The Vicissitudes of Simultaneity (4) Let us take the example of Stanley and Mavis again. The lightning strikes twice, and Stanley sees both bolts at the same time. Mavis, who is on a moving train, sees one before the other. Ha! How is that possible! Who are they kidding? Oh wait, the speed of light. I had completely forgotten about that. So Mavis sees the bolt that struck ahead of the train sooner than the one that struck behind. The following precision will certainly not be superfluous: "Stanley is stationary on the ground at 0, midway between A and B. Mavis is moving with the train at 0' in the middle of the passenger car; midway between A' and B'." Let us take a flash-picture of the exact moment that both bolts struck. And, to avoid misunderstandings, let us replace our friends with some automated sensors we know will react to the bolts instead of to every ray of light. At time t0 the lightening strikes (double), and at time t1 both sensors on the ground have registered the double event, and both bolts appear to be simultaneous. What about the sensors on the train? This is were the selective logic of Einsteinians is at its best. They all seem to agree on the fact that Stanley and Mavis will disagree. But why would they do that, or more precisely, why would the sensors on the train come to another conclusion that those on the ground? Because the train is moving? What does that have to do with anything? Everybody also agrees that light on a moving train has the same speed, c, as light on the ground. The sensors on the train will register the moment the lightning enters the train. The light rays will immediately start moving with their normal velocity in the train, as if the latter were stationary. There is therefore no reason for the sensors to come to any other conclusion than the simultaneity of both bolts. The question whether they will at the same time register the rays on the ground is irrelevant, and even if they did, that would not change anything to their first conclusion. In other words, both the sensors on the ground, and those on the train, come to the same conclusion: the lightening bolts at each end are simultaneous. Back to Mavis, she will see, just like Stanley, not two, but four strikes of lightning. Two on the train simultaneously, and two happening on the ground reaching her at different times. The mistake of the authors is to confuse between both pairs of events. And that is why they rightly say that Stanley and Mavis come to two different conclusions. That is also why they are right to say "Whether or not two events at different x-axis locations are simultaneous depends on the state of motion of the observer". The problem is that there is nothing "relativistic" to such an observation. Once we have accepted that time events can be perceived with such accuracy as in the example given, then it is absolutely normal that both Stanley and Mavis evaluate the simultaneity of the events on the ground and those on the train quite differently. In fact, whether c is a constant or not would be completely irrelevant. In both cases we are speaking of two distinct events A and A' on one end, and two other distinct events B and B' on the other end. Even with a constant speed of light Mavis (on the train) could only decide of the simultaneity of the events on the ground if she knew exactly how fast her train was moving. (And it would be the same if light had a different speed on the train than it had on the ground.) Otherwise she can only confirm her perception of the fact that B (not B') appears to her before A (not A') does. And, all things being equal, the same could be said of Stanley. So, what can we conclude concerning simultaneity of events? Either both the stationary and the moving observer can rely on the same coordinate system, in which case it would be no problem to calculate whether two events are simultaneous or not. Or, and that is the more interesting case, each has his or her own coordinate system, and then no one can say anything about simultaneity in the other system. Still, as I have tried to show, neither Stanley nor Mavis could say anything about how the other experiences the two pair of events without sufficient knowledge concerning the train velocity. Only then could they reconstruct the way their colleague would experience those events. But that would also mean that they should be able find common criteria that would make possible a judgment on the simultaneity of A/B and A'/B'. Meanwhile, they are both evaluating a different pair of events than their counter part: Stanley considers A and B as simultaneous, while Mavis thinks the same about A' and B'.
In other words, this is really a bad example to found Relativity Theory on. [By the way, all textbook writers base their stories on Section 9 of Einstein' s "Relativity", "The Relativity of Simultaneity", p.29 ff.]
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