Einstein Special Relativity

Einstein’s Special Relativity After the demonstration of the constancy of the speed of light by Michelson-Morley’s experiment and the formulation of Maxwell equations, many theorist, became interested in the implications derived from it. Voigt, Lorentz, Larmor and specially Pointcaré wrote about the theme. Pointcaré lecture in 1904, about “The Principles of Mathematical Physics” translated by George Bruce Halstead, mentioned

Einstein line of thoughts Grayed text is taken from: The Principle of Relativity, published in 1923 by Methuen and Company, Ltd. of London. The edition copied was prepared by John Walker.

From pages 3 and 4 of his article “On the electrodynamics of moving bodies” Einstein states:

We could write this equation as c=l/t for further discussion we prefer the form t = l / c seconds given that c is constant, for any other length l’ we will have t’ = l’ / c seconds On page 6 he reaffirms that: Linear equations have linear units of measurement, which means meters, seconds and meters per second. On page 10 he gives us the contraction formula for the length

Where the contraction factor can be expressed as f(v) = 1 − v 2 / c 2 dimensionless The units of v and c are the same and they cancel each other. It depends only of v because c is constant. For the possible values of the factor we have 0 >= v = c 1 <= f(v) = 0 Where f(v) = 1 means no contraction and f(v) = 0 is a 100% contraction. The relation between the length of a rigid moving body l’ and its length at rest l are given by l’ = l f(v) meters We will call t the time a beam of light takes to travel between the ends of a rigid rod of length l and t’ the time it takes to travel the contracted rod of length l’. The following relations are obvious t = l / c seconds t’ = l’ / c seconds where

t’ = l f(v)/ c = (l / c) f(v) = t f(v) segundos or

t’ = t f(v) seconds In the same page 10 the author proposes

Which evidently is expressed in seconds. Very strangely he continues

Where did that unit of measurement come from? Let’s review our equations: length contraction is: l – l’ = l – l f(v) = l ( 1 – f(v)) meters time contraction is: t – t’ = t – t f(v) = t ( 1 – f(v)) seconds also should be noticed that, given the constancy of c t – t’ = (l – l’) / c seconds

The implications derived from this wrongly established unit of measurements are wrong (pages 10 and 11)

With the contraction expressed in seconds, the effect is not cumulative. Wherever the clock that was moving stops, contraction will be 0, because f(v) will be equal 1 and (1 – f(v)) will be 0. t ( 1 – f(v)) = 0 Luckily, the live length of the muon is not affected by the change of unit. Neither will be affected the corrections made to satellites that do not take into account the duration of the flight. It depends only on the relative speed and the positional correction that we will see latter. What seems to be wrong are the measurements made by J. C. Hafele and R. Keating in 1971. Louis Essen strongly criticized their experiment.

The twin’s paradox As we saw in the pages 10 and 11 of the article, Einstein states that the moving clock will be delayed when he comes back to the point of departure. Based on these lines, Paul Langevin, known French physicist, created the twin’s paradox. It could be expressed as: At birth, one of the twins travels at high speed to some place in the universe. When the traveling twin returns, he is younger than the one that stayed on Earth. Of course, the twins substitute the synchronized clocks, but his paradox introduces gravity. I am not interested in discussing Langevin relativity or Langevin paradox. I will take into account only what Einstein said. We will call Einstein paradox the following: some where in space twins are separated and one of them travels at high speed. When the traveling twin returns, he is younger that the one that didn’t travel. You could also notice that Einstein doesn’t give the moving clock his own system of coordinates. The clock moves from a system that is already moving. This fact resembles the local time expressed by Lorentz. Let’s return to the article and notice that

