that speed and moves. Actually, not much talk of an electron occupying a particular position." "This is a lot to say a single word!", Alice said with irony. "Certainly," replied the mechanic, "but when I make a word work overtime as now, I always paid more. I can not explain what is really happening with the electrons. It is normally required of an explanation that she made sense in terms and words you already know and quantum physics does not. It seems that it makes no sense, but it works. Give up to say with certainty that nobody understands quantum physics. I can not explain to you but I can describe what is happening. Come to the backroom and I will see what I can do. " See footnote 2 at the end of the chapter. In quantum mechanics, particles are like waves and waves are like particles. They are the same. Both the electrons as the light show the effects of interference, but when detected, are perceived as individual and how each is observed in a fixed location. The interference between the possible paths that a particle can travel will result in a distribution of probabilities with minimum and maximum well pronounced, which is more likely that a particle is detected in a position than in another. They left the room, Gedanken, whose floor was back to his usual brilliant appearance, and continued for a corridor to another room furnished with a few seats. When the two had already been seated, the mechanic said: "When we talk about a situation like the electrons through the openings, we describe using a scale. It is more or less like the waves you saw, and is actually called, with frequency of the wave function. The range can pass through two openings at the same time and not always positive, as the likelihood. the less likely that you can have is zero, but the amplitude can be positive or negative, with different pathways it may cancel or add to each other and result in interference, as with the waves of water. " "Where are the particles then", asked Alice. "By opening up what they are, indeed?" "Indeed, the scale does not say that. However, it raised the magnitude squared, ie to multiply it by itself to always give a positive number, you can get a distribution of probabilities. If you choose any position determined, is that this distribution is likely to say, if you observe a particle, find it in that position. " "And that is all she says?" Exclaimed Alice. "I must say that I feel inadequate. You never know where something is." "Yes, this is true. You can not tell where a particle is, except that is not where the probability is zero, of course. If you have a large number of particles, however, be assured that you will find more particles where the probability is higher, much less one where the probability is low. If you have a very large number of particles, it is possible to say with much precision the place where many particles are. This is the case for those workers who you were talking . They knew what they were building because they were using a lot of bricks. In numbers too high, the reliability of the system is very good. " See footnote 3 at the end of Chapter "And there is no way to tell which one particle is doing without watching it?", Said Alice, just to be sure.

"No, no way. When you see what can happen in several different ways, you have a scale for each possible way, and the overall amplitude is obtained adding up all of them. You will have a superposition of states. In a way , the particle is doing everything it can to it. Not only do you not know what the particle is doing. The interference shows that the odds are all present and influence each other. In a way, are all equally real. It is not forbidden is compulsory. " "I saw a poster that said that in the Bank. Seemed very serious." "And it is! This is one of the most important rules here. How many things can happen, they happen. Take a look at the cat, for example." "What cat?", Alice asked, looking around, confused. "But the cat of Schrödinger here. He has left us to cuidássemos it." Alice looked to where the mechanic pointed and saw a large striped cat who slept in a basket in the corner of the room. As if awakened by having heard his name, the cat stood up, stretch out. Or better, got up and was not raised, lounge and not yawn. Alice saw that, beyond the slightly blurred picture of the cat's arched back, a cat was also identical, still asleep in the bottom of the basket. He was very hard in a very unnatural. Looking at him, Alice could swear he was dead. "Schrödinger developed a Gedanken experiment in which a poor cat got trapped in a box, along with a container of poison gas and a mechanism to break the bottle if a sample of a radioactive material were suffering decay. This is definitely a decay process quantum. The material may or may not fall and then, according to the rules of quantum physics, there would be a superposition of states, where some in the decay would have occurred and in others not. Of course, in those states in which the decay occurs, the cat die, and then we would have a superposition of states of cats, some dead and some alive. When the box was opened, someone to watch the cat and from then on he was dead or alive. The question was proposed by Schrödinger: "What state of the cat before the box is open? " "And what happened when they opened the box", Alice asked. "In fact, everyone was so excited discussing the issue that anyone opened the box, and that is why the cat was like that." Alice looked at the basket where an aspect of the cat licking itself with dedication. "He seems very much alive," she noted. Mal of the words had left his mouth, the cat became very solid and tangible version dead and gone. Satisfied purr, the cat jumped out of the box and began to chase a mouse that had left the wall. Alice noticed that there was a rat hole, she could see the mouse had just gone straight to the wall. The quantum mechanics of the eye followed the direction of Alice. "Ah, yes. This is an example of penetration into barriers: happens all the time here. Where there is a region that a particle can not enter in accordance with the laws of classical mechanics, the amplitude does not necessarily cease immediately on the border region, despite declining rapidly within it. If the region is well close, there will still be left some magnitude on the other side, and this gives room for a small probability that a particle can appear there, apparently having crossed a seemingly insurmountable barrier, a process called "tunneling." happens frequently. " Alice was passed in your head the things that had seen so far and noticed a problem. "As I got to watch the cat and set their condition if he could not do it by itself? What decides that a comment that was made and who is able to do them?" "This is a very good," replied the quantum mechanics, "but we are only mechanical and not so much in mind with these things. Just do the work and use methods that we know work in practice. If someone wants to discuss

extent of the problem with you, you have to go somewhere more academic. I suggest that there is a lesson from the School of Copenhagen. " "And what do I get there?", Alice asked, settling with the fact of having been passed on to another place. In response, the mechanism leading to the corridor and opened a door, which was not to the alley where she had entered, but to a forest. Notes 1. Quantum mechanics is usually contrasted with the classical or Newtonian mechanics. The latter, which deals with the detailed description of objects in motion, was developed before the early 20th century and is based on the original works of Galileo, Newton and others before and after them. The Newtonian mechanics works very well on large scales. The movement of planets can be predicted far in advance and great accuracy. It works almost equally well to artificial planets and space missions for exploration: their positions can be made years before. Works great also for apples falling from trees. In the case of an apple that falls, air resistance is significant about that. The classical mechanics describes the suit as the collision of a huge number of air molecules rebound in apple. When you ask about the air molecules, they respond to him that they are small groups of atoms. When you ask about the atoms, it is an embarrassing silence. The classical mechanics was not successful in trying to explain the nature of the world in atomic scale. Things must be different in some way for small objects than large objects appear to be. To use these arguments, you should ask: small or large compared to what? There must be some size, a fundamental constant setting the scale on which this new behavior becomes obvious. It is a definitive change in the way they observed the behavior of things, and it is universal. Atoms in the sun and distant stars emitting light in the same spectrum as the lamp on his desk-to-head. The transition to quantum behavior is not something that happens only locally, there is a fundamental property of nature involved. This property is denoted by the universal constant that appears in most of the quantum equations. The world is granulated in the scale defined by the constant character. On this scale, energy and time, position and momentum, are blur together. It is not necessary to say that the scale of human perception, character is very small and most of the quantum effects is not absolutely clear. 2. What the relations of the Heisenberg uncertainty tell us is that we see things so wrong. We believe beforehand that we should be able to measure the position and momentum of a particle at the same time, but found that we can not. The very nature of the particles does not allow us to make such measurements on them and the theory tells us we are doing the wrong questions, questions to which we have no viable answers. Niels Bohr used the word complementarity to express the fact that it is possible to have concepts that can not be precisely defined at the same time: pairs of concepts such as justice and legality, rationality and emotion. There is something fundamentally wrong with our belief that we should be able to talk about the position and momentum, or the exact amount of energy of a particle in a given moment. Do not you know that would be significant while talking to two very distinct qualities. It seems that this is not as significant. 3. Quantum mechanics is not a particle set classic in the traditional sense, instead dealing with states and amplitudes. If you amounts to a square amplitude (ie multiplied by its value) you get a distribution of probabilities gives the probability of obtaining various results when making an observation or measurement. The actual value obtained by measuring with any appears to be random and unpredictable. Just seems that the suggestion

made earlier in this book that nature is uncertain and that "everything" must, in the end, be true. It seems? Well .. no. If you make many measurements, the average result can be predicted with precision. Recording of bets do not know which horse will win each race, but confidently expected to make some profit by the end of the day. Unable to provide large and unexpected losses, as working with small numbers whose average can not be trusted. The number of gamblers would be a few thousands, instead of 1,000,000,000,000,000,000,000,000 atoms or more, existing even in a tiny piece of matter. These digits appear with a number less than the design of a repetitive wallpaper, but it is undeniably great. The mean expected statistical fluctuations in measurements of very large numbers of atoms are negligible, even if the results for individual atoms can be quite random. Amplitudes of quantum mechanics can be calculated with enough accuracy and compared with experiments. A much cited result is the magnetic moment of an electron. The electrons revolve as little pawns and have electrical properties: they behave like small magnets. The magnetic force and rotation of the electron are related, and this ratio can be calculated using the appropriate units. A classical calculation result reaches 1 (with arbitrary assumptions about the distribution of electric charge of an electron). The classic comes to the calculation result 2.0023193048 (± 8) (the error is the last decimal place). A measurement result reaches 2.0023193048 (± 4). And a good agreement! The probability of achieving, at random, so consistent values is similar to the probability of a dart throw, also at random, and adjust on the fly - when the target is as far as the Moon This result in particular is often given as an example the success of quantum theory. You can calculate, with the same accuracy, the amplitudes of other processes, but very few figures that can be measured with such accuracy. 2 Alice inside the woods and was followed by a path that winds through the trees, until you reach a fork. There was a plaque there, but not much help. The arrow pointing to the right said "A" and pointed to the left that said "B", nothing more. "Damn," Alice exclaimed, irritated. "This is the most useless card I have ever seen." She looked around to see if any could track where they were on the tracks, where surprised to see the Schrödinger cat sitting on a bough of a tree a few meters away. "Cat," she said, timidly. "Could you tell me which path should I take?" "That depends a lot on where you want to reach," said the Cat. "Do not know where ...", she began. "So, no matter where you are," interrupted the Cat. "But I have to decide between two paths," said Alice. "This is where you wrong," smiled the cat. "You do not have to decide, you can take all the paths. Sure, I know that now. I especially tend to do nine different things at once. The cats crawl anywhere, when not being observed. Speaking of observation, "he said, hurry," I think I'm about to be obs ... At this time, he disappeared suddenly. "What a weird cat," thought Alice, "and that weird suggestion. He should be referring to the superposition of states of the mechanic who spoke. I think it's like the time we left the Bank. Somehow, I go in several directions at the same time, then I think you should try to do the same thing again. " ******

Status: Alice (A1) Alice turned to the right, in plate, and continued by the winding road, looking at the trees while walking. Had not gone far when it came to another fork, this time the board had two arrows that said "1" and "2." Alice turned to the right and continued. While going, the trees were scarce and it was a road trails and steep rocky. The slope was increasing, until it was up the slope of a mountain alone. The trail led to a narrow path that a cliff edge, which in turn went to a small lawn. Its front, the slope of the cliff, she saw an opening as a mouth bocejante, and a passage, which took forward and down. The passage was very dark, but to their own surprise, and she ended up coming down. The floor and walls were smooth and went straight to the front, a slight slope in the direction of a distant light and brightness. As she walked, the light would gradually become stronger and more red and the tunnel was getting warmer. Small clouds of steam and she passed it heard a sound like that of a huge animal snoring in his sleep. At the end of the tunnel, Alice spotted a huge underground. Just gave to try to guess the dark vastness of the place, but close to his feet, she saw a great brightness. A huge red and gold dragon slept deeply, with its long tail coiled around him. Below him, serving him in bed, there was a high pile of gold and silver, jewelry and wonderful sculptures, all bathed in red light. Status: Alice (A2) Alice turned to the right, in plate, and continued by the winding road, looking at the trees while walking. Had not gone far when it came to another fork, this time the board had two arrows that said "1" and "2." Alice turned left and continued. As was walking, looked down and saw that the path followed by where a trail had changed from the forest to a narrow street paved with yellow bricks. She continued to follow through the trees until the forest is opened in a large grassy clearing. It was very long, run to where Alice could see, and the entire field was covered with poppies. The yellow brick road to follow through the gates of the clearing up of a distant city. It was, Alice could see that the high walls of the city were green and glowed, and the gates were nail emeralds. ****** Status: Alice (B1) Alice turned to the left of the plate, and continued along the winding path. There was no remarkable to see yet. She turned a corner and came to another fork, this time the board had two arrows that said "1" and "2." Alice turned right and continued walking. The vegetation was getting thicker and it was difficult to see anything that was not very close, although the path itself, is still clear and defined as followed by wind between the cerrado trees. Alice turned a bend and suddenly reached an open space. In the center of the clearing stood a small building with a sloping roof and a small tower with a bell in one of its ends. The words "Copenhagen School" were deeply marked a plate of stone above the door. "This must be the place where they said I should go," Alice said to herself. "Just do not know if I even go to a school! I step in my time quite! But perhaps the schools here are different from those to which I am accustomed. I get to see!" Without knocking, she opened the door and entered. ****** Status: Alice (B2) Alice turned to the left of the plate, and continued along the winding path. There was no remarkable to see yet. She turned a corner and

came to another fork, this time the board had two arrows that said "1" and "2." Alice turned left and continued walking. A little later, the road began to tilt and Alice began to climb a morrote. At the top of the hill for a few minutes she stopped and looked in all directions in the region - and that this region was curious! There were many streams across the region from one side to another, and the floor was divided into squares formed by living fences, which were of a stream to another. "Damn! The field is divided like a chessboard," Alice said to the final. ****** "Oh, my face, between! said a calm voice, and Alice realized it was being observed. She passed the door and looked around them for the classroom. It was a very big room with tall windows on all sides. There were a few rows of school desks and in the middle of the room. On one end was a blackboard and a large table, behind which was the Master. "It seems quite a normal school," Alice admitted to itself, while the children turned to look in the room. She saw, however, that the portfolios were not occupied by children but by an incredible collection of creatures stacked in front of the room. There was a mermaid with long hair and a scaly tail of fish. There was a uniformed soldier that observed more closely, and seemed to lead a ragged little girl with a tray full of matches. There was also a very ugly duckling and a fat man with size of royalty and that for some reason, was wearing only undershorts with. "Is he really?" Alice thought. When looked up, thought it had seen a man dressed in rich costumes and a robe of embroidered velvet. Looking back, however, that all could see was a burly man wearing only his underpants. "Hello, my dear," said the Master, a paternal figure with full eyebrows. "He came to join in our discussion?" "I do not know how did I get here," said Alice. "I thought I was in several places agorinha it, and I have no idea why did I get here and not elsewhere." "This is because we found you here, of course. You were a, superposition of quantum states, but was seen as being here, because it was here I was, of course. Of course, you was not observed in any of the other places." "What if I had been seen elsewhere", Alice asked, curious. "Why, then, the number of states would have collapsed to the other. You will not be here, but in the position where it was observed, of course." "I can not understand how this could be," Alice replied that he was already feeling terribly confused again. "What difference does it make if I was seen or not? Sure, I would be in one place or another, no matter who was watching me or not." "It's what you think! Is not to say what is going on in any system if you have not seen. There may be a variety of things could be happening, and you can even establish the likelihood of something or another, since that is not looking. In fact, the system is a mixture of states corresponding to all the things that might be happening. That is the situation until you look to see what the system is doing. The height of this process, an option is selected and this will be the only occurrence in the system. " "And what about all the other things that were happening there?" asked Alice. "Just disappear?" "Well, there are more things he can do than what he was doing, but this is exactly what happens," replied the Master, with a broad smile. "You understand perfectly. The other states simply cancel it. The Earth may become

of the Earth's ever been. At this time, all other states no longer true, either. They become, say, just dreams and fantasies, and the observed state is the only real. This is what we call the reduction of quantum states. You will soon get used. " "It means that when you look at something, you can choose what you see?", Alice asked, suspicious. The vision "orthodox" quantum mechanics is the Copenhagen Interpretation (second named Niels Bohr, the Danish physicist, Hans Christian Andersen and not). Where is possible that different things happen in a physical system, a range for each, and the total system state is given by the sum, or superposition of these amplitudes. When an observation is made, it is a value that corresponds to one of these amplitudes and the amplitudes not disappear in a process called reduction of the amplitudes. "Oh, no, you have no right to choose. What you see is probably determined by the probabilities of various quantum states. What you see is really a matter of pure chance. You do not choose what will happen, the quantum amplitudes only give the probabilities of different results, but do not what will happen. This is pure coincidence, and is only set when an observation is made. " The Master said that quite frankly, but so little that Alice had to strive to understand your words. "Making observations is important, then," Alice thought with itself. "But who can make comments? Obviously, the electrons can not see themselves through the cracks in a study of interference, as passed by the two cracks appear at the same time. Or maybe I should say 'when the amplitudes for the two cracks are present? " she corrected, imitating the way of speaking that both had heard this place. "It seems that I am not properly noticed when I was in a superposition of states, just now. "Actually," she said suddenly, surprised by a thought, "if the quantum mechanics says that you must do everything we can, then for sure you should see all possible results of any action you make. If the principle quantum superposition of works everywhere, you can not measure all! Anything you try to measure would have several possible results. It would be possible to see any result and in accordance with its rules, if you can see any of them, you must note to all. The results of their measurements were all present in a new version of this superposition of states of which you speak. You could never see anything of truth or could never be something that you could fail to observe. " Alice stopped to breathe, then to take leave for their new thinking. She noted that everyone in the room looked at her seriously. When she stopped talking, everybody was shaken, half impatient. "You're talking about something very important, of course," said Master sweetly. "It is known as problem of the measure and is exactly the subject we were discussing here." See footnote 1 at the end of Chapter The Master continued: "It is important to remember that this is a real problem. There must be a mixture of amplitudes such as occur in systems with one or two electrons, as the experience of the two slits you saw, because the amplitudes interfere with each other. There is only one way to say that an electron can be in a state, but you do not know what state it is. This could produce interference. We are then forced to accept that in a sense, each electron is in all states. I think not a question appropriate and want to know what the electron really doing because there is no way to find it. If you try to check, you change the system and just looking at something different. "As you said, it seems we have a problem here. Atoms and systems that contain a small number of particles always do everything they can do, never make decisions. We, on the other hand, always do one thing or another and never observed more than a result of each particular situation. My students

