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Here is a very good proof that simultaneity is absolute, not relative. The question: Is this proof wrong, or is Einstein? Can you prove it? What is the mistake in the proof, if any? If there is none, then simultaneity must be absolute:

  • (a) Production of absolutely simultaneous events: Take the following apparatus: a battery and switch placed at the mid-point X of two event locations A and B. Connect the switch with two long pairs of wires of equal length from X to A and X to B, and then to a lamp at A and B which produces a flash of light. The lengths of wires, lamps and their connections are assumed to be of exactly identical construction, so that when activated by a single switch, both lamps produce the flash of light after exactly the same time delay, i.e. both flashes are produced simultaneously. So far, we have assumed only one frame of reference. But now mount this apparatus on a moving train (assume the train to be long enough to support the wires and lamps from A to B) and activate the switch, and the flashes at A and B will still be simultaneous. They will also be determined (see Einstein's method below) as simultaneous from ground - they have to be because as seen from the ground, both lamps are activated by the same switch, and as measured by a clock on the ground, both lamps produce the flash after the same delay for A and B, since the construction of both is identical. Agreed that the clock on the train may be running slowly compared to the clock on the ground, so the time delay between pressing the switch and production of the flash as seen from the ground may be different, but it will be the same for A vs B and so the events will still be simultaneous. Also when mounted on the train, the events will be produced at different locations A' and B' instead of A and B, but still, the events at A' and B' will be simultaneous when seen from the ground (and from the train). Therefore, it is possible to generate events which are simultaneous in all inertial frames of reference.

  • (b) Determination of absolutely simultaneous events: We use Einstein's method from Einstein's book, chapter "Relativity of Simultaneity". If an observer at the mid-point X of event locations A and B observes that the events are simultaneous, then we conclude that the events are simultaneous. I feel quite sure that Einstein will agree that it is important that the observer must be at the mid-point X at the instant when he observes both events. If the observer is at some other location yesterday, or tomorrow, or even if he is at some other location at the same instant as when the flashes of light are actually produced at A and B, then all that is irrelevant to our experiment. We know that at the instant the flashes are produced at A and B, the observer may be somewhere else, because the light from the flashes has not reached him yet. But at the instant when light from both flashes reaches the mid-point X, and the observer is there to observe it, he will determine both flashes as simultaneous, because light from both will reach the mid-point simultaneously. We note that even in a single frame of reference, only the observer at the correct location can determine the events to be simultaneous. Observers at A or at B or at any other location cannot make that determination.

Now consider the simultaneous flashes on the ground and Einstein's observer on the train. The mistake Einstein made in his proof was the he assumed the observer to be at the mid-point X at the instant the flashes occurred. (assuming the train is going in direction from B to A) So of course, the light from A meets the observer first because the observer has travelled closer to A by the time the light meets him, and the light from B meets the observer later because he has moved away from B. He is no longer at the mid-point when he makes the observations. This can only be described as a flawed experimental technique which makes the actually simultaneous events look like non-simultaneous.

Instead, if we station a large number of observers on the train and the train is long enough, there will be one observer on the train, who will view both flashes as simultaneous, and that observer will be at the mid-point X at the instant when he makes his observation -obviously even though he is travelling on the train, if he is at the mid-point X at the instant when light from both A and B reaches him, both will reach him simultaneously and he will view both events as simultaneous. So for the observer who is in a position to make a correct observation, the events are simultaneous for observers, both on the ground and on the train. In fact, the events are simultaneous for ALL inertial frames in uniform motion relative to each other, provided their observers are at the correct location to view the events.

Observers who are not at the mid-point between A and B at the instant of the observation would observe the events as non-simultaneous not because the events are non-simultaneous in their (moving) frame of reference but simply because light takes unequal time to travel the unequal distance from A and B to the observer. That obviously says nothing about whether the events are really simultaneous or not. If this effect was to be called "Relativity of Simultaneity", then simultaneity would be relative even in the same frame of reference as the events. Observers in the same frame of reference as the events, who are closer to A will view A before B and observers closer to B would view B first. But that does not mean that A and B are not simultaneous. As given above, they can be generated simultaneously, so they are provably simultaneous. The different observations by different observers can only be attributed to observation error due to light from A and B travelling different distances to the observer in different amounts of time. The same observation error is also there for an observer in another frame moving with respect to the frame of the events. Why should we then say that the events are non-simultaneous in another frame, or that simultaneity is relative?

