Question on special relativity from "Basic Relativity"

[Ibix]

[Sorry for the late reply]

In any case for part b) there was no given event to transform.

Sure there is - the event is the one on the worldline of clock 2 that is simultaneous in the train frame with clock 1 reading 4:00. Taking 4:00 on clock 1 to be the shared origin, we know that this event has the same $t'$, so $t'=0$ and we know that the length $L$ platform is length contracted to $L/\gamma$ in this frame so $x'=-L/\gamma$. We just need to calculate $t$ for this event and relate that to 4:00.

 

[PeroK]

[Sorry for the late reply]

Sure there is - the event is the one on the worldline of clock 2 that is simultaneous in the train frame with clock 1 reading 4:00. Taking 4:00 on clock 1 to be the shared origin, we know that this event has the same $t'$, so $t'=0$ and we know that the length $L$ platform is length contracted to $L/\gamma$ in this frame so $x'=-L/\gamma$. We just need to calculate $t$ for this event and relate that to 4:00.

Isn't that equivalent to deriving the "leading clocks lag" rule in the first place? I don't see that every time you have the scenario of synchronised moving clocks, then you go back to the derivation from first principles.

 

[Ibix]

Isn't that equivalent to deriving the "leading clocks lag" rule in the first place? I don't see that every time you have the scenario of synchronised moving clocks, then you go back to the derivation from first principles.

I find the Lorentz-every-time approach easier than remembering rules derived from it. I appreciate that not everyone agrees.

 

[Chestermiller]

I find the Lorentz-every-time approach easier than remembering rules derived from it. I appreciate that not everyone agrees.

I agree with you. BTW, doesn't the problem statement say that, in the platform frame of reference (and the clocks are at rest in this frame), the front of the train passes clock 1 at 4:00 and the rear of the train passes clock 2 at 4:00. Don't these same readings have to be on the ground clocks, as observed by train observers at the front and rear of the train, when the front of the train passes clock 1 and the rear of the train passes clock 2?

 

[PeroK]

Don't these same readings have to be on the ground clocks, as observed by train observers at the front and rear of the train, when the front of the train passes clock 1 and the rear of the train passes clock 2?

These are spacetime events. They need no specific observer.

The physics is the same whether there is anyone on the train or not.

 

[Ibix]

Don't these same readings have to be on the ground clocks, as observed by train observers at the front and rear of the train, when the front of the train passes clock 1 and the rear of the train passes clock 2?

Yes. But the question is what time does clock 2 show when the front of the train passes clock 1 according to the train observer, and "front passes 1" and "rear passes 2" are only simultaneous in the platform frame.

 

[Chestermiller]

Yes. But the question is what time does clock 2 show when the front of the train passes clock 1 according to the train observer, and "front passes 1" and "rear passes 2" are only simultaneous in the platform frame.

Sorry. I guess I mis-read or mis-interpreted the question.

 

[kumusta]

I wonder if this drawing of the moving platform seen fom the top would help solve the problem in this thread.