prepared a short explanation about the problem of the measure. They consider that point, if there was any, stops working the quantum behavior that allows the presence of all states the same time, so that only comments can be made. You might want to sit and watch the presentations. " Alice could not dispense with this great opportunity. Sit in one of the books and was waiting with anxiety. "The first to speak," said the Master, his voice quiet noise appease the expectations of students, "is the Emperor." The portly gentleman, put clothes in the bottom of purple color with very good taste and the first to be noticed by Alice to enter the room, got up and went to the front of the room. See footnote 2 at the end of Chapter The Theory of the Emperor (The Mind of the Matter) "Our hypothesis," he began, a smile spreading snob the room, "is that everything is in the mind. "The laws that govern quantum systems," he continued, "the use of amplitudes to describe the physical states and the superposition of amplitudes when more than one condition as possible - these laws apply to all material things of the world. We say 'all material things' he repeated, "Our hypothesis is that because this overlap is not experienced by our conscious mind. The physical world is governed at all levels by the quantum behavior and any purely material system, large or small, will always be a combination of states, with a scale for this is that everything can or could have been. Only when the situation comes to the attention of the sovereign will of a conscious mind is that a choice is made. "Because the mind is something foreign, or in our case, cited above, are outside the laws of the quantum world. We are not tied to the need to do anything that could be done, instead, we are free to choose. When we found something this thing is seen, she knows that We observe the universe as we know it remains to observe and, thereafter, provided that it has been observed by Nós. And Our act of observation that requires a unique and defined the world. We can not have a choice about what we observe, but what we observe is only true at the time. " He stopped and launched mandões for all eyes in the room. Alice was strangely impressed by his confident, despite the undergarment color purple. "For example, when we look at our new and magnificent imperial costumes, we realize, of course, ornate splendor." He looked at himself and suddenly was dressed head to toes in rich robes. Its cover and its jacket was adorned with beautiful lace and velvet of her light robe of skin had edges of ermine. "It is possible that when our attention is diverted from our costumes, they are less real and tangible than now seem to be observed when all they are made of better fabric, they are, really." The Emperor raised his head and looked to their colleagues. Alice surprised that, despite its observation has the rich look of your clothes, so he turned to look, they immediately became transparent, showing the undergarment bearing a beautiful monogram. "It is therefore our view. All the material world is actually governed by the laws of quantum mechanics, but the human mind is beyond the material world and therefore is not restricted to these laws. We have the ability to see things just as we can. We cannot choose what to see, but what we see is reality in the world, at least while we were watching. When we finished our observation, the world may again enter into his customary condition of mixed states. " The interference between the possible paths that a particle can travel will result in a distribution of probabilities with minimum and maximum well pronounced, which is more likely that a particle is detected in a position than in another.

They left the room, Gedanken, whose floor was back to his usual brilliant appearance, and continued for a corridor to another room furnished with a few seats. When the two had already been seated, the mechanic said: "When we talk about a situation like the electrons through the openings, we describe using a scale. It is more or less like the waves you saw, and is actually called, with frequency of the wave function. The range can pass through two openings at the same time and not always positive, as the likelihood. the less likely that you can have is zero, but the amplitude can be positive or negative, with different pathways it may cancel or add to each other and result in interference, as with the waves of water. " "Where are the particles then", asked Alice. "By opening up what they are, indeed?" "Indeed, the scale does not say that. However, it raised the magnitude squared, ie to multiply it by itself to always give a positive number, you can get a distribution of probabilities. If you choose any position determined, is that this distribution is likely to say, if you observe a particle, find it in that position. " "And that is all she says?" Exclaimed Alice. "I must say that I feel inadequate. You never know where something is." "Yes, this is true. You can not tell where a particle is, except that is not where the probability is zero, of course. If you have a large number of particles, however, be assured that you will find more particles where the probability is higher, much less one where the probability is low. If you have a very large number of particles, it is possible to say with much precision the place where many particles are. This is the case for those workers who you were talking . They knew what they were building because they were using a lot of bricks. In numbers too high, the reliability of the system is very good. " See footnote 3 at the end of Chapter "And there is no way to tell which one particle is doing without watching it?", Said Alice, just to be sure. "No, no way. When you see what can happen in several different ways, you have a scale for each possible way, and the overall amplitude is obtained adding up all of them. You will have a superposition of states. In a way , the particle is doing everything it can to it. Not only do you not know what the particle is doing. The interference shows that the odds are all present and influence each other. In a way, are all equally real. It is not forbidden is compulsory. " "I saw a poster that said that in the Bank. Seemed very serious." "And it is! This is one of the most important rules here. How many things can happen, they happen. Take a look at the cat, for example." "What cat?", Alice asked, looking around, confused. "But the cat of Schrödinger here. He has left us to cuidássemos it." Alice looked to where the mechanic pointed and saw a large striped cat who slept in a basket in the corner of the room. As if awakened by having heard his name, the cat stood up, stretch out. Or better, got up and was not raised, lounge and not yawn. Alice saw that, beyond the slightly blurred picture of the cat's arched back, a cat was also identical, still asleep in the bottom of the basket. He was very hard in a very unnatural. Looking at him, Alice could swear he was dead. "Schrödinger developed a Gedanken experiment in which a poor cat got trapped in a box, along with a container of poison gas and a mechanism to break the bottle if a sample of a radioactive material were suffering decay. This is definitely a decay process quantum. The material may or may not fall and then, according to the rules of quantum physics, there would be a superposition of states, where some in the decay would have occurred and in others not. Of course, in those states in which the decay occurs, the cat

die, and then we would have a superposition of states of cats, some dead and some alive. When the box was opened, someone to watch the cat and from then on he was dead or alive. The question was proposed by Schrödinger: "What state of the cat before the box is open? " "And what happened when they opened the box", Alice asked. "In fact, everyone was so excited discussing the issue that anyone opened the box, and that is why the cat was like that." Alice looked at the basket where an aspect of the cat licking itself with dedication. "He seems very much alive," she noted. Mal of the words had left his mouth, the cat became very solid and tangible version dead and gone. Satisfied purr, the cat jumped out of the box and began to chase a mouse that had left the wall. Alice noticed that there was a rat hole, she could see the mouse had just gone straight to the wall. The quantum mechanics of the eye followed the direction of Alice. "Ah, yes. This is an example of penetration into barriers: happens all the time here. Where there is a region that a particle can not enter in accordance with the laws of classical mechanics, the amplitude does not necessarily cease immediately on the border region, despite declining rapidly within it. If the region is well close, there will still be left some magnitude on the other side, and this gives room for a small probability that a particle can appear there, apparently having crossed a seemingly insurmountable barrier, a process called "tunneling." happens frequently. " Alice was passed in your head the things that had seen so far and noticed a problem. "As I got to watch the cat and set their condition if he could not do it by itself? What decides that a comment that was made and who is able to do them?" "This is a very good," replied the quantum mechanics, "but we are only mechanical and not so much in mind with these things. Just do the work and use methods that we know work in practice. If someone wants to discuss extent of the problem with you, you have to go somewhere more academic. I suggest that there is a lesson from the School of Copenhagen. " "And what do I get there?", Alice asked, settling with the fact of having been passed on to another place. In response, the mechanism leading to the corridor and opened a door, which was not to the alley where she had entered, but to a forest. Notes 1. Quantum mechanics is usually contrasted with the classical or Newtonian mechanics. The latter, which deals with the detailed description of objects in motion, was developed before the early 20th century and is based on the original works of Galileo, Newton and others before and after them. The Newtonian mechanics works very well on large scales. The movement of planets can be predicted far in advance and great accuracy. It works almost equally well to artificial planets and space missions for exploration: their positions can be made years before. Works great also for apples falling from trees. In the case of an apple that falls, air resistance is significant about that. The classical mechanics describes the suit as the collision of a huge number of air molecules rebound in apple. When you ask about the air molecules, they respond to him that they are small groups of atoms. When you ask about the atoms, it is an embarrassing silence. The classical mechanics was not successful in trying to explain the nature of the world in atomic scale. Things must be different in some way for small objects than large objects appear to be. To use these arguments, you should ask: small or large compared to what? There must be some size, a fundamental constant setting the scale on which this new behavior becomes

obvious. It is a definitive change in the way they observed the behavior of things, and it is universal. Atoms in the sun and distant stars emitting light in the same spectrum as the lamp on his desk-to-head. The transition to quantum behavior is not something that happens only locally, there is a fundamental property of nature involved. This property is denoted by the universal constant that appears in most of the quantum equations. The world is granulated in the scale defined by the constant character. On this scale, energy and time, position and momentum, are blur together. It is not necessary to say that the scale of human perception, character is very small and most of the quantum effects is not absolutely clear. 2. What the relations of the Heisenberg uncertainty tell us is that we see things so wrong. We believe beforehand that we should be able to measure the position and momentum of a particle at the same time, but found that we can not. The very nature of the particles does not allow us to make such measurements on them and the theory tells us we are doing the wrong questions, questions to which we have no viable answers. Niels Bohr used the word complementarity to express the fact that it is possible to have concepts that can not be precisely defined at the same time: pairs of concepts such as justice and legality, rationality and emotion. There is something fundamentally wrong with our belief that we should be able to talk about the position and momentum, or the exact amount of energy of a particle in a given moment. Do not you know that would be significant while talking to two very distinct qualities. It seems that this is not as significant. 3. Quantum mechanics is not a particle set classic in the traditional sense, instead dealing with states and amplitudes. If you amounts to a square amplitude (ie multiplied by its value) you get a distribution of probabilities gives the probability of obtaining various results when making an observation or measurement. The actual value obtained by measuring with any appears to be random and unpredictable. Just seems that the suggestion made earlier in this book that nature is uncertain and that "everything" must, in the end, be true. It seems? Well .. no. If you make many measurements, the average result can be predicted with precision. Recording of bets do not know which horse will win each race, but confidently expected to make some profit by the end of the day. Unable to provide large and unexpected losses, as working with small numbers whose average can not be trusted. The number of gamblers would be a few thousands, instead of 1,000,000,000,000,000,000,000,000 atoms or more, existing even in a tiny piece of matter. These digits appear with a number less than the design of a repetitive wallpaper, but it is undeniably great. The mean expected statistical fluctuations in measurements of very large numbers of atoms are negligible, even if the results for individual atoms can be quite random. Amplitudes of quantum mechanics can be calculated with enough accuracy and compared with experiments. A much cited result is the magnetic moment of an electron. The electrons revolve as little pawns and have electrical properties: they behave like small magnets. The magnetic force and rotation of the electron are related, and this ratio can be calculated using the appropriate units. A classical calculation result reaches 1 (with arbitrary assumptions about the distribution of electric charge of an electron). The classic comes to the calculation result 2.0023193048 (± 8) (the error is the last decimal place). A measurement result reaches 2.0023193048 (± 4). And a good agreement! The probability of achieving, at random, so consistent values is similar to the probability of a dart throw, also at

random, and adjust on the fly - when the target is as far as the Moon This result in particular is often given as an example the success of quantum theory. You can calculate, with the same accuracy, the amplitudes of other processes, but very few figures that can be measured with such accuracy. 2 Alice inside the woods and was followed by a path that winds through the trees, until you reach a fork. There was a plaque there, but not much help. The arrow pointing to the right said "A" and pointed to the left that said "B", nothing more. "Damn," Alice exclaimed, irritated. "This is the most useless card I have ever seen." She looked around to see if any could track where they were on the tracks, where surprised to see the Schrödinger cat sitting on a bough of a tree a few meters away. "Cat," she said, timidly. "Could you tell me which path should I take?" "That depends a lot on where you want to reach," said the Cat. "Do not know where ...", she began. "So, no matter where you are," interrupted the Cat. "But I have to decide between two paths," said Alice. "This is where you wrong," smiled the cat. "You do not have to decide, you can take all the paths. Sure, I know that now. I especially tend to do nine different things at once. The cats crawl anywhere, when not being observed. Speaking of observation, "he said, hurry," I think I'm about to be obs ... At this time, he disappeared suddenly. "What a weird cat," thought Alice, "and that weird suggestion. He should be referring to the superposition of states of the mechanic who spoke. I think it's like the time we left the Bank. Somehow, I go in several directions at the same time, then I think you should try to do the same thing again. " ****** Status: Alice (A1) Alice turned to the right, in plate, and continued by the winding road, looking at the trees while walking. Had not gone far when it came to another fork, this time the board had two arrows that said "1" and "2." Alice turned to the right and continued. While going, the trees were scarce and it was a road trails and steep rocky. The slope was increasing, until it was up the slope of a mountain alone. The trail led to a narrow path that a cliff edge, which in turn went to a small lawn. Its front, the slope of the cliff, she saw an opening as a mouth bocejante, and a passage, which took forward and down. The passage was very dark, but to their own surprise, and she ended up coming down. The floor and walls were smooth and went straight to the front, a slight slope in the direction of a distant light and brightness. As she walked, the light would gradually become stronger and more red and the tunnel was getting warmer. Small clouds of steam and she passed it heard a sound like that of a huge animal snoring in his sleep. At the end of the tunnel, Alice spotted a huge underground. Just gave to try to guess the dark vastness of the place, but close to his feet, she saw a great brightness. A huge red and gold dragon slept deeply, with its long tail coiled around him. Below him, serving him in bed, there was a high pile of gold and silver, jewelry and wonderful sculptures, all bathed in red light. Status: Alice (A2) Alice turned to the right, in plate, and continued by the winding road, looking at the trees while walking. Had not gone far when it came to

another fork, this time the board had two arrows that said "1" and "2." Alice turned left and continued. As was walking, looked down and saw that the path followed by where a trail had changed from the forest to a narrow street paved with yellow bricks. She continued to follow through the trees until the forest is opened in a large grassy clearing. It was very long, run to where Alice could see, and the entire field was covered with poppies. The yellow brick road to follow through the gates of the clearing up of a distant city. It was, Alice could see that the high walls of the city were green and glowed, and the gates were nail emeralds. ****** Status: Alice (B1) Alice turned to the left of the plate, and continued along the winding path. There was no remarkable to see yet. She turned a corner and came to another fork, this time the board had two arrows that said "1" and "2." Alice turned right and continued walking. The vegetation was getting thicker and it was difficult to see anything that was not very close, although the path itself, is still clear and defined as followed by wind between the cerrado trees. Alice turned a bend and suddenly reached an open space. In the center of the clearing stood a small building with a sloping roof and a small tower with a bell in one of its ends. The words "Copenhagen School" were deeply marked a plate of stone above the door. "This must be the place where they said I should go," Alice said to herself. "Just do not know if I even go to a school! I step in my time quite! But perhaps the schools here are different from those to which I am accustomed. I get to see!" Without knocking, she opened the door and entered. ****** Status: Alice (B2) Alice turned to the left of the plate, and continued along the winding path. There was no remarkable to see yet. She turned a corner and came to another fork, this time the board had two arrows that said "1" and "2." Alice turned left and continued walking. A little later, the road began to tilt and Alice began to climb a morrote. At the top of the hill for a few minutes she stopped and looked in all directions in the region - and that this region was curious! There were many streams across the region from one side to another, and the floor was divided into squares formed by living fences, which were of a stream to another. "Damn! The field is divided like a chessboard," Alice said to the final. He stopped and looked around with a satisfied air. "Thank you for your work. It is very interesting," said the Master. "Anybody got any questions?" Alice had discovered that, yes. Perhaps the atmosphere of the school were affected, after all. She raised a hand. "Yes", the Master asked, pointing to her. "What is the question I would like to do?" "One thing I do not understand," she said. (This was not the whole truth, because there were many things she did not understand and that amount would increase at an alarming rate. But there was one thing in particular about what she wanted to ask.) "You say the world is strange that normally mixture of different states, but it is reduced to a single condition where you, as a conscious mind, the notes. suppose that anyone can become something real in this way. What then happens to the mind of others ? "We think we can not understand what you mean," replied the Emperor, threatening, but at this time the Master interrupted.