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  • $\begingroup$ The problem with this is that by specifying that "only the observer at the correct location can determine the events to be simultaneous" means exactly that simultaneity is relative to position, not absolute (i.e. independent of position). Same with your first example: the two flashes are only seen as simultaneous by an observer on the ground if the observer is halfway between the flashes when they occur. Otherwise a number of different conclusions can be made depending on the exact configuration of lights and observer at the time of flipping the switch. $\endgroup$ – Asher May 5 '15 at 18:33
  • $\begingroup$ But that was exactly my point. Simultaneity is considered to be relative only in another frame moving w.r.t the frame of the events. If it is considered relative just due to the position of the events, then it would be relative even in the same reference frame as the events. Then it would always be relative regardless of motion of the frame of reference. But the events themselves do not become non-simultaneous. So should we call it as an observation error, or should we call it as relativity of simultaneity? $\endgroup$ – Khushro Shahookar May 5 '15 at 18:51
  • $\begingroup$ This breaks with a simple variant of Einsteins train and platform gedankenexperiment. If we rig things to cause the observers to be coincident when the flashes arrive then one measures different distances for the flash-generating events and concludes (correctly) that they were not simultaneous. $\endgroup$ – dmckee May 5 '15 at 19:01
  • $\begingroup$ Khushro Shahookar: "[...] switch placed at the mid-point X of two event locations A and B" -- This seems mistaken. Einstein's coordinate-free defintion of (how to determine) "simultaneity" is mentioning the "mid-point between" two suitable participants ("material points": elements of an "embankment"); not "between event locations". $\endgroup$ – user12262 May 5 '15 at 20:25
  • $\begingroup$ What if the event locations ie lamps are at material points such as embankment points A and B, and the switch is at the mid-point of the material (embankment) points A and B? For the apparatus on the train, A, B and X would be material points on the train, such as train end=points and mid-point. How would this change any of the above logic? $\endgroup$ – Khushro Shahookar May 6 '15 at 4:44
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Let's take case a) first.

They will also be determined (see Einstein's method below) as simultaneous from ground - they have to be because as seen from the ground, both lamps are activated by the same switch, and as measured by a clock on the ground, both lamps produce the flash after the same delay for A and B, since the construction of both is identical.

That is not so, according to special relativity. When you say "the construction of both is identical", I take it is supposed to follow that the wires that connect the switch from A to B are the same length. However, length is frame dependent, according to special relativity -- "identity of construction" does not prevent the lengths from being different in different frames of reference.

Let A be the light in the opposite direction from the switch as the direction of travel of the train, and let B be the light in the same direction away from the switch as the direction of travel of the train. If the wires are the same length in the frame of reference of the train, then, from the ground's frame of reference, the wire to A is shorter than the wire to B, and, in the frame of reference of the ground, the signal takes less time to reach A then to reach B, and A produces a flash before B does.

Your case is actually not different in any significant way from Einstein's original train case; in both cases, a signal passes from the middle of the carriage to the ends of the carriage, and the description of events from the train, as compared with description of events from the ground, is precisely analogous in both cases.

Now b):

We note that even in a single frame of reference, only the observer at the correct location can determine the events to be simultaneous. Observers at A or at B or at any other location cannot make that determination

That's not true. What is true is that an observer will determine two events where the light reaches her simultaneously (in her frame of reference) to in fact be simultaneous if and only if she is the same distance from both events (in her frame of reference). But an observer is perfectly capable of accounting for differences in times the light takes to reach her from different distances, and determine which events are simultaneous in her reference frame even when the events are at different distances in her reference frame. Astronomers do this all the time.

The only reason that Einstein's thought experiments involve observers that are equidistant from the relevant events is because such cases are relatively simple to reason about; it adds irrelevant complication to make the events be at different distances from the observer.

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  • $\begingroup$ Your answer does not seem to be correct. Both the wires from the switch to A and B are parallel to the length of the train. To the observer on the ground, both will look SHORTER if the apparatus is on the train - length contraction, not length expansion. There is NO reason for one wire to be shorter than the other wire. SO the flashes of light must look simultaneous to both the observer on the train and on the ground, because both see the same apparatus with equal length wires. $\endgroup$ – Khushro Shahookar Mar 18 at 17:10
  • $\begingroup$ For answer (b), you say that the observer is capable to determine how much time light takes to reach him from different distances and so determine whether the events are simultaneous or not, but that is exactly what Einstein did not do in his experiment. The observer on the train was closer to A than to B, so he saw the flash A first and flash B later, so he falsely concluded that A and B do not appear to be simultaneous in his frame. Actually they did not appear simultaneous to HIM because he did not calculate how much time light would take to travel the different distances from A and from B $\endgroup$ – Khushro Shahookar Mar 18 at 17:17
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One way to understand how simultaniety can be relative is to understand the theory of general relativity. I already described how the theory of general relativity works here. The train must run at less than 8 km/s in order for the observer in it to stick to the ground but even at that speed, there are still some relativistic effects. Because the train does not change height, special relativity can be used to describe what the person in the train observers and special relativity predicts that the person in the train has no way to tell that the train isn't still and Earth moving with the lights actually having lit at a different time, and that if the apparatus is mounted on the train, the lights will light at the same time in the frame of reference of the train and not in the frame of reference of Earth.

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