How Do Relativity Principles Apply to Moving Clocks on a Train Platform?

[neutrino]

Homework Statement

A train passes a platform with velocity v. Two clocks are placed on the edge of the platform separated by a distance L and synchronized relative to the platform inertial system. Clock 1 reads 4:00 when it coincides with the front of the train, and clock 2 reads 4:00 when it coincides with the rear of the train. Answer questions relative to an observer on the train. [Emphasis mine]

(a) What is the length of the train?

(b) What is the reading of the clock 2 when clock 1 coincides with the front of the train?

(c) What is the time interval between the two end events?

Homework Equations

Lorentz Transformations

The Attempt at a Solution

Before answering a, b and c, I actually need to understand this question. Here are my qualms:

1. If the part of the question in bold refers to observations from the platform frame, then I don't understand how the clocks can be synchronised. The clocks read 4:00 at different times(events).

2. If it refers to observations from the train, then it seems to me to be in contradiction with what the author says a few pages earlier. It is proved that given a pair of clocks, which are synchronised in a frame in which they are at rest, moving in the the same direction and separated in space, the leading clock lags behind the trailing one(the exact amound being Lv/c², L- measured distance between clocks). If that is true, then howcome clock 1(leading clock) reads 4:00 before clock 2(trailing).

What am I missing?


For those interested, this is problem 2.4 from Richard Mould's Basic Relativity (Springer).

 

[nrqed]

Homework Statement

A train passes a platform with velocity v. Two clocks are placed on the edge of the platform separated by a distance L and synchronized relative to the platform inertial system. Clock 1 reads 4:00 when it coincides with the front of the train, and clock 2 reads 4:00 when it coincides with the rear of the train. Answer questions relative to an observer on the train. [Emphasis mine]

(a) What is the length of the train?

(b) What is the reading of the clock 2 when clock 1 coincides with the front of the train?

(c) What is the time interval between the two end events?

Homework Equations

Lorentz Transformations

The Attempt at a Solution

Before answering a, b and c, I actually need to understand this question. Here are my qualms:

1. If the part of the question in bold refers to observations from the platform frame, then I don't understand how the clocks can be synchronised. The clocks read 4:00 at different times(events).

what's the problem? This just means that the two clocks are simultaneously (in the frame of the platform) aligned with the front and back of the train.
That's all.

(this means that the distance between the two clocks (mesured in the frame of the platform) gives the length of the train as measured in the frame of the platform)

I don't understand your objection. The two events are different but they occur at the same time (in the frame of the platform). There is no problem with that.

Regards

 

[George Jones]

Before answering a, b and c, I actually need to understand this question.

I assume that a, b, and c all deal with quantities measured in the frame of the train.

Here are my qualms:

1. If the part of the question in bold refers to observations from the platform frame, then I don't understand how the clocks can be synchronised. The clocks read 4:00 at different times(events).

(Edit: As nrqed has said,) In the frame of the platform, the front passing clock 1 and the rear passing clock 2 are simultaneous events (i.e., they happen at the same time) that happen at different places in space.

2. If it refers to observations from the train, then it seems to me to be in contradiction with what the author says a few pages earlier. It is proved that given a pair of clocks, which are synchronised in a frame in which they are at rest, moving in the the same direction and separated in space, the leading clock lags behind the trailing one(the exact amound being Lv/c², L- measured distance between clocks). If that is true, then howcome clock 1(leading clock) reads 4:00 before clock 2(trailing).

This applies to the times of the clocks as observed in the frame of the train, not as observed in the frame of the platform.

It might help to draw a spcetime diagram with, say, the platform frame unprimed and the train frame primed. In my diagram, I took clock 2 to be the spatial origin of the unprimed frame, and clock 1 to have a spatial position x = L. I took the back of the train to be at the spatial origin of the primed frame.

Now, draw a spacetime diagram that shows the worllines of clock 2, clock 1, back of train, front of train. What are the important events on this diagram?

 

[neutrino]

*Slaps forehead*

I think this confusion arose because I numbered those clocks differently.

In my diagram, I took clock 2 to be the spatial origin of the unprimed frame, and clock 1 to have a spatial position x = L. I took the back of the train to be at the spatial origin of the primed frame.

Put clock 1 at the origin of the platform frame and let the front end of the train, moving to the right, meet it at 4:00, and then you'll see why I was confused. Thanks, guys. Your help is much appreciated.