"Maybe I can elaborate a little on top of the little girl's question. We were talking earlier of electrons passing through two slits. Suppose I could take a picture of an electron passing through one slit or the other. According to what you said, and the picture could show the electron in either of the two slits, would show that was in both. The film of the machine does not have a conscious mind and would be unable to reduce the function of wavelength, so he should file a superposition of two different images. Suppose now that I did a number of copies of that picture without, of course, look for them. You say that each of those copies would now also a mixture of different images, each corresponding to different apertures through which the electrons could have been? " "Yes," replied the Emperor with all care. "We believe that this would be the case." "If it were, we believe that send the copies to different people. The first to open the envelope and look at the photo would make images become one of the real, causing the disappearance of the other?" Again, the emperor agreed, cautious. "But in this case, the pictures that other people would have received a reduction to the same image, even though they are in other cities, the miles of distance. We know from experience that the copies of a photo must show the same image as the original . Thus, when the first person look at one of the copies of the photo, she would make a chance to become the only real and therefore this act presumably affect all other copies, which would have to agree with the first. So a person who looked for a picture in a city would make all other copies in many different cities in the world suddenly changed to show all the same. would as a kind of weird race, with the first person to open the envelope setting other copies of images before the envelopes were opened. I think that was a little girl wanted to say, "he concluded. "Naturally, this does not present any problem in our case," replied the Emperor, "because nobody would dare to look at this picture before we examine the. However, we agree that a situation should arise in this way to people of lower orders . In this case, the situation would be that you just described. " Alice was so impressed to see this seemingly ridiculous argument be accepted, nor understood that the Emperor returned to his seat and little mermaid going to the front of the skirt. The siren was a little unbalanced, since it had no feet. Therefore, the Master sat on the table and was shaking its tail. The attention of Alice returned to the classroom when the siren began to speak. The Theory of the Little Mermaid (Many Universes) "As you know," she began in a liquid voice and music, "I am a creature of two worlds. I live in the sea and I am equally at ease on land. But that is nothing compared to the number of worlds we all inhabit, as we are citizens of many worlds - many, many worlds. "The cabinet before me said that the quantum rules apply to the whole world, except the minds of the people who inhabit it. I tell them that they apply to the whole world, all things. There is no limit to the idea of superposition of states. When an observer looks at a superposition of quantum states, it is expected that he or she see that all the relevant selection of states. That is the case, an observer sees all results, or better, the the observer is also a superposition of different states and each state of the observer sees the effect corresponding to that original state in the mixture. Each state is simply expanded to include the observer in the act of seeing that particular state. "This is not how it seems to us, but that is because the different states of an observer unaware of the existence of each other. When one

electron through a barrier where there are two cracks, it can go both by the right as the left. What the observer can see is pure coincidence. You could see that the electron was left, but there is another you will have seen that the electron to the right. When you observe an electron, you can be divided into two versions of itself, one to see each possible outcome. If these two versions never meet, each will ignore the existence of another. The world is divided into two, with two slightly different versions of you. It is clear that when these their two versions begin to talk with others, you must have different versions of these people too. What then is the division of the world. In this case, it split in two, but for more complex observations it is split into a greater number of versions. " "But for sure this would happen very often," Alice could not avoid and stop the flow of the explanation of the siren. "Sometimes Always," calmly replied the mermaid. "Where there is a situation where a measure can provide different results, all possible outcomes will be observed and the universe is split in the number of versions. "Usually, the worlds remain separate and divided it away without ever making it to the existence of each other, but sometimes they come together again and present effects of interference. The presence of these effects of interference between the different states shows that they and can exist together. " The siren ended his explanation and was seated there, combing the endless threads of his long hair that fell side by side, but separately, over their shoulders. "This implies a large amount of universes. There would have to be as many universes as there are grains of sand on the beaches of the Earth," Alice protested. "Oh, no. There would have to be much more than that. Much more!" mermaid replied, closing the subject. "Much, much more," continued, dreamy. "Very, very, very ..." "This theory," interrupted the Master, "has the advantage of being very economical in relation to statements, but this is not the case with the universe!" He called the next to present his theory. It was the Ugly Duckling, who had to stand on the table in the master to be seen more clearly. The Theory of the Ugly Duckling (It's all very complicated) The Duckling began his explanation and Alice realized that, besides being very ugly, he seemed very angry too. His speech was so full of quacks and chiados that was difficult to understand what he said. For just as Alice thought she could see that he spoke to the superposition of states only worked well for small systems with few electrons and atoms. He said they only had to argue that the systems were often in a mixture of states because of the occurrence of interference, as a lonely and single state would not interfere with that. He said he did not know the truth if the interference occurs with objects that contain many particles. It is known that interference and therefore the superposition of states exist for groups with few particles, so it is assumed that the same applies to complicated things, like ducks. He did not believe it for anything in this world. A duck contains a bunch of atoms of duck, he continued, and before any overlapping states could interfere, all the atoms in each state should be separate exactly match with the appropriate atom in other states. Are many atoms that would not be possible. On average, the effect is canceled and not see any result set. Since then, he asked, you can be sure that the ducks are always in a superposition of states? Answer me if this is so smart. All this

superposition of states works well for a few particles at a time, but stop well before reaching a duck. He continued saying that he knew very well that means something and when not seen. He knew that was not in a superposition of states and that no one was for his chance. When he moved, he continued, determined, even changed from one state to another determined. The change was irreversible and there is no way back and recombining with other states. Nothing would interfere with him, he concluded. At that point, his gaggle was so exalted that Alice could not accompany him. She not surprised when he was so angry that fell from the table, out of his field of vision. There was then a pause and a moment of silence that was interrupted when a long, graceful neck appeared behind the table, followed by a body feather, white as snow. It was a swan. "How beautiful!", Exclaimed Alice. "Can I pet you?" The swan Chiou mad and hit the wings so scary. Alice noticed that, despite its change is certainly irreversible, his temperament did not seem to have changed much. At that time there was an uproar in the back of the room, and Alice heard a voice shouting, "Stop this farce! You are all wrong!" She looked toward the sound and saw a figure tall and angry, standing in the space between the tables. It was the classical mechanics. Its floor was seriously compromised because it carries a pinball machine, like those that Alice had seen in a cafe. (They are found most often in bars, but Alice was too young to have seen them in places like this.) The theory of classical mechanics (Wheels Within Wheels) The classical mechanics went to the front of the room and put your computer desk next to the Master. She had the form of a table in that way inclined writing "Interceptor electrons. At the top there were two openings through which the particles were fired and, below, was prepared a row of alternately Caçapa marked with "win" and "not win". The surface of the table, although painted with strong colors, strangely had the various obstacles and pitchers that Alice had seen in pinball machines. "You are only cheating themselves," announced the classical mechanics with firmness. "Look carefully this unit, which is basically a normal apparatus of interference of electrons with two slits, and I know what is really happening." Alice noticed that, despite all the striking decor, the unit was not more than a smaller version of the experiment shown to her room in the Mechanical Gedanken. The classical mechanics soon showed its operation, firing a stream of electrons by the two slits. At least Alice assumed they must have been, though not see through the cracks because they were the only ones present, where the electrons were indeed until his arrival was marked Caçapa in the lower part of the machine. As she expected, the electrons are grouped into cells separated by intervals, where very few electrons were found. Alice was intrigued to see that these intervals in the pattern of interference coincided well with the Caçapa saying "wins." "Seeing that the interference occurs, you argue that this shows that the electrons moved in some way by the two slits, since the combination of the amplitudes of each of them produces the interference pattern that we see. I say to you that the electrons actually pass individually for just a crack, so perfectly sensible. The interference due to hidden variables! Alice found it difficult to monitor what exactly happened at that point. The most that she saved that moment was that the mechanic pulled the table something that seemed covered with a cloth and it was not there before. No matter what happened, but now the surface of the table was covered with a

pattern of protuberances and deep channels leading to the two slits. "Look! Hidden variables", exclaimed the mechanic. "There are so well hidden," Alice pointed out, looking for strange infidel area that is now revealed. "My idea," began the classical mechanics, clearly ignoring the remark of Alice, is that electrons and other particles so they behave perfectly rational and classical as well as particles that are used in the World Classic. The only difference is that, as well as normal forces acting on the particles, they are also affected by a particular quantum force, or wave pilot. And she is causing the strange effect that interpret as arising from interference. In my statement with the pinball of electrons, each electron actually goes in a slot or another, by moving on the table and so normal and predictable. Any randomness in all of it originates from different initial speeds and directions that the electrons will be initially. When the electrons cross the rails you see here in the quantum potential, they are deflected by the quantum force, and a bicycle wheel attached to a rail train, which is why most of the electrons has been grouped. That is what produces the so-called effects of interference. " "Well," said the Master, "this is certainly a very interesting theory - very, very interesting even. However, if you do not mind what I say, it looks like you removed the difficulties they had with the behavior of electrons at the expense of a strange behavior and the quantum potential. "Because your strength is to produce quantum effects that give the interference, it must be influenced by things that occur in very different places. If a third slit was made on your desk, the forces on the quantum particle is changed, even if no particle move it. It must be, because the interference to three holes is different from that to two, and its strength needs to play all those quantum interference effects that we know they occur. Moreover, quantum potential, or network quantum forces, must be very complicated. In theory, there is nothing similar to the reduction of the wave functions that occurs in normal quantum theory, then its potential to be influenced by all the possibilities of all things that could have happened in any occasion. It is like the theory of Many Universes, accordingly. In theory, you say that what is observed depends on the trajectory that the particle will have when they are affected by the pilot wave and the wave itself retain the pilot information of all things that could have happened and there is no avoiding it. The wave would have to be incredibly complex as the sum of all the universes in the theory of many universities, even if it does not affect the particles in most of the time . "The pilot wave theory in its influences the behavior of particles, but the way in which the particles move individually has no effect on the wave. It depends only on the particles that could have done. There is no symmetry of action and reaction between particle and wave pilot. As a classical mechanics, this should be a hassle for you. You would not want to contradict Newton's law which says that action and reaction are always equal, would you like? " At this time the quantum mechanics, which had followed the classical mechanics into the classroom without saying anything, went to the front of the room and he's got the arm. "Come with me," he said. "Surely you do not want to be accused of heresy by counteracting the classical laws of Newton. All this academic discussion on what the electrons are no longer or do not for guys like us. We are Mechanical. As Mechanical, my main concern is Quantum laws that work and work well. When calculating the amplitude of some process, it tells me what is likely to happen.

There are many "answers" to the problem of the measure, but none is universally accepted. In practice, quantum mechanics is usually used to reach the amplitude and the various probabilities to give a physical system. Then, these probabilities are used to predict the behavior of large sets of atomic systems without too much concern about what would happen with a single system. The results for the sets can be compared with the action, again without much concern about the way in which these measurements were made. The practical answer to this problem is "close your eyes and calculate." The interpretation of quantum mechanics can be difficult, but there's no denying that it works well. She gives me the probability of different results and is accurately and reliably. It is not my job to be worried that the electrons are doing when I'm not looking for them, since I know what they are doing when I watch them. That is why I pay. " He took his silence in a corner, turned to Alice and asked, "I learned everything I know about that monitors and measures?" "Well," she began, "to tell the truth, I am more confused than when I arrived here." "Okay," suddenly interrupted the quantum mechanics. "I thought. You've learned what you wanted. Come along and see some of the results of quantum theory. Let me show you some of the attractions of the country of Quantum." Notes 1. The extent of the problem "is that the selection of a unique opportunity and the reduction of all other amplitudes is quite different from other quantum behavior and how that can happen is not obvious. The problem is contained in its simplest form, the question "how is it possible to measure anything?. The conventional view of quantum mechanics is that when there are multiple possibilities, a range for each scale and total system is obtained by the sum, or superposition of them all. For example, if several slits through which a particle can pass, the magnitude of the system contains a range for each opening, and there may be interference between the individual amplitudes. Without external influences , the amplitude change is so smooth and predictable. When you make a measurement on a system whose sum of amplitudes corresponding to different possible values of the measured quantity, the theory says you observe, with some probability, one or other of these values. Immediately after the measure, the value is a known quantity (because you just measure it) and then the sum of self-states (see box on page 85) is reduced to one, only for the actual value measured by you. The description of the measure in orthodox quantum mechanics has the disadvantage that the measurement procedure does not seem at all compatible with the rest of quantum theory. If quantum theory atomic theory is true, as seems to be, and if the world is made of atoms, then presumably the quantum theory should apply to the whole world and all things contained therein. This includes the instruments of measurement. When a quantum system can result in different values, its amplitude is the sum of states corresponding to each possible value. When a measuring instrument is itself a quantum system and there are several values that could be measured, he is not entitled to select only one. He should be in a state that was the sum of the amplitudes of all possible results that he could measure and no single observation could be made. The conclusion to be drawn is that: a) I never noticed anything of truth or b) The quantum theory is a bunch of bullshit. Neither of the two conclusions is sustainable (for the most tempting option (b) may appear). We know very well that we look at things, but we can

not deny that quantum theory has been successful insuperability to describe all the observations, while no other alternative theory does so well. We can not abandon it lightly.

Alice followed the quantum mechanics along the way that out of school. While progress, the path would be extended gradually to become a flat road. "I think the most interesting thing you've shown me so far," said Alice, "was the way those obtained interference effects even when there was only one electron present. It is true then it makes no difference if we have only one electron or many ? "It is true that you can see the interference with one or more electrons. But that does not mean make difference. Some effects are only seen when you have many electrons. See the Pauli principle, for example ..." "I heard of him," interrupted Alice. "The electrons told him that I came here. Can you tell me what it is, please?" "It is a law that applies when you have a bunch of particles equal completely identical in all respects. If you want to know more about it, it is better to ask here, since we are close by. They are experts in the behavior of many particles together. " Mechanic's words made Alice look around and realize that, while going, they had reached a high wall of rock that accompanied one side of the road. Well ahead of them was a large gate. The doors were made of twisted iron and is opened between two huge columns of stone, each with a painted crest in the center. The right of the gate above the wall, Alice could see a panel of wood which read: Academy Fermi-Bose - For electrons and photons In the center of the gate was an imposing figure, a wide and very portly man who looked even more massive and heavy with academic gown and hat of bachelor he used. His face was round and stained adorned by a large mustache and sideburns. Firmly attached to one of his eyes had a monocle, which hung a long black ribbon. "This is the Principal Director, the Mechanical whispered in the ear of Alice, who was nearest him. "I mean the principle of Pauli", asked Alice excited. She had been surprised by his grip of sudden appearance. "No, no," Chiou the Mechanic, "he is the Principal Director of the Academy. Although the Pauli principle to be the main principle of the Academy, he is the Director." Alice wanted to not have asked.

They crossed the street toward the imposing character. "Excuse me, sir," began the Mechanic. "You, by tenderness, could not say anything about the systems with many particles for my friend here?" "Sure, sure," said the Director with a powerful voice. "Never a lack of particles here, oh no. I am happy to show you the Academy. He turned, making his gown curl, and was showing the way to the Academy. While going, Alice saw some figures in and out of the bushes. In a moment, one of the put your head over a bush and made a face to them. Or at least so it seemed to Alice. As always, it was very difficult to see any detail. "Ignore him," rugiu the Director. "This school is only one electron, the electron Minor." They reached the door of the Academy, which is located in an old and honorable house that seemed a bit of a mansion with Tudor dynasty. Without a pause, the director led them through the main door into a hall with arch to the ceiling and then led them up by a large staircase. While going by the building, Alice saw small figures hiding behind the handrails, in and out of rooms and corridors by fire side when they approached. "Ignore him," again commanded the Director. "It is the electron Minor. Particulates are particles always!" "But the electron can not be minor, if I just see him on the road," protested Alice. "Sure, can not be the same particle in two places at the same time. This is how the experiment in which an electron can pass by the two slits?," She said to quantum mechanics. "No, not that. They have many electrons there. Not noticed? The electrons are all exactly equal. They are completely identical to each other. There is no way to distinguish between them, so all are, of course, Electronics Minor." "All right," confirmed with the Director as the decision led to his office, "and this is a problem, I say. You must imagine how difficult it is for a teacher to have twins two students in school and not knowing distinguish between them. Well here there are hundreds of identical particles entirely. This is a call from hell! "The electrons are not so bad," he continued. "We only count and see if the total is correct. At least the number of electrons remains the same, then we know how many should have, but with the photons, not even this works. Photons are bosons and therefore does not retain . You can start a lesson with, say, thirty, and finish the class with fifty. Or the number may fall to less than twenty - it is difficult to guess. That's life very difficult for employees of the school. " Alice noticed that an unknown word remark. "Will could you explain that?" She said, hopeful. "Could you tell me what a bóson?" The director was even more red than before talking with the mechanic. "I think you better take it to the class of suits of Symmetry for beginners. What do you think? That will explain everything about bosons and Férmions." "Absolutely right," said the Mechanic. "Come on, Alice. I think I remember the way." Walked in a corridor until you reach a room and at the time the class was starting. "Attention, please," said the professor. "As you know, you guys, electrons, are identical to each other as well as all of you, the photons. This means that there is no way to know if two of you have changed places. To an observer, you could have changed places and of course, changed to some extent. Everyone knows that you have linked to you, a function of wavelength, or amplitude, and that this amplitude is a superposition of all the things you could be doing. Where we can not say the they are doing, you will be doing all the things, or in any way, you have a scale for each of these things. Vejam so that any group of you is impossible to say when two of you

changed place, and that means wave function of the total will be a superposition of all amplitudes for which a different pair has been exchanged. I hope you all have noted that. " See footnote 1 at the end of Chapter "The probability of making an observation is given by the square of the wave function, ie the value of the function multiplied by itself. As you are all identical, it is obvious that if two of you change places, the difference not is observable and therefore the square of the wave function does not change. It may seem that there was no way. Tell me about what can change? " One of the electrons raised his hand, or at least inferred that Alice is what happened. It was not possible to see with great clarity. "The signal changes, teacher." "Very well, is an excellent response. I would be in your observation, saying it was a great response but unfortunately, can not distinguish it from others. Yes, as you know, the amplitudes do not have to be positive. May be positive or negative, so that two amplitudes can cancel each other when there is interference. This means that there are two cases in which the square of its amplitude does not change. It may be that the scale does not change when two of you change places. In this case , the particles are bosons, like you, the photons. But there is another possibility. When two of you change places, the range can be reversed. Muda of positive to negative and vice versa. In this case, the square remains positive and distribution of probabilities is unchanged, because the magnitude multiply itself takes two inversions, which results in no change. This is what happens to you as férmions, electrons. All particles are in one or other of these classifications: or are férmions are either bosons. "You may think it does not matter much if its amplitude is inverted or not, especially because the distribution of probabilities remains the same but in fact is very important, especially for férmions. The point is that if two of you are on the same state - to say, in the same place and doing the same thing - and move from place, is not only a change inobservável. Actually, there is some change. In this case, neither the distribution of probabilities or the magnitude can change. The interference between the possible paths that a particle can travel will result in a distribution of probabilities with minimum and maximum well pronounced, which is more likely that a particle is detected in a position than in another. They left the room, Gedanken, whose floor was back to his usual brilliant appearance, and continued for a corridor to another room furnished with a few seats. When the two had already been seated, the mechanic said: "When we talk about a situation like the electrons through the openings, we describe using a scale. It is more or less like the waves you saw, and is actually called, with frequency of the wave function. The range can pass through two openings at the same time and not always positive, as the likelihood. the less likely that you can have is zero, but the amplitude can be positive or negative, with different pathways it may cancel or add to each other and result in interference, as with the waves of water. " "Where are the particles then", asked Alice. "By opening up what they are, indeed?" "Indeed, the scale does not say that. However, it raised the magnitude squared, ie to multiply it by itself to always give a positive number, you can get a distribution of probabilities. If you choose any position determined, is that this distribution is likely to say, if you observe a particle, find it in that position. "

