Physics Project : Particle Physics

Physics Project

Particle Physics

What is UNIVERSE made from??????

By: Aditya ‘quark’ Tiwari Tushant ‘vacuum’ Jha Yusuf ‘string’ Jamal

Preface This topic is definitely less of Mathematics, and more of definitions, not because Particle Physics doesn’t consider mathematical aspects, but because our target audience may not be able to comprehend that level of mathematics in just half an hour. To some, initially it may sound chemistry too, but then not our fault, it’s there in Physics Book too. There is a video too, having basically some good ways to explain the topic. The project discusses The Standard Model of Particle Physics, by Tushant. Then Yusuf and Aditya will discuss about Dark Matter and Dark Energy respectively. We will also discuss about the ‘Theory of Everything’ and how it is different from ‘42’ (obviously this is our Physics Project and not a Hitchhiker’ Guide) We end our project on a note of hope… We thank Mrs. Vani Dutta ma’am to allow us take such a topic.

(where at least a few students could sleep and ask no questions… …sorry, it was just a comic relief)

The Standard Model of Particle Physics The Standard Model refers to the compiled formulation of all the elementary particles which have been both observed and mathematically formulated.

Fermions [matter particles]: Fermions, or the so-called ‘matter particles’, are heavy particles that make up our common matter. They are called so because they follow Fermi-Dirac Statistics. They have half-integral spin that is -1/2, 1/2, 3/2, etc. Spin is actually the quantized representation of Angular Momentum. Handedness of Spin refers to similarity of direction between direction of spin (z-component) and motion of particle. They also have electric charge, which makes them interact through Photons. Actually its important to know that any large enough collection of fermions (like this sheet or even ink itself) is visible not actually because it bounces back the photons (c’mon, no one can bounce a wave-particle so easily, at least I can’t bat a rope) , but because electrons and protons first absorb and then emit them. The Fermi-Dirac Statistics include Pauli’s Exclusion Principle, which state no two fermions can have same quantum numbers at same time and place.

The Fermions are found in 3 generations, each generation heavier and less stable than previous. It is important to note that in Quantum Mechanics, stability is counted in fractions of milliseconds. All Fermions have their Anti-Matter Counterparts which have exactly the opposite electric charge and opposite handedness, and everything else same. When a particle collides with its anti-particle (such as electronpositron), energy is created equivalent to their masses (E=mc2). As per Quantum Mechanics, at each and every point of time, particle-antiparticle pairs are created and destroyed (After all, it’s all uncertain[Heisenberg’s Uncertainty Principle]) The Fermions can be further classified into:

Quarks: These are the particles which make protons and neutrons. They are of two types, ‘more charged’(±⅔) and ‘less charged’(±⅓) They also have another kind of ‘charge’ known as ‘color charge’ (not to be confused with visible colors, it is just a naming convention). The color charge is of six types: 1. Red 2. Blue 3. Green 4. Anti-Red 5. Anti-Blue 6. Anti-Green These ‘color charges’ are named so because as mixing of red, blue, and green lights give white lights, similarly all

stable Baryons (called hadrons) are made only if there are 3 quarks of different color-charge. Or, a ‘meson’ would be formed if two opposing colors meet.

A Comic description by quarked.org

Leptons: These are the light-weighted particles which include electrons. They also include neutrinos, which are so light that they travel at relativistic speeds. Leptons act as particles to balance the electric-charge of a system which is already color-neutral.

Bosons [Interactions]: Bosons, or the so-called ‘force carriers’, are particles which follow Bose-Einstein Statistics, and have integral spin. Bose-Einstein Statistics allow more than one particle of same kind to be at same place and same time. All force in universe is ultimately made by these fundamental forces. Have you ever thought that even though 98% of atom is vacuum, whenever we push something why don’t we just get passed through it?? The answer is E-M force. At Planck’s Time (the smallest unit of time) after Big Bang, all Forces were unified as X and Y Bosons, but as the universe cooled, the three (as far we have known) main bosons were developed.

Gluons: The gluons are gauge bosons, which like the photons, travel at ‘c’. It carries the ‘color charge’ and is called the ‘STRONG FORCE’.

Photons: These are the particles which carry electromagnetic field. It is also the force that makes things visible. Its energy can be given by E=hν. It is also subject to interference addition, that is:

Weak Force: Two kinds of W bosons exist with +1 and −1 elementary units of electric charge; the W+ is the antiparticle of the W−. The Z boson (or Z) is electrically neutral and is its own antiparticle. All three particles are very shortlived with a mean life of about 3×10−25 s. These bosons are heavyweights among the elementary particles. With a mass of 80.4 GeV/c2 and 91.2 GeV/c2, respectively, the W and Z particles are almost 100 times as massive as the proton—heavier than entire atoms of iron. The masses of these bosons are significant because they act as force carriers; their masses thus limit the range of the weak interaction.

