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Relativity of simultaneity 
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#1
Mar1110, 04:33 AM

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Hello everybody,
I know that there are a lot of questions about simultaneity, but mine is based on a specific aspect of it. In the book University physics ( with modern physics) they explain the train example and how the person inside of it sees the events happening non simultaneously. However, they say that : "You may want to argue that in this example the lightning bolts really are simultaneous and that if Mavis at O' could communicate with the distant points without the time delay caused by the finite speed of light, she would realize this." and then they add "But that would be erroneous; the finite speed of information transmission is not the real issue. If 0' is midway between A' and B', then in her frame of reference the time for a sigual to travel from A' to 0' is the same as that from B' to 0'. Two signals arrive simultaneously at 0' only if they were emitted simultaneously at A' and B'. In this example they do not arrive simultaneously at 0', and so Mavis must conclude that the events at A' and B' were not simultaneous." This does not really convince me, I mean I always thought that simultaneity was based on the finite speed of light (if it was infinite , the limit of the ratio of t1/t2 = 1 {t1 and t2 being the time at which the observer inside the train actually 'sees' the light after the lightning had struck}. Thanks! 


#2
Mar1110, 05:54 AM

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#3
Mar1110, 10:59 AM

P: 4

Thank you A.T,
But i would appreciate it if you could elaborate more on the concepts. My problem is the following: We are saying that person A inside the moving train, is moving towards the light that was emitted at the front of the train, and away from the light emitted at the back of the train. Thus, person A will encounter the wave in front of him before the wave behind him. And since person A is midway between the front and behind of the train, he will think that the light coming from the front was emitted before. So it all seems to be that it is due to the finite propagation of light. I mean if it was infinite, then he will see both fronts in 0 time, so the times are equal. If my point is still not so clear, let me try to explain it with this example: Suppose there is a device that has 0 delay, attached to the back of the train, and another one attached to the front of the train. Now suppose these devices are connected to person A, and they shock him (again with 0 delay) when the lightning strikes any of the devices in the back or the front of the train, and he feels the strike with 0 delay. Does simultaneity still hold here? It seems to me that the event appears simultaneous or not, due to the propagation of light and speed of the observer. So the event APPEARS simultaneous or not, due to the speed of light being equal in all inertial frames, and the speed of the frame itself. But 'APPEARS' does not mean that this is the truth. 


#4
Mar1110, 11:13 AM

P: 3,913

Relativity of simultaneity



#5
Mar1110, 11:16 AM

P: 4

Can you please relate it to the example that I gave, with the sensors?



#6
Mar1110, 11:32 AM

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#7
Mar1110, 11:39 AM

P: 4

Okay Thanks for your effort A.T.
I will try to look for a similar thread, and in the mean time, I will wait for other people's useful comments 


#8
Mar1110, 12:16 PM

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I would put the logical sequence the opposite way compared to the textbook that samerking quoted. The Lorentz transformation can be derived from the symmetry properties of spacetime, without even mentioning light (Morin 2008, Rindler 1979). This analysis proves that spacetime has a frameindependent velocity c, and that particles with zero rest mass travel at c. If light has zero rest mass (the current upper bound is very low), then light happens to travel at c, but this is a consequence of the theory, not an assumption.
Now suppose that there exists some mechanism for sending signals at a velocity greater than c. Then causality would be violated, because there would exist cases where, in a certain frame, a signal propagates from event A to event B, but in another frame event B comes before event A, so the signal is received before it's sent. If we assume causality, it follows that light travels at less than or equal to the universal velocity c (equality holding in the case where the photon's rest mass happens to be exactly zero). In this logical framework c is the maximum speed of cause and effect, and therefore the assertion quoted in the textbook is exactly backwards. I'm not saying that the textbook is wrong and Morin and Rindler are right. It depends on what you take as your axioms. As a matter of taste, I think the traditional Einsteinstyle axiomatization is lousy, because it grants a special role to light. Light was the only fundametal field known in 1905, but we now know that it's just one of many fields, and it doesn't deserve to be singled out for special treatment. Morin, Introduction to Classical Mechanics, Cambridge, 1st ed., 2008 Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51 


#9
Mar1110, 02:10 PM

P: 3,967

Special Relativity requires that the speed of light is (1) finite, (2) independent of the speed of the emitter, (3) measured to be the same relative to the rest frame of any inertial observer and (4) is the maximum possible speed for the transmission of information. Remove any of those conditions and (I think) SR falls apart. 


#10
Mar1110, 03:22 PM

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#11
Mar1110, 03:29 PM

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