"And that is all she says?" Exclaimed Alice. "I must say that I feel inadequate. You never know where something is." "Yes, this is true. You can not tell where a particle is, except that is not where the probability is zero, of course. If you have a large number of particles, however, be assured that you will find more particles where the probability is higher, much less one where the probability is low. If you have a very large number of particles, it is possible to say with much precision the place where many particles are. This is the case for those workers who you were talking . They knew what they were building because they were using a lot of bricks. In numbers too high, the reliability of the system is very good. " See footnote 3 at the end of Chapter "And there is no way to tell which one particle is doing without watching it?", Said Alice, just to be sure. "No, no way. When you see what can happen in several different ways, you have a scale for each possible way, and the overall amplitude is obtained adding up all of them. You will have a superposition of states. In a way , the particle is doing everything it can to it. Not only do you not know what the particle is doing. The interference shows that the odds are all present and influence each other. In a way, are all equally real. It is not forbidden is compulsory. " "I saw a poster that said that in the Bank. Seemed very serious." "And it is! This is one of the most important rules here. How many things can happen, they happen. Take a look at the cat, for example." "What cat?", Alice asked, looking around, confused. "But the cat of Schrödinger here. He has left us to cuidássemos it." Alice looked to where the mechanic pointed and saw a large striped cat who slept in a basket in the corner of the room. As if awakened by having heard his name, the cat stood up, stretch out. Or better, got up and was not raised, lounge and not yawn. Alice saw that, beyond the slightly blurred picture of the cat's arched back, a cat was also identical, still asleep in the bottom of the basket. He was very hard in a very unnatural. Looking at him, Alice could swear he was dead. "Schrödinger developed a Gedanken experiment in which a poor cat got trapped in a box, along with a container of poison gas and a mechanism to break the bottle if a sample of a radioactive material were suffering decay. This is definitely a decay process quantum. The material may or may not fall and then, according to the rules of quantum physics, there would be a superposition of states, where some in the decay would have occurred and in others not. Of course, in those states in which the decay occurs, the cat die, and then we would have a superposition of states of cats, some dead and some alive. When the box was opened, someone to watch the cat and from then on he was dead or alive. The question was proposed by Schrödinger: "What state of the cat before the box is open? " "And what happened when they opened the box", Alice asked. "In fact, everyone was so excited discussing the issue that anyone opened the box, and that is why the cat was like that." Alice looked at the basket where an aspect of the cat licking itself with dedication. "He seems very much alive," she noted. Mal of the words had left his mouth, the cat became very solid and tangible version dead and gone. Satisfied purr, the cat jumped out of the box and began to chase a mouse that had left the wall. Alice noticed that there was a rat hole, she could see the mouse had just gone straight to the wall. The quantum mechanics of the eye followed the direction of Alice. "Ah, yes. This is an example of penetration into barriers: happens all the time here. Where there is a region that a particle can not enter in accordance with the laws of classical mechanics, the amplitude does not necessarily cease immediately on the border

region, despite declining rapidly within it. If the region is well close, there will still be left some magnitude on the other side, and this gives room for a small probability that a particle can appear there, apparently having crossed a seemingly insurmountable barrier, a process called "tunneling." happens frequently. " Alice was passed in your head the things that had seen so far and noticed a problem. "As I got to watch the cat and set their condition if he could not do it by itself? What decides that a comment that was made and who is able to do them?" "This is a very good," replied the quantum mechanics, "but we are only mechanical and not so much in mind with these things. Just do the work and use methods that we know work in practice. If someone wants to discuss extent of the problem with you, you have to go somewhere more academic. I suggest that there is a lesson from the School of Copenhagen. " "And what do I get there?", Alice asked, settling with the fact of having been passed on to another place. In response, the mechanism leading to the corridor and opened a door, which was not to the alley where she had entered, but to a forest. Notes 1. Quantum mechanics is usually contrasted with the classical or Newtonian mechanics. The latter, which deals with the detailed description of objects in motion, was developed before the early 20th century and is based on the original works of Galileo, Newton and others before and after them. The Newtonian mechanics works very well on large scales. The movement of planets can be predicted far in advance and great accuracy. It works almost equally well to artificial planets and space missions for exploration: their positions can be made years before. Works great also for apples falling from trees. In the case of an apple that falls, air resistance is significant about that. The classical mechanics describes the suit as the collision of a huge number of air molecules rebound in apple. When you ask about the air molecules, they respond to him that they are small groups of atoms. When you ask about the atoms, it is an embarrassing silence. The classical mechanics was not successful in trying to explain the nature of the world in atomic scale. Things must be different in some way for small objects than large objects appear to be. To use these arguments, you should ask: small or large compared to what? There must be some size, a fundamental constant setting the scale on which this new behavior becomes obvious. It is a definitive change in the way they observed the behavior of things, and it is universal. Atoms in the sun and distant stars emitting light in the same spectrum as the lamp on his desk-to-head. The transition to quantum behavior is not something that happens only locally, there is a fundamental property of nature involved. This property is denoted by the universal constant that appears in most of the quantum equations. The world is granulated in the scale defined by the constant character. On this scale, energy and time, position and momentum, are blur together. It is not necessary to say that the scale of human perception, character is very small and most of the quantum effects is not absolutely clear. 2. What the relations of the Heisenberg uncertainty tell us is that we see things so wrong. We believe beforehand that we should be able to measure the position and momentum of a particle at the same time, but found that we can not. The very nature of the particles does not allow us to make such measurements on them and the theory tells us we are doing the wrong questions, questions to which we have no viable answers. Niels Bohr used the word complementarity to express the fact that it is possible to have concepts

that can not be precisely defined at the same time: pairs of concepts such as justice and legality, rationality and emotion. There is something fundamentally wrong with our belief that we should be able to talk about the position and momentum, or the exact amount of energy of a particle in a given moment. Do not you know that would be significant while talking to two very distinct qualities. It seems that this is not as significant. 3. Quantum mechanics is not a particle set classic in the traditional sense, instead dealing with states and amplitudes. If you amounts to a square amplitude (ie multiplied by its value) you get a distribution of probabilities gives the probability of obtaining various results when making an observation or measurement. The actual value obtained by measuring with any appears to be random and unpredictable. Just seems that the suggestion made earlier in this book that nature is uncertain and that "everything" must, in the end, be true. It seems? Well .. no. If you make many measurements, the average result can be predicted with precision. Recording of bets do not know which horse will win each race, but confidently expected to make some profit by the end of the day. Unable to provide large and unexpected losses, as working with small numbers whose average can not be trusted. The number of gamblers would be a few thousands, instead of 1,000,000,000,000,000,000,000,000 atoms or more, existing even in a tiny piece of matter. These digits appear with a number less than the design of a repetitive wallpaper, but it is undeniably great. The mean expected statistical fluctuations in measurements of very large numbers of atoms are negligible, even if the results for individual atoms can be quite random. Amplitudes of quantum mechanics can be calculated with enough accuracy and compared with experiments. A much cited result is the magnetic moment of an electron. The electrons revolve as little pawns and have electrical properties: they behave like small magnets. The magnetic force and rotation of the electron are related, and this ratio can be calculated using the appropriate units. A classical calculation result reaches 1 (with arbitrary assumptions about the distribution of electric charge of an electron). The classic comes to the calculation result 2.0023193048 (± 8) (the error is the last decimal place). A measurement result reaches 2.0023193048 (± 4). And a good agreement! The probability of achieving, at random, so consistent values is similar to the probability of a dart throw, also at random, and adjust on the fly - when the target is as far as the Moon This result in particular is often given as an example the success of quantum theory. You can calculate, with the same accuracy, the amplitudes of other processes, but very few figures that can be measured with such accuracy. 2 Alice inside the woods and was followed by a path that winds through the trees, until you reach a fork. There was a plaque there, but not much help. The arrow pointing to the right said "A" and pointed to the left that said "B", nothing more. "Damn," Alice exclaimed, irritated. "This is the most useless card I have ever seen." She looked around to see if any could track where they were on the tracks, where surprised to see the Schrödinger cat sitting on a bough of a tree a few meters away. "Cat," she said, timidly. "Could you tell me which path should I take?" "That depends a lot on where you want to reach," said the Cat. "Do not know where ...", she began.

"So, no matter where you are," interrupted the Cat. "But I have to decide between two paths," said Alice. "This is where you wrong," smiled the cat. "You do not have to decide, you can take all the paths. Sure, I know that now. I especially tend to do nine different things at once. The cats crawl anywhere, when not being observed. Speaking of observation, "he said, hurry," I think I'm about to be obs ... At this time, he disappeared suddenly. "What a weird cat," thought Alice, "and that weird suggestion. He should be referring to the superposition of states of the mechanic who spoke. I think it's like the time we left the Bank. Somehow, I go in several directions at the same time, then I think you should try to do the same thing again. " ****** Status: Alice (A1) Alice turned to the right, in plate, and continued by the winding road, looking at the trees while walking. Had not gone far when it came to another fork, this time the board had two arrows that said "1" and "2." Alice turned to the right and continued. While going, the trees were scarce and it was a road trails and steep rocky. The slope was increasing, until it was up the slope of a mountain alone. The trail led to a narrow path that a cliff edge, which in turn went to a small lawn. Its front, the slope of the cliff, she saw an opening as a mouth bocejante, and a passage, which took forward and down. The passage was very dark, but to their own surprise, and she ended up coming down. The floor and walls were smooth and went straight to the front, a slight slope in the direction of a distant light and brightness. As she walked, the light would gradually become stronger and more red and the tunnel was getting warmer. Small clouds of steam and she passed it heard a sound like that of a huge animal snoring in his sleep. At the end of the tunnel, Alice spotted a huge underground. Just gave to try to guess the dark vastness of the place, but close to his feet, she saw a great brightness. A huge red and gold dragon slept deeply, with its long tail coiled around him. Below him, serving him in bed, there was a high pile of gold and silver, jewelry and wonderful sculptures, all bathed in red light. Status: Alice (A2) Alice turned to the right, in plate, and continued by the winding road, looking at the trees while walking. Had not gone far when it came to another fork, this time the board had two arrows that said "1" and "2." Alice turned left and continued. As was walking, looked down and saw that the path followed by where a trail had changed from the forest to a narrow street paved with yellow bricks. She continued to follow through the trees until the forest is opened in a large grassy clearing. It was very long, run to where Alice could see, and the entire field was covered with poppies. The yellow brick road to follow through the gates of the clearing up of a distant city. It was, Alice could see that the high walls of the city were green and glowed, and the gates were nail emeralds. ****** Status: Alice (B1) Alice turned to the left of the plate, and continued along the winding path. There was no remarkable to see yet. She turned a corner and came to another fork, this time the board had two arrows that said "1" and "2." Alice turned right and continued walking. The vegetation was getting thicker and it was difficult to see anything that was not very close, although the path itself, is still clear

and defined as followed by wind between the cerrado trees. Alice turned a bend and suddenly reached an open space. In the center of the clearing stood a small building with a sloping roof and a small tower with a bell in one of its ends. The words "Copenhagen School" were deeply marked a plate of stone above the door. "This must be the place where they said I should go," Alice said to herself. "Just do not know if I even go to a school! I step in my time quite! But perhaps the schools here are different from those to which I am accustomed. I get to see!" Without knocking, she opened the door and entered. ****** Status: Alice (B2) Alice turned to the left of the plate, and continued along the winding path. There was no remarkable to see yet. She turned a corner and came to another fork, this time the board had two arrows that said "1" and "2." Alice turned left and continued walking. A little later, the road began to tilt and Alice began to climb a morrote. At the top of the hill for a few minutes she stopped and looked in all directions in the region - and that this region was curious! There were many streams across the region from one side to another, and the floor was divided into squares formed by living fences, which were of a stream to another. "Damn! The field is divided like a chessboard," Alice said to the final. He stopped and looked around with a satisfied air. "Thank you for your work. It is very interesting," said the Master. "Anybody got any questions?" Alice had discovered that, yes. Perhaps the atmosphere of the school were affected, after all. She raised a hand. "Yes", the Master asked, pointing to her. "What is the question I would like to do?" "One thing I do not understand," she said. (This was not the whole truth, because there were many things she did not understand and that amount would increase at an alarming rate. But there was one thing in particular about what she wanted to ask.) "You say the world is strange that normally mixture of different states, but it is reduced to a single condition where you, as a conscious mind, the notes. suppose that anyone can become something real in this way. What then happens to the mind of others ? "We think we can not understand what you mean," replied the Emperor, threatening, but at this time the Master interrupted. "Maybe I can elaborate a little on top of the little girl's question. We were talking earlier of electrons passing through two slits. Suppose I could take a picture of an electron passing through one slit or the other. According to what you said, and the picture could show the electron in either of the two slits, would show that was in both. The film of the machine does not have a conscious mind and would be unable to reduce the function of wavelength, so he should file a superposition of two different images. Suppose now that I did a number of copies of that picture without, of course, look for them. You say that each of those copies would now also a mixture of different images, each corresponding to different apertures through which the electrons could have been? " "Yes," replied the Emperor with all care. "We believe that this would be the case." "If it were, we believe that send the copies to different people. The first to open the envelope and look at the photo would make images become one of the real, causing the disappearance of the other?" Again, the emperor agreed, cautious. "But in this case, the pictures that other people would have received a reduction to the same image, even though they are in other cities, the miles of distance. We know from experience that the copies of a

photo must show the same image as the original . Thus, when the first person look at one of the copies of the photo, she would make a chance to become the only real and therefore this act presumably affect all other copies, which would have to agree with the first. So a person who looked for a picture in a city would make all other copies in many different cities in the world suddenly changed to show all the same. would as a kind of weird race, with the first person to open the envelope setting other copies of images before the envelopes were opened. I think that was a little girl wanted to say, "he concluded. "Naturally, this does not present any problem in our case," replied the Emperor, "because nobody would dare to look at this picture before we examine the. However, we agree that a situation should arise in this way to people of lower orders . In this case, the situation would be that you just described. " Alice was so impressed to see this seemingly ridiculous argument be accepted, nor understood that the Emperor returned to his seat and little mermaid going to the front of the skirt. The siren was a little unbalanced, since it had no feet. Therefore, the Master sat on the table and was shaking its tail. The attention of Alice returned to the classroom when the siren began to speak. The Theory of the Little Mermaid (Many Universes) "As you know," she began in a liquid voice and music, "I am a creature of two worlds. I live in the sea and I am equally at ease on land. But that is nothing compared to the number of worlds we all inhabit, as we are citizens of many worlds - many, many worlds. "The cabinet before me said that the quantum rules apply to the whole world, except the minds of the people who inhabit it. I tell them that they apply to the whole world, all things. There is no limit to the idea of superposition of states. When an observer looks at a superposition of quantum states, it is expected that he or she see that all the relevant selection of states. That is the case, an observer sees all results, or better, the the observer is also a superposition of different states and each state of the observer sees the effect corresponding to that original state in the mixture. Each state is simply expanded to include the observer in the act of seeing that particular state. "This is not how it seems to us, but that is because the different states of an observer unaware of the existence of each other. When one electron through a barrier where there are two cracks, it can go both by the right as the left. What the observer can see is pure coincidence. You could see that the electron was left, but there is another you will have seen that the electron to the right. When you observe an electron, you can be divided into two versions of itself, one to see each possible outcome. If these two versions never meet, each will ignore the existence of another. The world is divided into two, with two slightly different versions of you. It is clear that when these their two versions begin to talk with others, you must have different versions of these people too. What then is the division of the world. In this case, it split in two, but for more complex observations it is split into a greater number of versions. " "But for sure this would happen very often," Alice could not avoid and stop the flow of the explanation of the siren. "Sometimes Always," calmly replied the mermaid. "Where there is a situation where a measure can provide different results, all possible outcomes will be observed and the universe is split in the number of versions. "Usually, the worlds remain separate and divided it away without ever making it to the existence of each other, but sometimes they come together