The electromagnetic force, by contrast, has an infinite range because its force carrier (the photon) is massless. All three types have a spin of 1. The emission of a W+ or W− boson either raises or lowers the electric charge of the emitting particle by 1 unit, and alters the spin by 1 unit. At the same time a W boson can change the generation of the particle, for example changing a strange quark to an up quark. The Z boson cannot change either electric charge nor any other charges, only spin and momentum, so it never changes the generation or flavor of the particle emitting it It is really important in Decays: udd → uud + e− + νe

Comparative Strength:

As compared to E-M Force, we see that Strong Force is stronger and Weak is weaker (wasn’t that obvious by their names?), but what amazes is that Gravity is much weaker than even the ‘Weak’ Force. But after all its E-M which stops us going through floors.

More Particles: There are still many questions left unanswered like why things have mass, and to find the answers to these questions, scientists are predicting new particles. The Higgs Boson, as postulated by Peter Higgs, is a kind of Boson which acts as a Higgs Field in the following way: Say a class is full of students (aka Higgs Bosons) Now a boring guy (like me) enters, and then eventually goes away. But if a celebrity (say Orlando Bloom or Megan Fox) enters, the whole class goes to take the autograph thus making it difficult for heavy particle (celebrity) to move, which it shows in form of Mass.

Dark MATTER In 1933, when Swiss Astrophysicist Fritz Zwicky, while studying nearby Coma Cluster, suddenly found that the galaxies were moving faster than expected, as if there was some ‘ghost’ making them do so. It was later hypothesized that there existed a non-baryonic species of matter which was exerting this unseen gravitational effect. They couldn’t be seen because they didn’t interact with Electromagnetic Waves, nor do they interact through Strong force.

The Reason: The Virial Theorem states that for a closed system,

EK = -∑(F*r)/2 Where

EK represents Kinetic Energy, F represents Force, r represents position But Fritz observed 400 times more energy than calculated, Since,

EK = ½mv2 And ‘v’ couldn’t had been 20 times more than what was observed, it would mean that there was 400 time more mass in the system.

For 40 years after Zwicky's initial observations, no other corroborating observations indicated the presence of dark matter. Then, in the late 1960s and early 1970s,Vera Rubin, a young astronomer at the Department of Terrestrial Magnetism at the Carnegie Institution of Washington presented findings based on a new sensitive spectrograph that could measure the velocity curve of edge-on spiral galaxies to a greater degree of accuracy than had ever before been achieved. Together with fellow staff-member Kent Ford, Rubin announced at a 1975 meeting of the American Astronomical Society the astonishing discovery that most stars in spiral galaxies orbit at roughly the same speed, which implied that their mass densities were uniform well beyond the locations with most of the stars (the galactic bulge). This result suggests that either Newtonian gravity does not apply universally or that, conservatively, upwards of 50% of the mass of galaxies was contained in the relatively dark galactic halo. Subsequent to this, numerous observations have been made that do indicate the presence of dark matter in various parts of the cosmos. Together with Rubin's findings for spiral galaxies and Zwicky's work on galaxy clusters, the observational evidence for dark matter has been collecting over the decades to the point that today most astrophysicists accept its existence. Recently, cosmologists have mapped the presence of dark matter with the help of gravitational lensing, or bending of light due to gravity. As a unifying concept, dark matter is one of the dominant features considered in the analysis of structures on the order of galactic scale and larger. Dark Matter Halos in a

galaxy are comparable to a Christmas Tree. We see the light bulbs (a.k.a. stars) from far off but are unable to see the structure on which it rests, the Tree (a.k.a. Halo).

Answers: The possible solutions to this problem are : 1. WIMPS, or Weakly Interacting Massive Particles which are particles which interact only through ‘weak’ or lower. 2. MACHO, or Massive Astrophysical Compact Halo Objects, which attributes this stuff to star-decays. It is also referred as Hot Dark Matter, as they will travel at relativistic speeds 3. RAMBO, or Robust Associations of Massive Baryonic Objects, which postulates quark-seas. 4. Or to check our Gravitational Concepts again. But everything is just postulated, and most theories themselves predict such particles which would be difficult to observe (they could be passing through us every second). Still, what we do know is that there is something which is beyond Baryonic Matter but provides gravitational structure to it.

