Relativity and simultaneity
Let's debunk one of Special Relativity's Great Myths: The relativity of simultaneity.
Let's start with a Gedanken Experiment (thought experiment) in the Einsteinian way:
Suppose Albert Einstein has rented a train for his personal experimental purposes. Suppose he has positioned two flashlights at opposite ends of the train and two lightsensors at the center of the train (equidistant from the flashlights), each facing a different flashlight. The lightsensors are connected to an electrical circuit (circuit A) designed to determine if, you guessed it, the lightsensors are receiving incoming lightwaves at the same time.
Practically this would mean defining an interval that passes for simultaneity. For instance: If the one lightsensor detects an incoming lightwave within 1 msec from the other, then this will be regarded as simultaneous. This convention doesn't affect the generality of our argument.
If circuit A receives both lightwaves at the same time then it will ring a bell, to celebrate simultaneity.
In this experiment the unprimed coordinates belong the train's passenger, Albert Einstein and the train are moving at a speed v with respect to Niels Bohr (primed coordinates), who is standing alongside the railroad track at a point we will call x' = 0. At x' = 0 Bohr has positioned his own lightsensors connected to a circuit A to detect simultaneity.
Prior to a time we call t = 0, the lights in the train flashed such that they arrive at the center of the train (x = 0) at t = 0. Circuit A detects simultaneity, the bell rings.
Should simultaneity be relative, then Einstein and Bohr's relative velocity could be chosen such that Bohr's circuit A would not detect simultaneity.
The constancy of the speed of light is sacred, that's what the special theory is based upon. Let's say the train is moving from left to right as seen by Bohr, then Bohr is moving from right to left as seen by Einstein. That would make Einstein think that Bohr "is running to meet" the lightray coming from the flashlight at Einstein's left. Let's say that the speed of light is 10 m/s and that Bohr and Einstein's relative velocity is 1 m/s. According to the Galilean picture Bohr's velocity with respect to the lightray "he is running to meet" would be 11 m/s and with respect to the other lightray 9 m/s. Then surely Bohr would detect the faster ray before the slower and would disagree with Einstein on simultaneity. Because Einstein knows the speed of light is constant, he must substract Bohr's relative velocity (v = 1 m/s) from the lightray coming from the left at 11 m/s add v = 1 m/s to the ray coming from the right at 9 m/s. Then he knows, as seen by Bohr, the speed of light is 10 m/s and because the lightray Bohr is "running to meet" is slower (remember, in his own frame of reference Einstein is making this virtual assumption to satisfy the constancy of the speed of light) than the ray Bohr is "running away from", Einstein will have to assume that Bohr too sees the two lightrays arrive simultaneously.
Conclusion: the relativity of simultaneity stems from intermixing Galilean with relativistic arguments.
Then how come the relativity of simultaneity is "demonstrated" by using Minkowski diagrams, see for instance Simultaneity in Special Relativity? Because Minkowski diagrams are constructed without the above-mentioned correction, see also relativity education and spacetime diagrams. In the latter document I wasn't ready to write off Minkowski diagrams completely, but I am now, they embody much of what's wrong in special relativity. The image in relativity education and spacetime diagrams actually forms the basis upon which Minkowski diagrams are constructed and in this image the constancy of the speed of light is violated.
Strictly speaking, the above "correction" is quite wrong and doesn't belong to the Special Theory at all, but it serves, as said, to illustrate how mixing Galilean with relativistic arguments can lead to the relativity of simultaneity.
We will now endeavour to prove that simultaneity is not relative.
Suppose there exists a relative velocity between two observers A and A', who are located in the origins (O and O') of their respective coordinate systems S and S'. Two flashlights are positioned stationary in S at equal distances from the origin O and they flash at a time t = 0. Since observer A sees both lighwaves coming in at the same time, he concludes simultaneity.
Observers A and A' synchronise their clocks when their origins O and O' coincide at a time t = t' = 0, which means that at t' = 0 the wavefronts of the lightsignals are at equal distances from O' (as they are in S from O). Because of the constancy of the speed of light, this must continue to be the case, that is, the wavefronts of both lightsignals must continue to be at equal distances from O'. This means they will arrive in O' simultaneously, as they do in O. c
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