again and present effects of interference. The presence of these effects of interference between the different states shows that they and can exist together. " The siren ended his explanation and was seated there, combing the endless threads of his long hair that fell side by side, but separately, over their shoulders. "This implies a large amount of universes. There would have to be as many universes as there are grains of sand on the beaches of the Earth," Alice protested. "Oh, no. There would have to be much more than that. Much more!" mermaid replied, closing the subject. "Much, much more," continued, dreamy. "Very, very, very ..." "This theory," interrupted the Master, "has the advantage of being very economical in relation to statements, but this is not the case with the universe!" He called the next to present his theory. It was the Ugly Duckling, who had to stand on the table in the master to be seen more clearly. The Theory of the Ugly Duckling (It's all very complicated) The Duckling began his explanation and Alice realized that, besides being very ugly, he seemed very angry too. His speech was so full of quacks and chiados that was difficult to understand what he said. For just as Alice thought she could see that he spoke to the superposition of states only worked well for small systems with few electrons and atoms. He said they only had to argue that the systems were often in a mixture of states because of the occurrence of interference, as a lonely and single state would not interfere with that. He said he did not know the truth if the interference occurs with objects that contain many particles. It is known that interference and therefore the superposition of states exist for groups with few particles, so it is assumed that the same applies to complicated things, like ducks. He did not believe it for anything in this world. A duck contains a bunch of atoms of duck, he continued, and before any overlapping states could interfere, all the atoms in each state should be separate exactly match with the appropriate atom in other states. Are many atoms that would not be possible. On average, the effect is canceled and not see any result set. Since then, he asked, you can be sure that the ducks are always in a superposition of states? Answer me if this is so smart. All this superposition of states works well for a few particles at a time, but stop well before reaching a duck. He continued saying that he knew very well that means something and when not seen. He knew that was not in a superposition of states and that no one was for his chance. When he moved, he continued, determined, even changed from one state to another determined. The change was irreversible and there is no way back and recombining with other states. Nothing would interfere with him, he concluded. At that point, his gaggle was so exalted that Alice could not accompany him. She not surprised when he was so angry that fell from the table, out of his field of vision. There was then a pause and a moment of silence that was interrupted when a long, graceful neck appeared behind the table, followed by a body feather, white as snow. It was a swan. "How beautiful!", Exclaimed Alice. "Can I pet you?" The swan Chiou mad and hit the wings so scary. Alice noticed that, despite its change is certainly irreversible, his temperament did not seem to have changed much. At that time there was an uproar in the back of the room, and Alice heard a voice shouting, "Stop this farce! You are all wrong!" She looked

toward the sound and saw a figure tall and angry, standing in the space between the tables. It was the classical mechanics. Its floor was seriously compromised because it carries a pinball machine, like those that Alice had seen in a cafe. (They are found most often in bars, but Alice was too young to have seen them in places like this.) The theory of classical mechanics (Wheels Within Wheels) The classical mechanics went to the front of the room and put your computer desk next to the Master. She had the form of a table in that way inclined writing "Interceptor electrons. At the top there were two openings through which the particles were fired and, below, was prepared a row of alternately Caçapa marked with "win" and "not win". The surface of the table, although painted with strong colors, strangely had the various obstacles and pitchers that Alice had seen in pinball machines. "You are only cheating themselves," announced the classical mechanics with firmness. "Look carefully this unit, which is basically a normal apparatus of interference of electrons with two slits, and I know what is really happening." Alice noticed that, despite all the striking decor, the unit was not more than a smaller version of the experiment shown to her room in the Mechanical Gedanken. The classical mechanics soon showed its operation, firing a stream of electrons by the two slits. At least Alice assumed they must have been, though not see through the cracks because they were the only ones present, where the electrons were indeed until his arrival was marked Caçapa in the lower part of the machine. As she expected, the electrons are grouped into cells separated by intervals, where very few electrons were found. Alice was intrigued to see that these intervals in the pattern of interference coincided well with the Caçapa saying "wins." "Seeing that the interference occurs, you argue that this shows that the electrons moved in some way by the two slits, since the combination of the amplitudes of each of them produces the interference pattern that we see. I say to you that the electrons actually pass individually for just a crack, so perfectly sensible. The interference due to hidden variables! Alice found it difficult to monitor what exactly happened at that point. The most that she saved that moment was that the mechanic pulled the table something that seemed covered with a cloth and it was not there before. No matter what happened, but now the surface of the table was covered with a pattern of protuberances and deep channels leading to the two slits. "Look! Hidden variables", exclaimed the mechanic. "There are so well hidden," Alice pointed out, looking for strange infidel area that is now revealed. "My idea," began the classical mechanics, clearly ignoring the remark of Alice, is that electrons and other particles so they behave perfectly rational and classical as well as particles that are used in the World Classic. The only difference is that, as well as normal forces acting on the particles, they are also affected by a particular quantum force, or wave pilot. And she is causing the strange effect that interpret as arising from interference. In my statement with the pinball of electrons, each electron actually goes in a slot or another, by moving on the table and so normal and predictable. Any randomness in all of it originates from different initial speeds and directions that the electrons will be initially. When the electrons cross the rails you see here in the quantum potential, they are deflected by the quantum force, and a bicycle wheel attached to a rail train, which is why most of the electrons has been grouped. That is what produces the so-called effects of interference. " "Well," said the Master, "this is certainly a very interesting theory - very, very interesting even. However, if you do not mind what I say, it

looks like you removed the difficulties they had with the behavior of electrons at the expense of a strange behavior and the quantum potential. "Because your strength is to produce quantum effects that give the interference, it must be influenced by things that occur in very different places. If a third slit was made on your desk, the forces on the quantum particle is changed, even if no particle move it. It must be, because the interference to three holes is different from that to two, and its strength needs to play all those quantum interference effects that we know they occur. Moreover, quantum potential, or network quantum forces, must be very complicated. In theory, there is nothing similar to the reduction of the wave functions that occurs in normal quantum theory, then its potential to be influenced by all the possibilities of all things that could have happened in any occasion. It is like the theory of Many Universes, accordingly. In theory, you say that what is observed depends on the trajectory that the particle will have when they are affected by the pilot wave and the wave itself retain the pilot information of all things that could have happened and there is no avoiding it. The wave would have to be incredibly complex as the sum of all the universes in the theory of many universities, even if it does not affect the particles in most of the time . "The pilot wave theory in its influences the behavior of particles, but the way in which the particles move individually has no effect on the wave. It depends only on the particles that could have done. There is no symmetry of action and reaction between particle and wave pilot. As a classical mechanics, this should be a hassle for you. You would not want to contradict Newton's law which says that action and reaction are always equal, would you like? " At this time the quantum mechanics, which had followed the classical mechanics into the classroom without saying anything, went to the front of the room and he's got the arm. "Come with me," he said. "Surely you do not want to be accused of heresy by counteracting the classical laws of Newton. All this academic discussion on what the electrons are no longer or do not for guys like us. We are Mechanical. As Mechanical, my main concern is Quantum laws that work and work well. When calculating the amplitude of some process, it tells me what is likely to happen. There are many "answers" to the problem of the measure, but none is universally accepted. In practice, quantum mechanics is usually used to reach the amplitude and the various probabilities to give a physical system. Then, these probabilities are used to predict the behavior of large sets of atomic systems without too much concern about what would happen with a single system. The results for the sets can be compared with the action, again without much concern about the way in which these measurements were made. The practical answer to this problem is "close your eyes and calculate." The interpretation of quantum mechanics can be difficult, but there's no denying that it works well. She gives me the probability of different results and is accurately and reliably. It is not my job to be worried that the electrons are doing when I'm not looking for them, since I know what they are doing when I watch them. That is why I pay. " He took his silence in a corner, turned to Alice and asked, "I learned everything I know about that monitors and measures?" "Well," she began, "to tell the truth, I am more confused than when I arrived here." "Okay," suddenly interrupted the quantum mechanics. "I thought. You've learned what you wanted. Come along and see some of the results of

quantum theory. Let me show you some of the attractions of the country of Quantum." Notes 1. The extent of the problem "is that the selection of a unique opportunity and the reduction of all other amplitudes is quite different from other quantum behavior and how that can happen is not obvious. The problem is contained in its simplest form, the question "how is it possible to measure anything?. The conventional view of quantum mechanics is that when there are multiple possibilities, a range for each scale and total system is obtained by the sum, or superposition of them all. For example, if several slits through which a particle can pass, the magnitude of the system contains a range for each opening, and there may be interference between the individual amplitudes. Without external influences , the amplitude change is so smooth and predictable. When you make a measurement on a system whose sum of amplitudes corresponding to different possible values of the measured quantity, the theory says you observe, with some probability, one or other of these values. Immediately after the measure, the value is a known quantity (because you just measure it) and then the sum of self-states (see box on page 85) is reduced to one, only for the actual value measured by you. The description of the measure in orthodox quantum mechanics has the disadvantage that the measurement procedure does not seem at all compatible with the rest of quantum theory. If quantum theory atomic theory is true, as seems to be, and if the world is made of atoms, then presumably the quantum theory should apply to the whole world and all things contained therein. This includes the instruments of measurement. When a quantum system can result in different values, its amplitude is the sum of states corresponding to each possible value. When a measuring instrument is itself a quantum system and there are several values that could be measured, he is not entitled to select only one. He should be in a state that was the sum of the amplitudes of all possible results that he could measure and no single observation could be made. The conclusion to be drawn is that: a) I never noticed anything of truth or b) The quantum theory is a bunch of bullshit. Neither of the two conclusions is sustainable (for the most tempting option (b) may appear). We know very well that we look at things, but we can not deny that quantum theory has been successful insuperability to describe all the observations, while no other alternative theory does so well. We can not abandon it lightly.

Alice followed the quantum mechanics along the way that out of school. While progress, the path would be extended gradually to become a flat road. "I think the most interesting thing you've shown me so far," said Alice, "was the way those obtained interference effects even when there was only one electron present. It is true then it makes no difference if we have only one electron or many ? "It is true that you can see the interference with one or more electrons. But that does not mean make difference. Some effects are only seen when you have many electrons. See the Pauli principle, for example ..." "I heard of him," interrupted Alice. "The electrons told him that I came here. Can you tell me what it is, please?" "It is a law that applies when you have a bunch of particles equal completely identical in all respects. If you want to know more about it, it is better to ask here, since we are close by. They are experts in the behavior of many particles together. " Mechanic's words made Alice look around and realize that, while going, they had reached a high wall of rock that accompanied one side of the road. Well ahead of them was a large gate. The doors were made of twisted iron and is opened between two huge columns of stone, each with a painted crest in the center. The right of the gate above the wall, Alice could see a panel of wood which read: Academy Fermi-Bose - For electrons and photons In the center of the gate was an imposing figure, a wide and very portly man who looked even more massive and heavy with academic gown and hat of bachelor he used. His face was round and stained adorned by a large mustache and sideburns. Firmly attached to one of his eyes had a monocle, which hung a long black ribbon. "This is the Principal Director, the Mechanical whispered in the ear of Alice, who was nearest him. "I mean the principle of Pauli", asked Alice excited. She had been surprised by his grip of sudden appearance. This is no problem for bosons, but for the férmions, which always have to reverse its scope, this is not allowed. For such particles is the principle of exclusion of Pauli, which states that two identical férmions can never be doing exactly the same thing. They are in different states. "See footnote 2 at the end of Chapter For bosons, as I said, this is not a problem. Their amplitudes do not have to change when two of them change places, so they may be in the state. In fact, they can go further: they not only can be in same as like to be in the same state. Normally, when there is a superposition of states and amounts to amplitude squared to obtain the probability of observing the individual states in the mixture are high and contribute separately to the square more or less the Similarly for the final probability. If there are two bosons in the state, when it brings two to four square is obtained. Both contributed to not twice, but with four times more. if three particles in the state, the contribution would be even larger. The probability is much greater when you have a large number of bosons in a state, so they tend to come all in the same state, if it is possible. This is the name given to the Bose condensation. "And this is the difference between bosons and férmions. Férmions are individualistic. Two of them never make the exact same thing, while bosons are sociable. I love walking in gangs, where each is behaving itself in a way that the other. As you will see later, is this behavior and this interaction

between the two types of particles that are broken that you are responsible for the nature of the world. In a way, you are the rulers of the world. " At that time, quantum mechanics took Alice out of the classroom. "There it is," he said. "This is the principle of Pauli. Férmions He says that two of the same type can never be doing the same thing, so you can only have one in each state. The principle applies to férmions of all types, but not bosons. This means, among other things, that the number of férmions should remain the same. Férmions not appear or disappear when they give the roof. " "I really think not!" Said Alice. "That would be ridiculous." "I do not know if it would be correct to say that, you know? Bosons appear and disappear. A number of them never stays the same. You could say that the number of férmions must be a defined number, if there is one and only one in each state, as that a specific number of occupied states requires the same number of férmions occupying them. The same idea does not apply to bosons, because you can have the bosons you want in any state. In practice, the number of bosons is never constant. "If you look through this window," he said suddenly, while going, "and see the difference between bosons and férmions." Alice looked through the window and saw that a group of electrons and photons was doing a test on the lawn of the Academy. The photons were going very well, and turning to one side to another in perfect sync, with no difference between any of them. The group of electrons, however, was behaving in a way that, of course, left the sergeant in charge of the test completely desperate. Some marched to the front, but at different speeds. Some marched to the left and right, or even backward. Other pulavam up and down, some planted a banana and was lying on the floor, staring at the sky. "He is in the fundamental level," said Mechanic, looking over the shoulder of Alice. "I believe that the other electrons want to join him in that state, but only one can take this state. Unless the spin of the other is in the opposite direction, of course - would be much difference between them. "The difference between bosons and férmions clear here. The photons are bosons and therefore easy for them to do the same thing. In fact, they like to do the same thing others are doing so well march together. The electrons, on the other hand, are férmions and the Pauli exclusion principle to prevent two of them do the same thing. They have to do different things from each other. " "You talk a lot of states where the electrons are," said Alice. "Could I explain what are these states?" "Again," he replied, "the best way you learn is to attend a school here. The Academy as world leaders, since it is the interaction of electrons and photons that governs the physical world for the most part. If they should be world leaders, of course we have to take lessons on how to govern. Come and see me. " He took Alice to a broad construction of one floor, the back of the Academy. By entering, he saw that Alice was a kind of workshop. Electrons was working on several benches. Alice approached to see a group that was too busy raising a fence around one of the benches. She could see that there were several structures on the bench and when the students moved about, all the structures changed. "What are they doing?" She said to his companion. "They are building the conditions for control to the states. The states are controlled largely by the limitations that surround. In general, what you can do is governed by what can not be done and the restrictions serve to define the possible states . Something similar to the notes that you can take advantage of a sound. An organ is composed of tubes whose length defines the notes to be drawn from each. Changing the length of a tube, it

also changes the notes that it leave. The quantum states are given by the amplitude or the wave function of the system may have, which is quite similar to the acoustic sound wave in a body. "As you discovered, it is usually impossible to say what an electron is doing, because watching him, you select a specific scale and reduce all amplitudes to that choice. The only occasion on which they can really be sure about its electron is when he has a single scale instead of an overlay, and when your comment can give only one value. In this case, the probability of achieving this value with its measure is 100 percent, and for any other value is the probability of 0 per cent - simply impossible. In making the comment you get the expected result. In this case, the reduction in amplitude to that observed by you does not make any difference because you was in that state. The state is not changed by their observation and this is called state. In this class, the electrons are building state. " Alice gave back the bench, looking at the states that the electrons were building. For her, seemed boxes, eight in all. There was a very large, a slightly smaller than the largest of all six pequenininhas and all more or less the same size. Passing through one of the corners of the bench she was surprised to see that the states had changed completely. Now seemed shelves and shelves of cake, on high pedestals. Two of them were much higher than the others, four had the same width but with pedestals successively larger than the previous, and two were small. She went quickly to the side following the bench. Now the area had become a board that was nailed to hanger covers. There were two rows of three hangers and other insulated hangers on top and bottom of the table. "My God, what are you going?" she asked the mechanic. "The states are different depending on the direction of where I look at them." "But of course," he replied. "You're seeing different representations of the states. The nature of a state depends on how you notes. The very existence of a state depends on a remark for which he always produces a result set, but a state can not give defined for all the comments you can do. For example, the relations of Heisenberg prevent you from seeing the position and momentum of an electron at the same time. Therefore, a state for an observation is no longer state to another. The observations used to describe the states are called its representation. A state describes the condition of a physical system. It is the basic concept of quantum theory - the best description that can have real world. In general, the amplitude of a state gives the probability of various possible results of any observation. For some states, there can be only one possible outcome for a particular measure. When a system is in such a state, any measurement of this quantity will make one and only one possible result. Repeated measures reach the same result every time. Hence the name state, or the frequently used German term eigenstate (self-state). "The nature of a state may be very different, depending on how you notes. In fact, even the identity of different states can change. The states seen in an office may not be the same in another representation. As you may have noticed, the only thing that should remain unchanged is the number of states. If you put an electron in each state, you must have the same number of states to sustain them, even if the individual states have changed. " "And quite vague to me," Alice called. "And as if it were impossible to know for sure what really is there." "Okay", responded the Mechanical happily. "I had noticed yet? Can speak with certainty of comments but what really is there to be seen is another story.

