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I have done a lot of reading on relativity of simultaneity on this site and elsewhere, and still cannot figure out the following:

Relativity principle: No experiment can reveal the absolute motion of the observer.

Einstein's train: "Hence the observer (on the train) will see the beam of light emitted from B earlier than he will see that emitted from A"

https://www.bartleby.com/173/9.html

Now, please explain me the following: Let's replace two lightning bolts with two light bulbs at points A and B attached to the ceiling of the train. And the traveler on the train, located in the middle of A and B, has a switch that can turn these bulbs On and Off. Same thing as lightning bolts hitting A and B, agreed? Or NOT? (If disagreed, please explain the principal difference).

So - with this setup, a traveler can easily conduct and experiment, within his own reference frame, that will reveal his motion. He simply turns the bulbs On.

  • If he sees both flashes at the same time, then he is not moving.
  • If he sees flashes at different times, then he is moving.

What am I missing here?

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  • $\begingroup$ I think you have to remember that this experiment is only useful if we compare the observer on the train with an observer at the station. So while one of them might see the lights simultaneously (in this case the observer on the train) the observer at the station will not. $\endgroup$ Aug 26, 2021 at 15:57
  • $\begingroup$ In Einstein's train, it's the opposite - observer on the station sees the lights simultaneously; on the train - at different times. $\endgroup$ Aug 26, 2021 at 16:03
  • $\begingroup$ that's just one example used. It would be easy to set up the exact opposite situation. The point of the thought experiment is to show that a stationary observer and a moving observer will always see different timing of the lightening flash, and both of them are "correct". $\endgroup$ Aug 26, 2021 at 16:25
  • $\begingroup$ The proposed experiment will always produce the same outcome, regardless of the speed of the train. $\endgroup$
    – Dale
    Aug 27, 2021 at 0:17

4 Answers 4

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If the bulbs are attached to the train, and if the observer is at the middle of the train, and if the observer turns them on simultaneously in the frame of the train, then the observer will always see the light arriving from the bulbs simultaneously, regardless of the motion of the train.

The point is that either the events are simultaneous in the frame of the train, or they are simultaneous in the frame of the platform- they cannot be both. It does not matter whether the events are lighting strikes or the turning on of light bulbs- if the lightening strikes were simultaneous in the frame of the train, then the person in the middle of the train would see them at the same time.

If you just consider lightning strikes, there are two possibilities. One is that the lightning strikes the two ends of the train simultaneously in the frame of the train, in which case the person in the middle will see both flashes together, or the lightning strikes simultaneously in the frame of the platform, in which case the person on the train will see one strike before the other.

Likewise with the bulbs. Either the bulbs can be switched on simultaneously in the frame of the train, in which case the person on the train will see them happening together, or they can be switched on simultaneously in the frame of the platform, in which case the person on the train will see the forward bulb lighting ahead of the rear one.

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  • $\begingroup$ Indeed, the key here is in what frame you define "simultaneous". A person who sees non-simultaneous flashes knows they are in a different frame from that, but neither frame is preferentially "at rest". $\endgroup$ Aug 26, 2021 at 17:50
  • $\begingroup$ @Marco Ocram Marco, that's exactly what I thought and that's the reason I wrote up that question. But Einstein says: "Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A". So - light bulbs attached to the train are fundamentally different than lightning bolts? Can you explain why? $\endgroup$ Aug 26, 2021 at 19:38
  • $\begingroup$ @user1390208 You're quoting a thought experiment my answer addressed, in which the lights aren't on the train. When they are on the train, they're in your rest frame. $\endgroup$
    – J.G.
    Aug 26, 2021 at 20:22
  • $\begingroup$ @J.G. My question is ONLY about the case when lights are on the train. So according to Marco's answer, the observer on train will see lights at the same time. So why he would see lightning bolts at different times? I asked that in the comment to your answer as well. $\endgroup$ Aug 26, 2021 at 20:57
  • $\begingroup$ the point is that either the events are simultaneous in the frame of the train, or they are simultaneous in the frame of the platform- they cannot be both. It does not matter whether the events are lighting strikes or the turning on of light bulbs... $\endgroup$ Aug 26, 2021 at 20:59
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Your setup assumes the bulbs' locations are stationary, and hence in the same rest frame, and your experiment tells whether they're in your rest frame. We could do something similar with the Doppler effect, which only requires one light source. (This saves us "if you're moving, do the on/off signals take the same time to arrive?" quibbles.) But what you're missing is this doesn't reveal your absolute motion, because it only reveals your motion relative to the bulbs.