Dark Energy

When Albert Einstein first formulated his General Theory of Relativity, he found it contradictory without an extra energy, which he termed ‘Cosmological Constant’, to keep the universe static and counter the effects of gravity. But as Edwin Hubble discovered that universe was expanding, suddenly the utility of cosmological constant was put into question. Einstein termed it as his biggest ‘blunder’. But later when Dark Matter was studied, cosmologists discovered that the net energy of universe was more than first thought. The total amount of Baryonic Matter and Dark Matter put together was observed to be insufficient to produce the amount of Space-Time curvature we observe. Putting the newly found facts into Hubble’s Theory, it was postulated that the expansion of universe should decelerate as matter shows Gravitational effects. In the 1998 and 1999 two teams of astronomers, the Supernova Cosmology Project and the High-Z Supernova Search were looking for distant type ‘1a supernovae’ in order to measure the expansion rate of the universe with time. They expected that the deceleration of expansion would be indicated by the supernovae being brighter than their red-shifts as the Hubble’s Law would indicate. Instead, they found the supernovae to be fainter than expected. Hence, the expansion of the universe was accelerating!!!!!!

Observations using the Chandra X-Ray Observatory have shown that the growth of clusters of galaxies by gravitational attraction has slowed over time. Astronomers think that this stifled development of larger and larger clusters of galaxies is likely caused by dark energy that is accelerating the expansion of space between galaxies. Also the Theory of Large Scale Structure, which governs the formation of structure in the universe (stars, quasars, galaxies and galaxy), suggests that the density of baryonic matter and dark matter in the universe is only 30% of the critical density. There should be something to account for the remaining mass in and that something is dark energy. (Mass and Energy are related. Remember E=mc2). Thus Dark Energy was postulated, a mysterious form of energy that physicists believe is the single largest component of the universe. Dark energy is spread throughout the universe and appears to make up about 74 percent of its content. Dark energy is thought to be an ‘inherent property of space’ itself. Dark energy is the only way to explain recent observations that the universe appears to be expanding at an accelerating rate although the gravity produced by baryonic and dark matter should have decelerated this expansion or even started contracting the space. It is found to be ‘Vacuum Energy’ or the ‘Energy of Nothing’ as no matter or energy particle explains it, but only some property of space-time curvature. Two Models of Dark Energy 1. Cosmological Constant: A possible explanation of dark energy that fits very simply within the framework of Einstein’s General Theory of Relativity is the existence of a cosmological constant. Einstein originally introduced the cosmological constant into his equations in an attempt to render the universe static (neither expanding nor contracting). Einstein’s equations for general relativity predicted that the universe could not be static, but at the time Einstein formulated them, he and other

scientists believed that the universe was unchanging. So Einstein introduced the cosmological constant to balance gravity in his modified field equations.

But after the discovery of expansion of Universe by Edwin Hubble in 1929, Einstein left this concept. The possibility that the equations of general relativity should include a cosmological constant is now being seriously reconsidered because of the discovery of dark energy. Instead of having the value needed to keep the universe static, however, the cosmological constant would now have the value required to make the expansion of the universe accelerate at the observed rate. However, when this concept is applied to Quantum Field Theory it gives its value of order 10120 which if applied actually would have accelerated the universe at unimaginable rate and never allowed matter to form. 2. Quintessence: To overcome the shortcomings of Cosmological constant, one such theory proposed is that there may be a previously unknown type of force in the universe that produces the observed acceleration. This would constitute a fifth fundamental force. This class of theories is often referred to as “quintessence”. These models predict that the nature of dark energy changes over the lifetime of the universe, whereas the cosmological constant is exactly that—constant for all time. Precise measurements are now being planned to determine whether the properties of dark energy do change with time. Implications of Dark Energy on our Universe: The concept that Einstein called his ‘blunder’ is today found to be the determining factor behind the fate of universe. If cosmologists could rightly study the mechanism of Dark Energy, they could tell if the universe would die in ‘fire’ or ‘ice’. Cosmologists estimate that the acceleration began roughly 5 billion years ago. Before that, it is thought that the expansion was decelerating, due to the attractive influence of dark matter and baryons. If the acceleration continues indefinitely, the ultimate result will be that velocity of the expansion of space will exceed the speed of light. This does not violate the Special Theory of Relativity as it only

applies to flat space-time and not to curved space-time. Thus, local clusters would soon be invisible to us.