"Come with me. It is time for the night meeting of the Academy. You will find very interesting." The mechanic took her back to the main building, leading her across the room with a bow at the ceiling. The floor was completely filled with electrons, squeezed the maximum they could. At the top, a box surrounding the entire room and it Alice could see the vague and distant figure of a few electrons running for the exit. There was only a small space on the floor near the entrance where they had been, and an electron that came behind them went to occupy it and stopped immediately and prevented by the dense crowd that blocks any progress. See footnote 3 at the end of Chapter There are certain quantities that can not share the same state, position and momentum are two examples. If you have a self-state that gives a set value for the position of a particle, the measure of its momentum can result in any value. This leads us to the relations of the Heisenberg uncertainty. With a mixture of states corresponding to different values for position, for the measurement position may result in any of the appropriate values. The position became "uncertain", though now the dispersion of values of momentum can be reduced. This dispersion is not caused by poor techniques of measurement, it is inherent in the physical state. 0 undefined value of a physical quantity that can be inherent in a particular state, will allow effects such as penetration of barriers, the exchange of heavy particles inside the nuclei, photons in electric interactions and the existence of virtual particles in general. Trading of virtual particles and particles are discussed in Chapters 6 and 8. "Why is so full in here?", Alice asked, impressed by the scene before you. "This is the level of strength," replied one of the helpful electrons. "All the spaces are filled valence level because the level of valence electrons is always full. None of us can move because there are states free to go where we can." "This is horrible!" She said. "How will be able to walk the hall to get out that everything is so crowded?" "We can not," said the electron with a certain resignation satisfied. "But you can if you want. You can walk around at will, because there is no other room in Alice. This means that several states of Alice free to occupy you. You will have no problem with the Pauli Exclusion. " Despite finding it very strange, Alice began to force way through the crowd and realized compact, and when the wagon had tried to enter the crowded train station, which for some reason, she could move without any hindrance. Alice through the crowd of electrons toward a platform on the opposite side of the room. On he was the Director, always impressive in his dress and hat of BA. When approaching, Alice began to hear his soft voice echoing through the crowded hall. "I know you all had a busy day, but I need not remind you of the important role you play in the world and to which they must be prepared. You, electrons, each occupying its rightful state, form the substance of we know of. Some of you are related to atoms and have to work in its various levels, controlling all the details of chemical processes. Some of you may find its place in a crystalline solid. There are relatively free of any connection to any atom in particular and can move to where the Principle of Pauli and his colleagues allow electrons. It may be that you are to compose a banda driving where they can move freely and where their duties will be running from one side to another , carrying their electric charges as part of an electric current. Furthermore, it could end in a valence band in a solid. Perhaps you feel stuck there, where no member free entry for you. It is not discouraging.

Not all electron can be in states of higher energy and, remember, the lower states must also be met. " See note at end of Chapter 4 "Have you, the photons, are the leaders and agitators. Alone, the electrons remain complacently on their due status and nothing is ever done. It must interact with the electrons all the time and produce the transitions between the states, the changes that make things happen. " By this time the speech of the Director, Alice was brilliant account of the forms of photons running through the crowd of electrons and the occasional flashes from different parts of the room. She turned to see what was happening. It was difficult to see very far, because she was surrounded by many electrons. "Damn!" Alice could not avoid the comment when faced with all the pictures captive, trapped in fixed positions by the crowd that formed them. "Will no one way to move?" "Only if we are excited to a higher level," a voice replied. Alice could not see who had spoken. "But that does not matter," she thought with herself. "Since they are all the same, must have been the same ever spoke to me." At this time a flash appeared next, and Alice has a photon came running through the crowd and accept an electron in full. The electron was rising and reached the cabin, which he left in for the fired output port. Alice was paying much attention to the electron withdrawing than seen in other photon running in his direction. There was a flash and felt that she was floating. When you looked around, saw that was in the cabin, looking at the mass of electrons down there. "It must be that what you mean by the electron 'be excited to a higher level." I do not think that is so exciting, but at least much more room here. " She looked down the hall and could see flashes here and there, each followed by an electron that ran up to the cabin where, after landing, he or she ran at high speed to the output port. One landed in the cabin and close to where Alice was. She looked down and saw a small hole in the shape of an electron at the place where he was before levitate. Was visible and clear as the color of the floor contrasted strongly with the mass of compressed electrons which covered the entire surface of the room. Noting that space, she saw another electron Clever occupied the space that had just been created, although not able to move more away from where it was. In the place where that electron was, however, now had another hole that was once occupied by another electron which had recently arrived. "How curious!", Alice thought. "I used to see electrons, but not expecting to see the presence of any electron so clearly!" She noted with interest the movement throughout the cabin of the electron that had been raised to create the original hole was offset by the movement of the electron as a hole that gradually progressed toward the door through which she had entered. See footnote 5 in the final chapter. When both the electron and the hole was left of his field of vision, Alice walked over to the cabin door of exit. She thought it had heard enough of the speech of the Director. Through the small door, Alice was in a large hall. Waiting for it beside the door, was the quantum mechanics. "Like?" He asked. "I really enjoyed, thank you," she replied, with education. That thought was expected of her. "It was very interesting to see the director leading the assembly." "You say that," started the Mechanic, "but were the electrons that were leading, since all were excited by the level of driving. All electrons have an electric charge, as you know. So when we move, create an electric current. The charge that carry is negative, which means that the electrical current flow in the opposite direction to the movement of electrons, but it

is not so important. If all the states that an electron can reach is already full of electrons as the level of valence, there can be no motion and you end up with an electrical insulator. All the electrons and their cargo are stuck in their positions and therefore there can be no electric current. In this case, is only possible to obtain a current when the transfer of electrons to the level of conduct which have very empty space to move freely. So you get both a current produced by electrons in the holes they leave behind them. " "But how can a hole to create a chain?" Protested Alice. "A hole is something that is not there." "First, you agree that when the electrons are all in the lower level of strength they can not move and then there is this," said the Mechanic. "The current would be exactly the same as negatively charged electrons were not present. " "Yes," agreed Alice. It seemed quite reasonable. "So must admit that when an electron is the least, this looks like the one that occurs when there is less than any electron. The hole in the valence level acts as a positive charge. You saw the movement of the hole toward the door was caused by electrons that gave a step forward in the opposite direction. The electric current generated by negatively charged electrons away from the door is the same as that produced by a positive charge was driving to the door. Like I said, the photons produce a stream of electrons both from the band that put on the driving holes they leave behind. " "The photons seem to be a huge nuisance to the electrons," said Alice, wanting to change the subject now. " "Well, they certainly are hyperactive, but at the same time are naturally bright. It's like the director says:" Particles are always particles! " Today some of them should be stimulating electrons in housing. " "Excuse me," said Alice, but you do not mean thereby?. I am confident that this was the word that I heard being used to describe trotes of students. " "It is causing or stimulating. Come and see." They kept the corridor until you reach a door. The mechanic opened it and entered, and the Alice followed. They were long in a room with bunk beds lined up along the walls. Alice saw that many of the top of the bunk beds were occupied by electrons, but the low was empty, mostly. "Sometimes it is easier to see them on top of beds than in low," said the Mechanic. "This is called inversion of population. Only when they are so that the laser stimulation can occur." It did not take long and a photon came running into the room. He went to one of the bunks and crashed with one of the electrons that occupied a high position. With a thud, the electron was launched for the low bed and Alice is amazed to see that there were now two photons at the room. They have fun with such synchronicity that seemed to be one. "This is an example of stimulated emission," muttered the mechanisms within the ear of Alice. "The photon has made the electron makes a transition to a lower level and the other photon has energy released. See now as the laser stimulation." The two photons ran from one extreme to the other room. One collided with an electron and then there were three photons and one electron in the lower level. Alice saw the photons interacting with more electrons, producing even more photons. Time or another it was shocking by a photon with an electron that was already in bed from a low of berths. When that happened, the electron fired from up to bed and photon disappeared but, as from the beginning there were very few electrons in the beds of down, a fact that was not very frequent. See footnote 6 in the final chapter. The room was soon taken by a horde of identical photons, all running from one side to another in perfect sync. There were now many electrons in

beds of low as the one above, which was that the probability of an electron is excited to a higher position, with the loss of one of the photons, they were the same for a possible downgrade, with the creation a new photon. The flow of photons inside the door at the end of the bed and walked the corridor aligned and attached to a light beam current. Before you reach the middle of the corridor, the photons are shocked with the large and heavy body of the Director, who walked toward them. He stopped immediately, making his presence felt full, and opened the flaps of her gown, one for each side, showing his body and dense black and completely blocking the corridor. The photons hit the dark material such as ink and disappeared completely. The Director was a moment where it was, cognate heat and wipe the sweat from his face stained with a handkerchief. "I will not tolerate this behavior," bufou. "We have warned that any photon to act in this manner will be immediately absorbed. It is hot work but because the energy released has to go somewhere, and usually ends up, transformed into heat." "Excuse me," said Alice. "Could you tell me where were all those photons? "There were anywhere, my face. He was absorbed. There are no more." "Damn, that tragedy," exclaimed Alice, feeling sorry for the poor photons that disappeared so abruptly. "None, none. It is part of the life of a particle not retained. The photons are well. Easy come, easy go. They are always being created and destroyed;. It's nothing serious." "I bet that for a photon, must be," replied Alice. "I would not so sure that. I do not think that makes much difference to the time a photon is that it exists for us. They travel at the speed of light because, after all, they are light. For anything that is moving at that speed, The time for, actually. Thus, although the time seems long survived to us, for them no time elapsed. The whole history of the universe would a flash for a photon. I suppose that is the reason that they are never bored. "As I said in the meeting, the photons have very important roles to play Exciting electrons, making them move from one state to another, and creating the interactions that give rise to the states, after all. For this, they must be created and destroyed all the time. It is part of its function, we could say. Create interactions, however, is more a function of virtual photons. not deal much with them here. If you are interested in the states and goes from one to the otherwise, you should visit the broker of states. Your friend here will show you the way there. "

The Director followed up to the gates of the Academy. Walking down the road, Alice turned and waved to the Director, he held firmly the space between the gates in the same place where she had seen first. Notes 1. If you have many particles, you have some kind of amplitude of each and a total amplitude to describe the whole system of particles. If the particles are all different from each other, you know (or can know) the state in which each one is. The total amplitude is just the product of amplitudes for each particle separately. If the particles are identical to each other, things get a little more complicated. Electrons (or photons) are completely identical. There is no way to distinguish one from another. If you saw one, saw all. If exchange between two electrons occupying the states themselves, not be seeing that this happened. The total amplitude is, as always, a mixture of all the

amplitudes indistinguishable, which now include all the permutations in which particles have switched states. The exchange of states between two identical particles does not make any difference with respect to the observation, which means that it makes no difference as to the distribution of probabilities, which is obtained by multiplying the amplitude by itself. This could also mean that the amplitude does not change, or it could mean that the amplitude changes sign, passing, for example, from positive to negative. It's like multiplying by the magnitude-1. When multiplied by the scale itself to obtain the amplitude of probability, this factor-1 is multiplied by itself, resulting in the factor +1, which does not produce any change in probability. The move appears to signal an academic detail, but has surprising consequences. 2. There is no obvious reason for a change of signal amplitude must not only be shown because it is impossible, but Nature seems to follow the rule that anything not prohibited is compulsory and must happen in all its possibilities. There are particles in which the amplitude changes sign when two of them are exchanged. They are called férmions, whose electrons are an example. There are also particles whose amplitudes do not change when they are never exchanged. Are bosons, and photons are of this type. Is that really matters is the signal of an amplitude for a system of particles or changes does not change when two particles change their states between them? Surprisingly, it. And very important. You can not have two férmions in the state. If two bosons are in the same state and you do with that exchange of place between them, does not really make any difference, you may not change the sign. These ranges are not allowed to férmions. This is an example of the Pauli principle, which says that two férmions can never be in the same state. Férmions are individualistic ends; two of them never fully harmonize. The Principle of Pauli is very important and vital to the existence of atoms and matter as we know it. Bosons do not obey the Pauli Principle of - quite the opposite, actually. If each particle is in a different state and you raise the total amplitude squared calculai a paw paw the probability distribution of particles, each contribute an equal amount to the total probability. If two particles are in the same state and you raise it to the square, you get four times a contribution of only two particles. Each contributes proportionately more, so that two particles in the state is a situation more likely than each come in different states. Three or four particles in the state is a situation even more likely, and so on. This increased likelihood of having many bosons in the state gives rise to the phenomenon of condensation of bosons: the bosons like to be together in the same state. They are easily led and inherently Gregarious. The condensation of bosons is seen, for example, in the operation of a laser beam. 3. Electrical forces involving electrons may operate to hold atoms together, as discussed in Chapter 7, but do not give rise to any force of repulsion that can separate the atoms. Why then the atoms maintain a reasonably uniform distance between them? Why are not the solid comprimíveis? That atoms can not be pushed one into the other, causing a block of lead as an object is too heavy for atomic size? Again, it is a consequence of the Pauli principle, which says that two electrons can not be in the same state. Because the atoms of a given type are all equal, each has the same range of states. But that does not equal the electrons of each atom in the state? And that is not prohibited? Indeed, the atoms are in different positions and therefore the states are slightly different. If you could superimpose the atoms, then the states would be the same, and the Pauli principle forbids that.

The atoms are kept apart by what is called the Fermi pressure, which is indeed a strong rejection of electrons from an atom to be the same as your neighbor. The matter is incomprimível because of the extreme individualism of electrons. 4. In a solid, the electronic states of individual atoms combine to form a large number of electronic states belonging to the solid as a whole. These states are grouped into bands of energy within which the energy levels of the states are so close they are almost continuous. In correspondence with the separations, higher, levels of energy in individual atoms, there are breaks in the bands of energy in the solid. The lower bands are filled with electrons from the lowest levels of the atom. The highest of these bands filled with electrons is called the valence band, and above it, separated by an interval of band that does not contain any state, is another band: the band driving. This band is completely empty or, or, at most, partially filled. In the valence band electrons can not move. Any movement of electrons requires that they change from one state to another, but there are no empty states for which they can go. When an electrical potential is imposed on some substance, it applies a force on the electrons of the valence band, but they can not move. If no electrons in the conduction band of the substance act as electrical insulation. 5. If given enough energy for an electron in a full valence band, or by collision with a photon or by an occasional concentration of thermal energy, the electron can overcome the gap between the bands and penetrate the conduction band. Because there are enough empty states in band, the electron can move at will, and would conduct an electric potential. Moreover, there would be a vacant space in the level of valence, where the electron was. Another electron could occupy this hole, and so on. An area would be opened in the valence band, which was full before, and he moved in the opposite direction to the movement of electrons. This hole or empty space, it behaves like a particle with positive charge. This is the description of the behavior of semiconductor materials such as silicon, widely used in electronics. The electrical current is carried by both the level of conduction electrons as holes in the valence level. 6. When a photon with certain energy interacts with an electron in an atom, it can produce a transition from one energy level to another, as described in Chapter 6. In most cases, the transition will be a lower energy level to a higher, since usually the lower levels are all filled. The photon is also capable of producing a transition from a higher to a lower, if it is empty. If, by chance, a substance has many electrons in a high and a lower level is mostly empty (a condition known as inversion of the population), a photon can then do with that one electron is transferred from a more high to a lower. This change releases energy and creates a new photon, besides that which caused the transfer. This photon can, in turn, induce more electrons to move to lower levels. In a laser, the light produced is reflected from one side to another by mirrors placed at the ends of a cavity, producing more emissions of photons in each time through the substance. A little of that light escapes through the mirrors, which are not perfect reflectors, producing an intense beam of light and narrow: the laser light. Because the photons are emitted in direct response to the photons already present, the light is all "in the bar, or on stage, and has unique properties to produce interference effects on a large scale, as seen in holograms. (Not all laser hologram needs, but it helps.)

