Question

Imagine a boxcar with a lamp on the left end and a mirror on the right end, so that a light signal can be sent down and back. The boxcar is moving to the right with velocity v. They find the length of the boxcar with respect to the car itself and then with respect to an observer on the ground using time dilation. They use the round trip time, which is fine and makes sense. However, what if you don't use the round trip time. What if you just measure the distance and time it takes light to travel to the end of the boxcar and thats it. For an observer on the car, it would be t'=d'/c. For an obser

Answer 1

Imagine a boxcar with a lamp on the left end and a mirror on the right end, so that a light signal can be sent down and back. The boxcar is moving to the right with velocity v. They find the length of the boxcar with respect to the car itself and then with respect to an observer on the ground using time dilation. They use the round trip time, which is fine and makes sense. However, what if you don't use the round trip time. What if you just measure the distance and time it takes light to travel to the end of the boxcar and thats it. For an observer on the car, it would be t'=d'/c. For an observer on the ground, it would be the distance he measures the boxcar to be plus how much the boxcar has progressed in time t. So for him it would be t=(d+vt)/c. Now, if you use the fact that lorentz contraction says that d' and d should be related by d'=(gamma)*(d), and plug d into the time it takes the light to reach the end according to the observer and relate t to t', you do not get the time dilation relationship. You actually just get t=(t')*((c+v)/(c-v))^(1/2). This is a problem because t and t' should be related by gamma, not this other factor. I thought the time it takes for light to travel to the end in the frame of the car should be related by gamma to the time it takes to rwach the end in the frame of the ground. Can you please explain why this is not so?