Lambda-C.D.M. Model: The Lambda-CDM Model is the simplest known model that is in general agreement with observed phenomena. It takes into account: 1. Λ (Lambda), or the cosmological constant, which is a dark energy term that allows for the current accelerating expansion of the universe. The cosmological constant is often described in terms of ΩΛ, the fraction of the energy density of a flat Universe in the form of the cosmological constant. Currently, 0.74, implying 74% of the energy density of the present universe is in this form. 2. Cold dark matter is the model where the dark matter is explained as being cold (i.e. its velocity is non-relativistic or much less than ‘c’ at the epoch of radiationmatter equality), which is possibly nonbaryonic, dissipationless (can not cool by radiating photons) and collisionless (i.e., the dark matter particles interact with each other and other particles only through gravity). This component makes up 22% of the energy density of the present universe. 3. The remaining 4% is all of the matter (and energy) that makes up the atoms (and photons) that are the

building blocks of planets, stars, and gas clouds in the universe. This fraction of universe (strangely having more matter than anti-matter) is involved in nucleosynthesis in stars. 4. It also assumes that universe has no ‘observable’ topology or space-time rips, so that the universe is much larger than the observable particle horizon. These are predictions of cosmic inflation. 5. It takes many parameters like: a. Hubble’s Constant, which describes the speed of recession between galaxies. b. Baryon Density, the absolute density of baryonic matter c. Dark Matter Density, the density of dark matter present in universe d. Critical Density, the relation between gravity and anti-gravity (dark energy), etc. Lambda-CDM model as of 2006 is consistent with a series of increasingly rigorous cosmological observations, the latest being the 2005 Supernova Legacy Survey.

Theory of Everything Strings, Superstrings, Fields, Extra Dimensions, and Everything else… Scientists have been working on to ‘GENERALISE’, that is to define more than one concept in just one theory. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes. — Essai philosophique sur les probabilités, Introduction, PierreSimon Laplace, 1814

The history of a quest for such a theory is long, but recently the efforts of unification have seen many upsand-downs 1713: Newton unifies Galileo’s on terrestrial gravity, Kepler's laws of planetary motion, and the astronomical studies on Jupiter’s and others Moons into a single law of universal gravitation 1873: Maxwell works on previous works of Oersted and Faraday to unify Electricity and Magnetism into mere 4 equations. 1915: After General Relativity, Einstein tries to unify E-M with Gravity, but fails

1919: Theodor Kaluza adds a fifth dimension to General Relativity to adjust it for differences between EM and Gravity. 1930’s: Uncertainty Principle hinders development of Theory of Everything 1940’s: Heisenberg works on S-Matrix approach, triggering work on Unified Field Theory. 1960’s: Strong and Weak discovered. But now Gravity has no place in newly formed Standard Model 1964: Higgs Boson proposed to accommodate in Unified Field Theory 1967: Abdus Salaam and Steven Weinberg unify EM and Weak, thus forming ElectroWeak Theory 1969: Few Scientists propose that everything is made of strings 1974: Scientists propose Grand Unified Theory, combining all forces 1980’s: Dark matter and dark energy discovered, pose problems 1990’s: Scientists work on modified version of initial String Theory, now called Superstring Theory, predicting up to 26 dimensions.

says that everything is made from some kind of vibrating strings, obviously this could account for Particle-Wave duality. According to it all particles are made from different tones of vibration in strings. But the one of the few problems this has is that it predicts many smaller dimensions, but first lets understand what is a smaller dimension:

So in a similar way there more dimensions which don’t really affect us, but at quantum levels, it can have amazing impacts being the medium for vibration of strings.

But String Theory, to some extent, contradicts General Relativity, as it asks for a particle to mediate gravity, while relativity attributes gravity to space-time curvature.

The importance of extra dimensions, as many scientists say, lies in making the universe ‘possible’. The universe is possible only because there are about 20 constants which have ‘fine tuned’. eg.- If the ratio of Dark Matter and Hubble’s Constant would have had been changed, the universe would have had crunched long before we could evolve. The Multiple Dimensions allow parallel universes, thus making our universe one of the ‘privileged’ universes. But String Theory has a problem, its too difficult to test it…

…due to the high-energy required to test its effects.

Sources: WIKIPEDIA (that’s obvious) Elegant Universe, NOVA TVPBS, by Brian Greene Particle Adventure, CPEP Youtube, etc.

We shall hope that one day scientists are successful in unifying Standard Model, Lambda-CDM Model, General Relativity, Superstring Theory, and Unified Field Theory into one consistent ‘Theory of Everything’ (definitely not ‘42’)……so that the twenty years down the line students don’t make group project but individual ones on this topic.