3 The quantum mechanics led Alice down the road until an iron gate that guarded the entrance of a beautiful park, where they entered. Beautiful beds with an incredible variety of flowers, lined on both sides of the road, produced a nice effect while Alice and her companion passed under a summer sun that shines strong, spreading its light on the idyllic scene. Along the way, colorful butterflies passing through flashy buttons and a small bubble on a stream bed of round pebbles, which here and there the way water is poured into a miniature waterfall. Alice found it very nice and was delighted to watch his back when he saw someone approaching on the road. The newcomer was clearly another girl, but there was something strange in it. Somehow, she seemed the very Alice, but was more similar to the figures that Alice had seen the negative of your photos. Alice thought she had seen antielétrons of the Bank. To her surprise she noticed that although the girl is coming to them, she was looking in the opposite direction and walk back. Alice was so absorbed by the remarkable similarity of this strange girl who did not assess the speed with which the two were approaching. Before you give, they collided. Appeared a gleam cegante that has no meaning. Back to you, she surprised herself by walking a path where he had been another girl. Looking back, she saw the girl-reversed away, even going back in the path where the original had been Alice. Now, however, she was accompanied by another figure that walking in negative amicably back to his side. This second figure seemed his former companion, the quantum mechanics. Looking around, Alice was surprised to find that the landscape has also changed dramatically. Everything seemed to be reversed. In the sky, the sun shone dark, suckin the light of the scene below. Along the way, butterflies colorless passed through dark buttons and a small brook ran unlike on a bed of round pebbles, here and there where the water course rose to the top of a waterfall in miniature. Alice had never seen anything like it. She was so fascinated by the incredible scene that again saw a girl not reversed fast approaching. Alice turned and the time when the two collided, producing another flash cegante. When recovered, Alice saw that the girl was moving on the path from where it had come. Realized that the landscape was back to normal. "More and more curious," said Alice to herself. "The first collision was with which everything is reversed, while the second put everything back to normal. I have no idea how this could happen. How could my shove with that girl, for it has been more violent, have affected the stream and the sun? makes no sense. " Alice continued discussing with herself the meaning of that last experience. Had been so impressive that she barely paid attention when he heard a bang and saw the turn, then, a very energetic photon run through it. She had not yet reached any satisfactory explanation for his experience as the way out of the park led to a broad plain. There was nothing in it, unless a large commercial building, whose entrance, a little ahead, was turned towards Alice. When approaching, she saw that there was a poster in front of the building, right in the middle of the facade, a bit above your head. On one hand, the poster said "of the broker and the other," Virtual Affiliated to the Association. " In front of the building had a door and a small window, full of warnings. Real REDUCTIONS IN SETTLEMENT OF AMPLITUDE Great Features Periodicals

Properties located in coveted bands of Energy Attractive prices for immediate transition As Alice did not see anyone outside, opened the door and entered. Behind the door had a small desk, and behind him, a large hall, empty except for rows of shelves that stood in the midst of the shadows in the distance. In the center of the room, if only by a single individual sitting behind a desk, talking on the phone. To see Alice, he got up and came running. He put his hands on the counter and opened a smile full of teeth, a very sincere way. "Between, between," he said, ignoring the fact that Alice had already entered. "What can I have the pleasure to show you? Maybe you planning to move to its first state? I'm sure that I can offer you any satisfaction." "To tell the truth," began Alice, resisting the temptation to lie, I am not looking for anything. I said you could tell me something about how electrons and other particles move between states. " "You come to the right place. For a long time that we established in the business of transition of particles. If you come with me to one of our rentals, try to clarify the situation to your complete satisfaction." Alice thought about that he explain something. Passed across the counter and followed the man to a series of shelves, or whatever they were. Or were too far and were too great, or maybe she and the broker to shrink when approached. As it was, she saw that he was now approaching, they appeared as a large block of buildings. There was a poster that said: Mansions Periodicals The shelves were well open in front and Alice could see the electrons are moving at each level. "There is a good example of the states of quality built in levels of energy well spaced. Each is occupied by the allowed number of electrons, to the highest occupied level. Above it there are several vacant states, but currently there is no room for more electrons at the lower levels. When an electron is a former tenant there is, of course, room for another electron. Normally, if anyone meddles, the electron does not have any inclination to leave a state since the occupation. But if we wait a bit, may be forced to see a movement. " Alice waited, looked at the building, and soon after, saw a photon enters at the front door. There was a restlessness and an electron in the lowest level rose and disappeared from view. Alice looked around to see where the photon was coming. Parked near the building had a small truck with the following words painted on the side: CHANGES Fóton We do all the work of Transition "What luck," exclaimed the content of the broker. "A photon has donated their energy to an electron to the lower level and the excited states led to a vacant from upstairs. There is always a change that occurs at the fundamental. This creates a wave and attractive. I must take action immediately." He ran out and returned soon after with a poster that he preached a stake in the ground fincas. The poster said: PROPERTY VAGA! - Great State in Primary Mal had he put the poster in place, and one of the electrons in the second level has a cry and fell to the floor from below. Once there, he is quiet and continued as if nothing wrong had happened. When he fell, Alice has a photon running out. Because the electron had not fallen much, the energy contained in the photon is much smaller than that in the photon that hit the first electron.

The broker of the sighed, took a brush that had brought the bucket with the sign, began to cover the words "Primary" and write "Second Tier" in place. The ink had barely dried when Alice heard another squeal. An electron of the third level had fallen to the vacant space of the second. The broker of the curse and changed the poster again writing "Third Level". Threw the brush into the bucket and looked at the building. Another squall. An electron from the top of the building had fallen to the third level. The broker of the cutting off of the poster, threw him down and began to trample it. See footnote 1 at the end of the chapter. "Excuse me," said Alice, hesitating to stop this show of emotion. "You had said that the electrons remain in their states indefinitely if left alone, but these seem to have fallen spontaneously." "So it may seem," said the broker, is pleased to entertain some of your momentary attack of nerves. "In fact, all the transitions of electrons were stimulated by photons, but you do not understand because they are virtual photons. Virtual photons have a very important role in all interactions of electrons. They not only cause these seemingly spontaneous transitions between states but also help to create the states. The same particles that have one electron in its steady state are also those that force the electron to leave him. "Before I will talk about virtual particles, we take a look into normal particles, those that are not virtual. They are commonly known as real particles. What distinguishes it is that there is a close relationship between their masses and individual energy and momentum that may be. This is what that warning. " The broker pointed to a small sticker, printed in phosphorescent green paper, which had been placed at the entrance of the building. Was written: Real particles do everything in Layer Mass "I can see that everyone likes a lot of posters here," Alice thought with itself. "That sounds quite suggestive, but I must admit I do not understand what he says." "A layer of pasta," said the broker, as if responding to his thoughts, "is the region where energy and momentum are related to a specific need for real particles. It is the path straight and narrow particle tracks by conventional and inflexible. "If you want to have force in the community and can move things around here, you must be able to transfer momentum. If you want something to move the place where you, or you want to prevent something away, you must transfer momentum. In either case, you are dealing with motion and movement means momentum. It matters little if you want to start a movement or impede movement. These are the changes in momentum objects that deviate from their paths and make things change. And also, is the control of the momentum that makes particles take a certain path. Electrons can be stimulated by photons to make transitions in either direction, causing stimulated absorption or stimulated emission. Electrons have been excited to higher energy levels just dropped to a lower state, if any available, even if apparently no photons present. The so called spontaneous decay. The Quantum Mechanics says that any transition is caused by something, they do not happen without any reason. The apparently spontaneous falls are actually caused by photons, but not real photons. They are stimulated by virtual photons: quantum fluctuations of vacuum. Around all electrical charge is a cloud of virtual photons, which interact with other charged particles creates an electric field. By

assembling the electric field, these virtual photons are always present in an atom and can produce seemingly spontaneous falls of electronic states. "In the layer of pasta, you can not have momentum without the kinetic energy of the body you have. A particle with high mass, which has already invested much energy in your body at rest, does not need much additional kinetic energy to it provide a certain amount of momentum as a particle would need more light. All real particle must have a certain amount of energy if they want to have momentum. This applies even to the photons, which have no mass at rest. " The broker put his hand in his pocket and took a bunch of documents. "The conditions are quite specific. If the particles obey the real, are free, free of any debt energy. They can move as you want, how you want. They are free to come and go. You should have seen the rule 'What does not is prohibited is compulsory. " "I saw, yes," replied Alice, anxious to show their knowledge. "It was the Bank Heisenberg, the manager told me about momentum e. .." "There is another rule," continued the excited broker, without even stopping to hear the answer to Alice, "which says: 'What is forbidden to be done quickly." This is the rule followed by the virtual particles. They are not discussed in polite society and classic, but have a very important role for the world. The virtual particles are behaving in a way that the classical laws they not be allowed. " "How can this be?" Alice asked, somewhat naively. "Certainly, if something is forbidden, no particle can do it." The broker heard and answered: "They are the quantum fluctuations that allow that to happen," he said. "If the Bank has been, will remember that the particles may require energy loaned for a short time. The more energy, less time, of course. You've heard the expression: 'The difficult we do now, the impossible takes a little longer. " Well, in quantum mechanics not the impossible takes a little longer, but lasts a bit less. Virtual particles can enjoy all the benefits of energy that do not have, for a short period of free experimentation. This includes being able to transfer momentum. " "Must be a very short period," said Alice, pensive. "And it is. But it is free. So all want. You'll have a better appreciation of where the virtual particle has seen." "But I can not see them," demanded Alice. "The question is this." "You can not see them now," the broker replied sharply, "but will put my helmet when virtual reality." He started walking quickly toward where Alice had been twisted and that he had not offended. Was relieved to see him back, carrying a helmet that seemed highly technological. Had a transparent display that covered the entire front, and a long wire that was attached to a plug in the back. The wire run all the way from where they had come to disappear from view. In quantum theory, the concept of a particle is not as precise as in classical physics. Charged particles and energy transfer in a "quantized" in discrete packages. In many cases, they have defined mass, which distinguishes them clearly from other particles and allows them to carry specific amounts of other quantities such as electric charge. Photons have zero rest mass (which is also a set amount). Real particles, those with long duration of existence, have strict relations between the values of mass, energy and momentum. Where the particles are created and destroyed and have an ephemeral existence, they do not comply with such strict rules, and quantum fluctuations in its energy can be large. This is especially true for those particles that are exchanged to promote interaction between other particles. All the energy of such particles is a quantum fluctuation. They are literally

created from nothing. The vacuum is not an absolute vacuum, but rather a structure of such a dazzling short-lived particles. "Here," he said, triumphant, "a marvel of modern technology. Just ask and you will see the world of virtual particles." Alice was a little nervous looking at the helmet. It was great and seemed quite complicated and even, she thought, a little sinister. But since it would reveal the world of virtual particles that either she had heard, that there was no try. She put the helmet on your head. Was very heavy. The broker moved into something and made some adjustments on the side of the helmet, where she could not see. The view through the viewfinder was blurry dots with bright e. .. When your vision clear, everything had changed dramatically. Alice also via the electrons in its various levels, but now, rather than appear to be inside a tall building, the way it positioned in a network of lines that connected an electron to another, as if they were flies trapped in the bright wire a giant spider web. Looking more closely to the wire, she realized that they were made of photons, but photons very different from those she had seen at the Academy. All photons that she had known until then moved with great speed, but at least moved normally. They began in a somewhat later and were in a new position. Even if those positions were not well defined, in the range between one and another, the photons passed by all points intermediaries. Alice never thought it would be possible to travel in some other way, but some of these virtual photons seemed to do exactly that. Looking at them, Alice was very hard to tell in which direction they were going, or even whether they were really moving the normal way. One particular thread of the web, representing the behavior of a photon, seemed the same time the positions of the two electrons it interconnected, without apparently being normal way of moving from one side to another. That link disappeared, while others appeared in other places of the great web of photons which linked the electric charges of all electrons. It was a beautiful and unusual sight. The virtual photons are moving in every possible way, while a few photons appeared to have mastered the art of travel from one point to another without really need to pass the time between the two events. Alice looked concerned as the strange scene, she began to hear a noise in the helmet near his ear, which was immediately followed by a "click". The vision that she had to go wobbly again and have the mundane aspect that was before she put the helmet. Alice claimed that table top by losing fascinating. "Excuse me," said the broker. "Unfortunately there is a mechanism built into the mechanism of time. My idea was making it work with coins." In quantum theory, particles exhibit properties classically associated with continuous waves. In parallel, the fields of force are composed of classical particles. The electrical interaction between two charged particles is caused by any exchange of photons between them. These photons have a short existence, which means they are well located in time and therefore their energy is indefinite. Are virtual particles, whose energy and momentum may float away from values that would be normal for a particle of long duration. Alice was still too impressed by the vision to give some attention to the broker and attempted to apologize to describe what he had seen. As all people know that Alice had strange world, he began immediately to give a lengthy explanation.

"This is just another example of how a virtual particle is a particle normal things that can not do. It's a bit like the penetration of barriers. I think you should have already seen a case of penetration of barriers." "I said yes," replied Alice, with care. "I saw someone crossing a door so I came here and told me he could do this because its wave function to spread into and through the door, creating a small probability that it is observed on the other side." "It's true. This part of the wave function of allowed his friend penetralia a barrier that would have held a classical particle." He had enough energy to cross the barrier. Therefore, crossing the door he was a kind of virtual condition. A few particles, if there was one, which is entirely real. Almost all have some things online, though some are more virtual than others. The photons of exchange that you were watching is almost entirely virtual. "The rule says that virtual particles do not obey the rules but still can not escape them for long. That means they can do things for which they have not enough power. These virtual particles exchanged, as the photons that you see , produce interactions between other particles. They can penetrate through the barriers that hold a classical particle, and that includes the barrier of time. They move on a type-space, while particles can only be realtime type. This means that despite a real particle can remain in the same position as time passes, she is unable to remain at the same time as its position changes. A virtual particle can do both. It can move sideways in time, if they choose. " "Very curious," said Alice. "I am not surprised to know that real particles can not do that and move only in the past toward the future." See footnote 2 at the end of Chapter "Actually, not quite," said the broker, as an excuse. "Certainly it is true that the majority of particles moving in time, as you thought. Most of the particles, however, it is a little virtual occasionally, during a collision, for example. This means that a real particle is capable to change. At a time is moving forward in time, so obedient and respectful. In another, discovers that it reversed its path and is moving backward, toward the past. It may be surprising, but is allowed that a real particle to behave this way. " "Oh," cried Alice, scaring the broker, which continued with its careful description. "I think that is what happened to me earlier. I could not imagine what would have been with me when I was walking by the park and saw everything around me was reversed, but now I know that was not the stream or the butterflies that were going back was that I was going back in time! " Alice said to his companion managed to remember everything about what happened and he agreed with the interpretation of it. "Certainly I think a typical case of antiparticle production," he said. "Antiparticle", exclaimed Alice. "I did not know it had to do with antiparticle. I remember having seen them in the Bank Heisenberg, but do not understand what they may have to do with what happened here." "I would say that obviously," said the broker, even though Alice does not find anything obvious. "You do not see that when a particle moving backward in time, it appears to the observer as something completely opposite, advancing in time the normal way. See the case of the electron, for example. He has a negative charge. When you move the past to the future, the normal way, he takes this negative charge in the future. Moreover, when it moves the future to the past, it leads to negative charge of the future to the past, which is a positive charge moving the past to the future. In any event, it is making the general cargo of more positive future. To the observer, is as a positron, or antielétron.

"What happened to you would like for the rest of the world as a photon unusual high-energy releasing their energy to create an anti-Alice and Alice. The anti-Alice move up a clash with Alice and the two are annihilated to each other, converting their energy into photons again. " "How can this be?" Alice said amazed. "I see this as anti-Alice Alice could find another with whom conflict. There is only one of me and I certainly was not annihilated," she concluded, challenging. "But what I described is what seems to the rest of the world. For you, what would happen is totally different. For you, the annihilation was before the creation, of course." "I see nothing to clear it," said Alice sharply. "How is that anything can be destroyed before being created?" "This is the natural order of things when you're back in time. Typically, when moving in time, is expected to come before creation of the destruction, is not it?" "Of course it is," replied Alice. "In this case, if you're going back in time, you naturally expect that the creation comes after destruction. Ultimately, you are living the events in reverse order. I hope you understand it myself. "You were walking quietly to the side of quantum mechanics when suddenly collided with the anti-Alice. In view of his companion, you and Alice were both anti-destroyed its mass and energy was carried by photons but highly energized." "My God! Poor Mechanic," exclaimed Alice. "He must be thinking that I was destroyed, then! How can I find him to reassure him? "I do not get too excited about it," said the broker, quieting her. "Certainly the mechanic knows the annihilation of antiparticle and know that you just came back in time. Without doubt, he is waiting to touch you at any time, sooner or later, depending on how you went back. Anyway, the process you become of annihilation in anti-Alice and you traveled to the past to be created, along with Alice, a photon of high energy. This is what an observer would have seen. The impression you have is that they stopped back in time and again move forward, usually. You would not have seen the photon that caused it. I could not see, because it no longer exists at the moment when you reversed its crossing by the time. So far as Alice and as anti - Alice, you were in a future that never reached the photon. "You see now that, although any observer say that for some time there were three of you, two and one anti-Alice Alice, they all actually you. You have gone back in time, was living the same period in which it had been when walking with quantum mechanics. When you return to the normal process of creating peers, you lived the same period for the third time, again advancing in time. "That was part of his life as a zigzag road in the slope of a mountain, rising to the east and making a sharp curve to the west before rising again to the east again. If you go up the hill toward the north, you might think that crossed three different roads, when in fact three times through the same road. It is more or less what happens to the production of antiparticle. The antiparticle is the road that goes to the other side. " At this time the helmet started to make noise again and a green light lit in the corner of the display. "I think the helmet is sufficiently loaded for another demonstration," said the broker. "If you pay attention this time will be able to see the effects of second order." He adjusted his helmet and once again became blurred vision of Alice ... The image became clear again and revealed that the landscape was all united by a network of lines of photons that permeated everything. When Alice looked carefully for a region, she could see that some of the links were

interrupted bright. In the middle of a shoe-shining photons she saw a guy back, where the photon in the middle of the road, turns into something that she recognized as an electron and a positron, a antielétron. The two joined up again, almost immediately, to form a cordon of photon that would bind to an electron of truth. Looking more closely, he saw another photon Alice timidly out of the electron, in which the cord was around. Near the path of that photon, she saw the faint outline of another round electron-positron. That photons emerged further back and deleted if it looked good even up close, she could see little laps set of electrons and pósitrons. See how far it was possible to distinguish photons that create rounds of closed pósitrons and electrons and electrons or pósitrons emitting photons that create more electron-positron pairs. And it continued in a seemingly infinite variety, but everything was becoming less defined at each stage of complexity. Alice was getting dizzy from trying to force the eyes to see the end of that sequence. Finally, an order is submitted. She heard the wheezing and "click" of the helmet, and it disappeared from his face. "I thought you had said that the electrons are joined by an exchange of photons," she said in an accusing tone. "I'm sure you saw electrons in the middle of virtual particles. Many of them, actually." "Certainly. The real original electrons act as the sources of electric field, although it is more correct to say that electric charges are charged by electrons that produce the field. The photons do not care about anything besides the electric charge, but where they there is a load of them, there will always be a cloud of virtual photons around. If another particle laden approaching, these photons are available to be exchanged and produce a force between two particles. exchangeable particles should be created to be exchanged and destroyed then, when caught. Their number is obviously not constant. Therefore, they must be bosons. "The relationship between photons and loads of works two ways. As particulate laden produce photons, photons would like to create particles with charge, but not only can produce a charged particle, because the total electric charge can not be changed. Then we have a rule, and that does not allow uncertainties. What photons can, however, is to produce an electron and a antielétron or positron at the same time. It has a negative charge and the other, positive, the total load in the universe not was changed. Is that what you saw. The virtual photons produce pairs of electrons and virtual pósitrons, which cancel each other and return to be a photon. During the short life of the two, however, since both particles are loaded, they can create more photons, which can in turn produce more pairs of electrons and pósitrons, and so on. "Damn," said Alice. "It seems very complicated. Where does it all end?" Not only photons can be created, but particles as electrons, which must be produced in the company of its antiparticle to no change in the total electric charge. It takes energy to create the rest mass of two particles as such, but the energy required may be available for a brief period as a fluctuation of energy. This fluctuation can occur even if no energy to this principle, and the particles can be created literally from nothing. "Empty space" is actually a seething broth of particle-antiparticle pairs. "It ends. Keep it up forever and gets more complicated. But the probability of a photon producing an electron or a photon producing an electron-positron pair is very small. This means that the more complex amplitudes are weaker, is sometimes too weak to be seen. You should have seen it. "

