Question about relativity of simultaneity

[AlonsoMcLaren]

In the train example that supposedly shows the relativity of simultaneity, why, in the frame of the observer on the ground, the "midpoint" of the train in the train's frame is still the midpoint?

Does it have anything to do with Lorentz contraction? If so, there might be some circular reasoning here as Lorentz contraction is usually later than relativity of simultaneity in a textbook.

 

[Doc Al]

In the train example that supposedly shows the relativity of simultaneity, why, in the frame of the observer on the ground, the "midpoint" of the train in the train's frame is still the midpoint?

Not sure what you mean. The midpoint of the train is a point on the train. That fact is independent of reference frame. (Just like the end of the train is still the end of the train, no matter who is watching.)

 

[Dale]

why, in the frame of the observer on the ground, the "midpoint" of the train in the train's frame is still the midpoint?

I am not clear what you are asking. The embankment observer is at the midpoint between the flashes in the embankment frame. The train observer is at the midpoint between the flashes in the train frame. Neither stays at the midpoint for more than an instant in the others frame.

 

[AlonsoMcLaren]

I am not clear what you are asking. The embankment observer is at the midpoint between the flashes in the embankment frame. The train observer is at the midpoint between the flashes in the train frame. Neither stays at the midpoint for more than an instant in the others frame.

On "six ideas that shaped physics" p.43 the author says

"The observer in the Home Frame (ground) will agree that the right and left clocks in the Other Frame (train) are always equidistant from the center clock in the Other Frame,"

I don't understand why. Are we in a position to be sure about this before learning Lorentz contraction? Before we learned about Lorentz contraction, how can we have any clue about the distance between the right clock and the center clock (and the distance between the left clock and the center clock) as observed from the Home Frame(ground)?

 

[Mister T]

In the train example that supposedly shows the relativity of simultaneity, why, in the frame of the observer on the ground, the "midpoint" of the train in the train's frame is still the midpoint?

Are you looking at the version where the flashes are emitted from the center, or received at the center?

 

[Doc Al]

"The observer in the Home Frame (ground) will agree that the right and left clocks in the Other Frame (train) are always equidistant from the center clock in the Other Frame,"

How about this equivalent restatement: Everyone agrees that the midpoint of the train is equidistant from the ends of the train in the train frame.

 

[Doc Al]

Before we learned about Lorentz contraction, how can we have any clue about the distance between the right clock and the center clock (and the distance between the left clock and the center clock) as observed from the Home Frame(ground)?

Aren't these clocks on the train?

 

[sweet springs]

I don't understand why. Are we in a position to be sure about this before learning Lorentz contraction?

Homogenity is underlying in the theory. If something changes, the change is homogeneous in the front half and back half of the train.
Such a case that only front half is contracted or only back clock is delayed does not take place. This assures that the middle point remains middle in transformation.

 

[Dale]

"The observer in the Home Frame (ground) will agree that the right and left clocks in the Other Frame (train) are always equidistant from the center clock in the Other Frame,"

Hmm, that is indeed a very confusing quote. I am not sure what the author is trying to convey. If this quote is indicative of the writing in the rest of the book then I would recommend looking for some other learning material.

Are we in a position to be sure about this before learning Lorentz contraction? Before we learned about Lorentz contraction, how can we have any clue about the distance between the right clock and the center clock (and the distance between the left clock and the center clock) as observed from the Home Frame(ground)?

Length contraction is a derived result in most formulations of SR. Typically you would start with the two postulates, derive the Lorentz transform, and then use that to derive time dilation, length contraction, and the relativity of simultaneity. Alternatively you can start with the spacetime metric or with some basic symmetry assumptions. Either way you would derive the Lorentz transform from those assumptions, and then derive the relativistic effects.

 

[FactChecker]

Assume any length contraction, if it existed, would be uniform. Then all reference frames will agree on which point is the midpoint between the two end points. They will only disagree on the distance from that midpoint to the ends. With that assumption, the equations can be worked out and they agree with experimental results. The assumption is a very natural one to make. The logic is not "circular". In fact, the relativity of simultaneity explains the Lorentz contraction without assuming that it exists at all.

 

[peety]

The platform observer agrees with the train observer that the distance from the midpoint to the right-hand end is equal to the distance from the midpoint to the left-hand end but because she sees this midpoint moving towards the flash at the right end she observes that it has less far to travel to reach that end. The flash from the left end has further to travel to catch up with the midpoint. Both agree that the midpoint is the midpoint, but the train observer thinks it is stationary while the platform observer thinks it is moving.