I Relativity of simultaneity in actuality

[vibhuav]

I’m attaching two figures from the book, Basic concepts in relativity and QT, by Resnick and Halliday. They are describing the relativity of simultaneity from a theoretical pov, which I understand. Basically, the lightning strikes at AA’ and BB’ can be deemed simultaneous either in frame S, in which case they will not be simultaneous in frame S’, and vice versa. Only in one of the frames are the two events simultaneous, but not in both, and this claim of simultaneity can be done by either of them.

My question is, keeping aside these analysis on paper, IN REALITY, what would the two observers say about the times (two pairs of times, btw) of the lightning strikes when they meet up sometime later? Will their recorded times show simultaneousness in one of the frames, S or S’?

 

[Dale]

All of our experiments done to date over more than a century indicate that reality is accurately described by special relativity on a local scale.

 

[Ibix]

Note that the figures you've reproduced show two different experiments. In figure 2-1 the strikes are simultaneous in S, and if that experiment were carried out results would agree with that in reality. In figure 2-2 the strikes are simultaneous in S', and if this experiment were carried out results would agree with that.

Many people find it simpler to study an experimental setup where a lamp at the center of the train (or platform, or both) emit a flash when the center of the train passes the center of the platform. Receivers at the ends of the train and ends of the platform record the arrival times of the pulses. You can analyse which frame will regard which reception events to be simultaneous without worrying about the coincidence of lightning flashes. The implications are the same as the traditional Einstein train setup in your book.

 

[vibhuav]

Ah, I think I got it. I misinterpreted the statement that, with two frames in relative motion with each other, each can regard itself as being stationary and the other frame is moving, to be the “actual reality,” and therefore the two frames (and the two figures) are equivalent. But in REALITY, one of them is actually moving (frame S’ in fig 2.1 and S in fig 2.2) and the other is actually stationary. The observer in the stationary frame will report simultaneity and the observer in the moving frame reports non-simultaneity.

 

[PeterDonis]

in REALITY, one of them is actually moving (frame S’ in fig 2.1 and S in fig 2.2) and the other is actually stationary.

No, that's not correct.

What is correct is that the lightning strike events have a particular relationship in spacetime, and in any given scenario, they can only have one such relationship. And whatever that relationship is, it will only correspond to being simultaneous in one frame. In the first scenario, that's frame S. In the second, it's frame S'. But that doesn't mean either frame is "really at rest" or "really moving" in either scenario. All it means is that the two scenarios are describing two different relationships in spacetime between the two lightning strike events. That is the only difference IN REALITY between the two.

 

[Dale]

each can regard itself as being stationary and the other frame is moving, to be the “actual reality,” and therefore the two frames (and the two figures) are equivalent.

Yes.

in REALITY, one of them is actually moving (frame S’ in fig 2.1 and S in fig 2.2) and the other is actually stationary

No.

The observer in the stationary frame will report simultaneity and the observer in the moving frame reports non-simultaneity.

No. The flashes are simultaneous in at most one frame. That frame will report them as being simultaneous, others will not.

 

[Ibix]

I misinterpreted the statement that, with two frames in relative motion with each other, each can regard itself as being stationary and the other frame is moving, to be the “actual reality,” and therefore the two frames (and the two figures) are equivalent.

The two frames are equivalent - either may regard itself as "at rest" and the other as moving. The two figures are not - they are showing different experiments, one where the light arrived simultaneously at O and one where it arrived simultaneously at O'.

Students often seem to struggle to accept that "two things happened at the same time" can be a frame dependant statement. Nevertheless, it is the truth. The exception is two things happening at the same time and place, such as two cars reaching a certain point at the same time, because this has immediate physical consequences (a crash)

Look at figure 2-1. You can see in figure 2-1(c) that the light arrives simultaneously at O. The observer there knows that the flashes were emitted from the ends of the train, equidistant from him. He received them simultaneously and he knows that the speed of light is always $c$ as measured by any observer (including himself). Hence he may conclude that the pulses were emitted simultaneously. O', however, did not receive the flashes simultaneously (see 2-1(b) and (d)) but also knows that they were emitted from the ends of the train equidistant from him, and that the speed of light is always $c$ as measured by any observer (including himself). He must therefore conclude that the pulses were emitted non-simultaneously.

Notice that this is all an immediate consequence of the two postulates of relativity. Thus we must accept that if those two postulates are correct, simultaneity is not an absolute concept but depends on your choice of frame.

 

[PeroK]

I’m attaching two figures from the book, Basic concepts in relativity and QT, by Resnick and Halliday.

Just to note that, in my opinion, that way of teaching/demonstrating the relativity of simultaneity is extremely clumsy, with several extraneous and potentially ambiguous elements.

My advice is to find a much simpler explanation, such as the one given by Morin in his introductory book.

 

[A.T.]

Many people find it simpler to study an experimental setup where a lamp at the center of the train (or platform, or both) emit a flash when the center of the train passes the center of the platform.

I like this video:

 

[cianfa72]

You can see in figure 2-1(c) that the light arrives simultaneously at O. The observer there knows that the flashes were emitted from the ends of the train, equidistant from him. He received them simultaneously and he knows that the speed of light is always $c$ as measured by any observer (including himself). Hence he may conclude that the pulses were emitted simultaneously. O', however, did not receive the flashes simultaneously (see 2-1(b) and (d)) but also knows that they were emitted from the ends of the train equidistant from him, and that the speed of light is always $c$ as measured by any observer (including himself). He must therefore conclude that the pulses were emitted non-simultaneously.

Note the following: O' is at rest in S' frame and can use S' coordinates to locate events. Now when lightning strike both ends of the train (simultaneously w.r.t. observer O) they mark off two spots on the railway tracks. O' knows they are equidistant from him (since O' coincides with O when lightning strike simultaneously w.r.t. O).

 

[anuttarasammyak]

@vibhuav The author explains these figures from the perspective of S (or S′). Therefore, there is a possibility that readers may misunderstand these figures as referring to the same event.　A pair of lightnings which are simultateous in S and not so in S' and another pair of lightnings which are simultateous in S' and not so in S are different events. Same naming of contact points, i.e., O-O', A-A', B-B' helps misunderstanding.