The head of Alice gave laps while trying to understand what she had seen and heard. "I can only say that I have never seen anything like it before." "It's quite possible you've seen, yes," replied the broker. "What you see is only the Nothing anywhere. But I am surprised to hear that you had seen nothing before coming here." "I would not say so," replied Alice outraged. "I can not be traveled, but I know some things. Do not forget that." "No doubt that is even," said the broker. "I am sure that you came from a very pleasant, but it is relatively easy to see something. Hard to see it is nothing. I do not know how you could see nothing without the help of my helmet for virtual reality." "One moment," interrupted Alice, who had begun to suspect that something was up. "Maybe you could tell me what you mean by 'nothing'?" "Certainly. I mean nothing: the complete absence of any real particle. You know: the vacuum, the vacuum, where all things are forgotten ... there is the name you give it." Alice was wonder with the concept of negative. "And this is different with the use of his helmet, I thought it seemed nothing with nothing, no matter how you look." "Of course it is. The vacuum can not be the best neighborhood, but there are many activities secret. Come I show you." The broker started walking with a step and accelerated the following Alice through his office. It was increasingly difficult for her to believe they were still within an office or a building, because everything seemed very large. Walked for some time with Alice fighting with the weight of the helmet and the cable, that would be stretching behind her. "I hope this thread is very long," she said to herself. "I am sure that once I reach the end of it." The periodic Mansions, where Alice had observed the states of electrons, were soon left behind, and they still continued to walk. Just as Alice was about to beg for a stop to rest, she saw in front of you one thing that seemed a lake or the beach of a sea very calm. When they came near, she could see it was a very large lake, that is, if even a lake. He extended to disappear from sight, a seemingly limitless expansion. But if it were a sea, the sea would be more strange that she had seen. Everything was very calm, not to be completely stopped by a tremor very subtle, almost imperceptible, near the surface. It was not blue, or green, or color of wine or any other color that Alice had heard used to describe water. Was completely without color. It was like a night light, open skies, but without the stars. "What's that?" Muttered Alice, thunderstruck by the vacuum that way and that seemed to eat the eyes. "Nothing," replied the broker. "This is nothing. It is the Vacuum! "Come on," he continued. "Let me call your helmet, and you can see the activity inside the vacuum." He extended his hand toward the helmet and repeated what was done before. The vision of Alice, his vision of Nothing, was diffuse e. .. His clear vision and showed a scene very similar to last it through the turns helmet. Again she saw a brilliant web of wires. This time, however, the wires not finished in real electrons, which before seemed to be trapped in the network, but which were actually their own source. Now there was no real particles present, only the virtual. Create pairs of photons and electrons pósitrons. Pósitrons produce more electrons and photons, as she had seen before. The network, first, documents are the actual electrons, which were its source and its anchor in the world of real particles. Where was the source now? The pairs of electrons and pósitrons were produced by photons, the photons were produced by pairs of electrons and pósitrons, which were

produced by photons. Alice tried to browse the rows of particles back to the front to see if could find the source, but realized it was going in circles. She felt that should have lost the thread of the skein and was trying to follow the lines more carefully, when he heard the familiar noise and "click" of the helmet, and the whole scene disappeared. Alice again explained to the broker that he had seen and said that this time she had been unable to decide which other particles created particles. "I'm not surprised," said the broker. "They create one another. It's like the story of the egg and the chicken. All are born and putting eggs at the same time." "And how is that possible?", Asked Alice. "There must be a source. They can not come from nothing." "It may come as" was the answer. "The only thing that prevents the production of particle and antiparticle is usually the need to provide energy to the rest masses of particles and virtual particles are not inhibited by it. And all one big quantum fluctuation." "And the truth, then?", Asked Alice. "All these particles are even there?" "They are, yes, and they are very real, even if not in the technical sense of real particles. They are a part of the world as vital as any other. I think you've seen the helmet everything that needed to know," he said, taking the helmet of the head of Alice. "We will not need it now. I will trigger the mechanism of retraction of the cable." He pressed a button and the helmet began to wrap cable and was pulled by him, rolling in the direction from which Alice and the broker had been, like a mechanical spider, to disappear from view. Even after the helmet has disappeared, the head of Alice was filled with beautiful scenes that she had seen, which rake in silence as she walked beside the broker of states along the beach in infinite vacuum. Notes 1. Inside atoms, the states allowed for the electrons have very spaced energy levels, and only those levels that the electrons can occupy. An electron can only transfer from one state to another if (empty) and by doing so, its energy has changed from a given quantity, the difference in energy between the two states. An atom in its normal state, or fundamental, have their lower levels of energy uniformly filled with electrons, but higher levels are usually empty. When an electron is excited out of its original position, it stops in one of these higher levels empty or abandoned entirely the atom. An electron has been excited to a higher level may fall back to a lower energy level if there is empty space available. When the electron is transferred to a lower energy level, he must get rid of surplus energy, and emitting a photon does this. And so that the atoms emit light. Because all the electrons occupy states defined within the atom, a photon that is emitted may have an amount of energy equal to the difference between the energy contained in the initial and final states of the electron. This opens a wide range of possibilities, but still imposes a restriction on the energy that a photon can have. The energy of the photon is proportional to the frequency and hence its color. Therefore, the spectrum of light produced by an atom consists of a set of "lines" of specific frequencies. The spectrum of a given type of atom is always characteristic of him. The classic has no physical explanation for these spectra. 2. Virtual particles have a vagueness, both in time and in energy. This inaccuracy appears as fluctuations in energy, where the particles are behaving as if they had more (or less) power than should. Another manifestation it appears as an uncertainty in time. In a quantum system, the

particles seem to be able to be in two places at once (or at least have amplitudes that are). The particles can even reverse time. The physicist Richard Feynman explains the antiparticle as "particles which go back in time." 4 This explains how the properties of the antiparticle are opposite to those of particles: a negative electrical charge carried back in time equivalent to a positive charge is moving toward the future. In both cases, the positive charge of the future is increasing, and a negatively charged electron moving toward the past is seen as a positively charged positron, which is its antiparticle. All particles have their antiparticle, which was to be expected since they are in practice the same particle is behaving differently. Alice went to the broker along the edge of the Vacuum, noting the brilliant and subtle surface that continually buzzes with the activity of virtual particles, born and died without anyone if this account. A little away from the beach, Alice noticed a disturbance on the surface, some kind of uniform circular depression in the surface. Further, she could see other holes, and many of them were in clusters. Some groups were very small and sometimes contained only a pair of circular objects. Others gathered extensive collections. One of the groups that she saw was a ring, with six of the objects forming a circle, while others have joined in back, outside. The distance she could see large groups gathered around the area. The largest contained many hundreds of things circular, whatever it be. During their observation, Alice noticed that there were photons is high and rising, as we did for one of the ways they were ahead. The photons, with their bright colors seemed flags thrown vessels. The broker followed the direction of her gaze. "I see you see swim the atoms in a vacuum. In one way or another, the atoms are responsible for most of our work in the business of electronic states. It is possible to see the many molecular partnerships established between them. They range from small companies from two atoms to vast conglomerates organic. Each different type of atom has a characteristic spectrum of colors for emitting photons. Therefore, the photons are like signs that help identify the different types of atoms. " See footnote 1 at the end of Chapter "I was thinking these things scattered around," Alice admitted candidates. "I can not see them very clearly. You can get closer?" "If you want the atoms look more closely, we will follow up to the quay of Mendeleyev. There, you'll see every kind of atom to the shows with all the various elements arranged in order." The broker took Alice along the beach until you reach an extremely long and narrow pier, which extended into the vacuum. Beside him, on the beach, had an entry in arch, on top of which is read the following poster: PIER PERIODIC ownership of D.I. Mendeleyev. Built in 1869 "Here we are," said the broker. "This is where the atoms contribute before leaving to form different chemical compounds. Normally the call of 'Marina Mendeleyev' or 'Pier Atomic', although sometimes people call him 'Construction of the Universe." You will find all types of atoms represented here. " Together, they passed beneath the sign and moved up the edge of the pier. Walked slowly along the anchor, while Alice looked a long line of atoms anchored in sequence on one side. Each seemed a trumpet-shaped hole in the smooth surface of the Vacuum. This form has to remember those small rodamoinhos that form when you empty a sink or a bathtub, though, here, the

forms have not seen any rotation. The smooth surface sink into the hole and still building around the hole. She sink with a slope almost imperceptibly at first, but would increase to as close to the center. There were signs that some activity occurred in the depths of the hole. "Why this hole so deep", Alice asked, curious. "Since we are looking for nothing, I thought it would be flat and without relief." "This is a well of potential," was the reply. "What kind of shaft is this?" Alice continued. "I know well in the garden, where water flows, and oil wells. I also vaguely remember to have read something recently on wells of molasses, but which is in a well of potential?" "The source of the potential is clear. You must have a source to provide water from a well in the garden. Here, in the well of potential, an electric charge is the source of electric potential. You should already know what's in the well . It contains virtual photons. They provide the attraction that makes the electrical potential energy of a negative charge becomes increasingly below the vacuum that the fence, while moving toward the source in the center of an atom. And the source creates the potential that well, actually. " The first well was very shallow, but Alice saw that the other would become successively deeper as they moved away from the beach. The pier sumia the horizon ahead of you, with atom after atom, all contributed to one side. From each of them had a small sign marking the anchorage. The first said: 1H, the second, 2He, the third, 3Li. Each position had a different poster. "All these atoms will one day leave to combine and form groups like those on the surface of the Vacuum", Alice asked. "Most of them will, of course, but some not, as this one, for example." They stopped next to an atom whose poster said 10Ne. "This is a noble gas atom. They are a group aristocrat, and that means refusing to participate in any trade. They are very reserved. They are perfectly happy with the way they lead their lives and do not want to mix with anyone else. When traveling alone admirably. You never see those taking part in any compound. " Walked a bit more and broker explained that, besides the hidden atoms Noble, there was considerable variation in the enthusiasm with which the different atoms are joined to the compound. "This, for example, is particularly active," he observed, when the two approached a poster that said: 17Cl. Alice decided it was time to examine one of these atoms more closely, and has one foot out of the pier. To their delight, it does not sink. His foot was on the surface, causing a mild depression, as if some insects glide over the surface of the water. When she tried to walk towards the atom, however, found that there was friction in vacuum. The surface was extremely slippery, and she could not get up. With a little cry, she slipped and fell down slope into the well. By fall, Alice realized she had enough time to look around them. The sides of the well would become more likely and it is close. Alice soon realized it was falling through the transparent outline a series of rooms with very low right-foot. The first rooms were very low indeed, too low even for a dollhouse, but the more she fell, the rooms were gradually getting higher. In the beginning, were totally empty and deserted, but then she saw a room that had a large round table surrounded by chairs. On the ground, saw desks and shelves, as if through a kind of office. The time passed and Alice was increasingly thunderstruck to discover that continued falling, with no sign that would reach the bottom. Falling, falling, falling, will drop that never came to an end?

Alice gradually began to realize that his fall did not come to an end. She had not reached the bottom of the hole, and more was coming down. She was floating without any support in the center of the funnel, the level of one of the rooms open. She looked around and realized it was not alone. Near it were two electrons, immersed in intense and hectic activity. Around them, she could distinguish the slight outline of a small, crowded office. "Excuse me," she said. "Will could stop for a moment and tell me where I am?" "There is no space, no space," they replied. The states that electrons can occupy within an atom tend to be grouped in sets of levels, separated by significant intervals of energy. If an atom has its last level occupied completely full, then any extra electron that is added will have to go to a state of higher energy. He usually has a lower energy than would have been in their original state atomic. Atoms of this type, whose outer layers are completely filled with electrons, form the noble gases and does not interact chemically with anything as conventional. "Excuse me, but do not understand," she claimed, without finding meaning in the response it had received. An atom is contained by the electric field generated by the positive charge of its nucleus. This charge produces a potential well of the nucleus around which in turn requires that states are available to receive electrons. The selection of states is a vague form of the effect of interference, similar to the range of notes that can be drawn from an organ or the sound of a violin string. A tube of a body is possible only a few notes, those with a wavelength fit inside the tube. Similarly, the electronic states available fit within the well of potential. The states available to meet different levels of energy. Any other function of wavelength that does not correspond to one of these states is eliminated by destructive interference. "There is no space here to reduce the activity, much less to stop" they replied. "As you know, when the position of a particle is restricted, the ratio of Heisenberg means that its momentum is large, and is so tight here that we have no choice but to continue to move on. If we had so much space as we higher levels, we could move more freely in, but this is impossible. This is the lowest level and therefore it is expected that we are always very busy. " "Really?", Asked Alice. "What do you do that is so important?" "Nothing special. Nobody cares which the electrons are the fundamental level, provided that we keep moving." "In this case, could you tell me where I am without stopping to move?" She asked. "Because I do not know where I came. What prevents us from continuing down into the pit?" "You are at the lowest level of an atom of chlorine, as I said. Here, we are so close to the source of the potential that there is very little space. So we must move quickly to keep our momentum high. This means that our kinetic energy is also very high. As you see, none of us is in a particular virtual state. Electrons have secured positions in the atoms, with plenty guarantee. Most atoms have been so much time and energy quantum fluctuations are small. So for us, electrons, energy and momentum are connected properly. "You probably know that when an electron or any other thing falls within a potential, it depends potential energy that is converted into kinetic energy," he continued. "And I explained that the Bank Heisenberg," Alice agreed. "Here, in this well of potential, the closer we come to the center, there is less space, so we have more kinetic energy. If fell further to near the center, be necessary to more kinetic energy than we can convert potential energy, and therefore it is not possible for caiamos more. In fact,

paradoxically, we do not have enough energy to continue falling and we can not get energy loaned as quantum fluctuations, as it be necessary for long. "Only two states at this level and therefore there is only room for two electrons, one in the spin-up and another in the spin-down. There are more states available in the higher levels, and there you will find more electrons . The next two levels can support up to eight electrons in each level. In any atom the lowest levels, those with less potential energy, are the first to be completed. The principle of Pauli allows only one electron in each state. So that when all states of a given level have KaRen electron, an extra electron has no choice except to go to a higher level. The levels are filled from the bottom up until all electrons are accommodated. The highest level that contains electrons is called for any level of valence. It is there that do the valence electrons, even with very vague space up there in the attic. The valence electrons to take all decisions and control the compound that we atom can join. If you want to know how an atom works, it would be better if you were there talking with them. " See footnote 2 at the end of the chapter. "And how do I get there?" She asked. "Well, if you were an electron, would be expected to be excited to a higher level by a photon that would give you the extra energy needed. In your case, however, those who think there will be the porter of Escada. " "You do not want to tell the porter of the lift, the lift", said Alice. "I was in the elevator of a large department store and there was a porter who took people to walk on deck, but I never heard of a ladder that needed one." To look around them, but Alice had a kind of ladder with rungs very separated from each other. Beside it was a figure who could barely distinguish. "May I ask who you are?", Alice asked, curious. "I am the porter of Escada. I am not a creature material, only a mathematical construction. My job is to transform a system from one state to another lower or higher." He made a complicated operation that Alice could not understand but that resulted in his carriage, step by step, until the highest level. In a certain moment, Alice reached the level where he had seen a large round table. This level contains more electrons than the first. She has run eight in all, but it was not easy. As all the electrons that she had seen until that moment, they were fun quickly. Many gave laps on the table, some in one direction, some in the opposite direction. Others clearly were not in rotation, but they were still moving. None of them was sitting quietly in chairs around the table, but jumping up and down, others up and down the table without stopping. The electrons never stayed quiet though, at this level, are not moving so frantically as the other to the lower level. "Hi, Alice," they said, when she appeared. "Come and let us show you how reliable an atom-sized. The way in which the Corporation conducts its business Chlorine is decided by us, the seven levels of the valence electrons." "But you are eight!," Alice protested. "This is because entering a society with another atom, the Union of sodium, to form a molecule of sodium chloride. Working together in this way, we like to think that we are the salt of the earth. An atom works with more harmony when all levels containing electrons are completely satisfied. Alone, we have only seven in the level of valence electrons, and Sodium has only one, despite having room for eight. They only have to gain the level of valence electron of sodium were sit with us on our level of valence and complement our Board. And of course that means that we now have one more

electron, which makes our loading is negative. The sodium atom has one electron less than normal, which means that the load is positive. The electric force between these charges is that opposite holds two atoms together. This is what is known as tonic connection between atoms, one of the most common forms of corporate structure. " "It seems that there is much cooperation between the two sides," agreed Alice, with diplomacy. "Which of you is the electron which has the sodium atom?" She asked. "It's me," cried all at once. For a moment, silent and looked all have each other. "No, he is," said all in perfect unison. Alice noticed that there were questions that tried to differentiate identical electrons.