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  • $\begingroup$ I edited my question, articulating that light bulbs are attached to the ceiling, i.e. they move with the train. So I don't understand your answer, unfortunately. $\endgroup$ Aug 26, 2021 at 16:04
  • $\begingroup$ @user1390208 That's a completely different question. The effect you claim you would observe doesn't even occur in that scenario. $\endgroup$
    – J.G.
    Aug 26, 2021 at 16:54
  • $\begingroup$ Please explain why it wouldn't occur. Einstein says: "Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A". So - light bulbs attached to the train are fundamentally different than lightning bolts? Can you explain why? $\endgroup$ Aug 26, 2021 at 19:40
  • $\begingroup$ @user1390208 Sorry, I've just realized my reply to this ended up under Marco Ocram's answer. $\endgroup$
    – J.G.
    Aug 26, 2021 at 21:06
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This experiment will reveal whether or not an observer is moving relative to the bulbs, but not whether or not he is moving in an absolute sense. Suppose the entire system is loaded on an even larger train that's moving in the opposite direction - the two observers in the original scenario can't even tell they're on a second train - they see exactly what they did before (simultaneous or non-simultaneous flashes), despite the fact that their absolute velocities have changed. We know that the two observers are moving differently with respect to the bulbs, but we can't say that one is moving in an absolute sense and the other is not - there is no universal absolute reference frame which is "at rest".

One thing to note is observers who move relative to one another will disagree about the simultaneity, but that doesn't indicate which one of them witnesses simultaneity. In the original problem, we defined simultaneity in the non-train frame and therefore see non-simultaneity in the train fame. But we could just as easily change the timing so that the train observer sees simultaneity and the non-train observer sees non-simultaneity. If we define simultaneity in the "rest" frame, non-simultaneity means we're not at rest, but that depends entirely on your original arbitrary choice of in what "rest" frame to define simultaneity in the first place! Instead of the train and a station, one of which is sort of intuitively (but falsely) "at rest", consider two observers on space ships moving relative to one another (it's the exact same problem) - there is no preferred choice of which ship to define as the "at rest" ship which sees simultaneity.

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  • $\begingroup$ You are saying: "This experiment will reveal whether or not the observer is moving relative to the bulbs"! But the bulbs are attached to the ceiling of the train! An observer on the train does NOT move relative to the bulbs! Right? $\endgroup$ Aug 26, 2021 at 16:09
  • $\begingroup$ @user1390208 Right, the observer on the train can discern that he is not moving relative to the bulbs. An observer not on the train can discern that he is moving relative to the bulbs. That only tells you relative motion between observers and bulbs. The experiment does not tell you anything about the absolute motion of either observer. $\endgroup$ Aug 26, 2021 at 16:10
  • $\begingroup$ I am talking about observer ON the train. What's wrong with my statement that if he sees flashes at different times, he can say "I am not at rest, I am at motion!" ? $\endgroup$ Aug 26, 2021 at 16:13
  • $\begingroup$ @user1390208 Well, he'd need to compare to someone not on the train in the first place. Seeing bulbs flash at different times may just mean they're different distances apart, only when he notes the differences in simultaneity from another observer not on the train can he reason about motion. Suppose the train itself is on an even larger train going the other way - the observer on the train still notes the exact same difference in simultaneity despite having different absolute motion. You can only have motion with respect to something. $\endgroup$ Aug 26, 2021 at 16:19
  • $\begingroup$ @user1390208 In this case, the train observer notices differences in simultaneity between himself and the non-train observer. There is relative motion between them. If there's another train going down a parallel track with another observer, the two train observers will see no difference in simultaneity and conclude no relative motion between them. Non simultaneity only indicates motion if you can compare it to a reference frame where things are simultaneous. I think you're implicitly comparing to the non-train frame with the knowledge that the flashes "should" be simultaneous. $\endgroup$ Aug 26, 2021 at 16:22
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So - with this setup, a traveler can easily conduct and experiment, within his own reference frame, that will reveal his motion. He simply turns the bulbs On.

If he sees both flashes at the same time, then he is not moving.
If he sees flashes at different times, then he is moving.

The more accurate way to put it would be
If he sees both flashes at the same time, then he is not moving, relative to the bulbs
If he sees flashes at different times, then he is moving, relative to the bulbs

So, he can only figure out whether or not he is moving relative to the bulbs. He can still never figure out whether or not he is undergoing any kind of absolute motion . In fact, there IS no such thing as absolute motion in relativity.

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