# Forgive my ignorance

1. Feb 9, 2004

### Bigniko

I am attemting to help my son with a Physics problem, and it has been 20 years since my last Physics class. I would be most appreciative if someone could give me a quick refresher. Here is the problem. I am sure it will all come back to me.

Two clocks are positioned on the front and rear of a train with proper length L0 moving at a velocity v with respect to the ground. They are synchronized in the frame of reference of the train.

(a) Using only Einstein’s postulates, find the difference in their readings as viewed by an observer at rest on the ground.
(b) Check your answer by deriving the same result using the Lorentz transformation equations.
(c) What is the maximum time difference that could be measured for a 100 m train? What is the physical significance of this time?

I'll give you some equations...

g = 1/(1 - v²/c²)½
this is the gamma factor

L0 = gL
where L0 is the proper length (the length of the object at rest with respect to the reference frame) and L is the length of an object moving with respect to the reference frame.

x' = g(x - vt)
y' = y
z' = z
t' = g(t - vx/c²)
Lorentz transformations. x, y and z are the coordinates of an object at rest for the frame of reference. x', y' and z' are for an object moving with respect to that frame of reference.

and Einstein's postulates

1. The speed of light is the same for all observers in all frames of reference. It is a universal constant (equal to 300 000 000 m/s).
2. The laws of physics hold under all frames of reference.
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