time accumulates every second, or we could say continuously. This fact is very important. Contraction doesn’t jump from one value to another. It accumulates continuously. So we don’t have to wait to the return of the traveling twin to make calculations. In the very first second accumulation already took place. Contraction is not a property of the moving body Let’s say that an experiment was thought to measure time contraction, and the expected value was t seconds. But exactly in the middle of the experiment, when contraction was already t/2 the twin at rest disappears due to a catastrophe. The traveling twin knows nothing about it and he continues to travel inertial as before. Which of the following outcomes would be true? - Contraction on the traveling twin continues to grow, but now with respect to whom? - Contraction stops at the moment of the disaster, but stays as t/2, with respect to whom? - Physical contraction disappears because there is no one to compare with. None of them is right, because contraction is not a property of the moving body but of the observer. So physical, permanent, absolute contraction, caused by the observer doesn’t make much sense. The counter paradox of quintuplets Let’s name the quintuplets as A0, A1, A2, A3 and A4. They are separated at birth and each one travels in his own ship with his own synchronized clock. A0 knows his relative speed to the other four and after some time he decides to calculate his own age. He knows the age given by his own clock is a0, and calculates that relative to the other brothers his age is a1, a2, a3, a4. But he can’t have five different ages at the same time. So he decides that his only possible age is a0 and that the contractions his brothers see on him can’t be permanent. If someone is preoccupied about the acceleration, we could rephrase the experiment. Five different persons travel in space inertial, at different speeds. They will coincide at the same place at the same time; they can synchronize their clock at this moment. After that, they continue to travel inertial as they did before. Some time latter one of them decides to know his age and… What is demonstrated for the quintuplets is valid for every pair of brothers. So it demonstrate the absurdity of Einstein paradox, even when they are only twins The monster twin paradox Even after the demonstration, some girl may decide to take the risk. I wouldn’t recommend it. If time contraction is given in seconds per second, then to maintain some equilibrium in the formula t=l/c

we should believe that length contraction is in meters per second and also permanent. This makes the gain of mass permanent also. Then, if the girl sits looking in the direction of the movement she will suffer the following consequences. Her face and her chest will become flattened, her tight will become shorter and will weight more than before. She would be a younger monster. I could think of twenty more absurdities, but it will be boring. If you are not convinced yet, nothing will. Let’s take another look at what we have gone through. We are not interested in Langevin relativity and paradox. Time contraction doesn’t jump, it accumulate continuously, so we don’t have to wait the reencounter. Contraction is more a property of the observer than the observed. Any body is moving relative to billions of close objects, so permanent contraction relative to one of them, is absurd. Contraction is relative and depends only on the speed of the moving body, not on the duration of the movement. We could say also that the twin’s paradox is against Pointcaré’s relativity because then you could know which of them moved, so his movement won’t be relative. Positional correction You have probably read or heard about the tower clock in downtown Bern that inspired Einstein. They mention that traveling away from the clock, Einstein thought of holding a light ray and traveling with it. Time stopped for him. (It meant that, seconds or seconds per second didn’t flow?) Let’s change the clock with the gigantic screen of a drive in theater. Film frames are reaching the screen at a frequency of 30 frames per second. We arrived at intermission and the screen is showing a big clock with high precision. Let’s fix two points A at 150,000 kilometers and B at 300,000 kilometers from the screen.

At any moment a viewer at point A will have seen 15 frames (1/2 seconds) that the observer in B hasn’t seen. So we could say observer at B has a delay of half a second. If another observer moves from A to B, in his way he will be seen les frames than A, so for him, the screen clock is delaying. When he reaches B, he will be delayed in half a

second. His delay doesn’t depend on his speed or time duration, but on their product. It depends on the distance traveled. Delay = l / c seconds l = v t meters This time contraction is permanent, as long as the observer stays at B. Maybe this fact made Einstein assume that relative time contraction was permanent. If the same viewer decides to go back to A, then time goes differently. He will see more than 30 frames per second. His time is not contracting, but expanding. When he reaches point A, he will be half a second ahead of the time B sees. Again, speed doesn’t matter but the product of speed and time, or distance. May be Einstein didn’t look at the tower when he was returning to work.