Time dilation yes, why no contraction?

fatdad

The example I have read to show time dilation is that of a light clock on a train. Two mirrors are one metre apart. Light is beamed from the first mirror to the second. An observer on the train sees that it takes the amount of time for light to travel 1m for the light to reach the second mirror. T a second observer at a train station, the light travels more than 1m, as the train, and thus the second mirror, has moved away from its original position between the light leaving the first mirror and hitting the second. As light speed is a constant, more time must pass for the observer on the platform than for the observer on the train in order to cater for the extra distance.

However, when the light rebounds from the second mirror to the first, while the observer on the train still perceives the light to travel 1m, for the observer on the platform, the light travels less than 1m as mirror one has moved closer to the point of the rebound (relative to the observer on the platform).

Where is the fault in my logic? It would seem that I am using the same arguments as those who thought that light travelled through "the ether". I can't see my error, however.

Doc Al

I don't understand why you think the platform observer would see the light travel less than 1m. According to him, the light going from mirror 2 back to mirror 1 takes a similar tilted (and longer) path as it did when going from mirror 1 to mirror 2.

Draw yourself a diagram of the light path as seen by the platform observers. (Realize that the line between the two mirrors of the light clock is oriented perpendicular to the direction of travel.)

fatdad

Thanks. I was confusedly thinking of the mirrors in the direction of travel.

Bill_K

It doesn't matter whether they are oriented parallel or perpendicular to the motion. It's the round trip time that counts, and this is where you'll see the effect of time dilation (same for all orientations).

Doc Al

While it's certainly true that time dilation will be exhibited regardless of orientation, the analysis of a parallel light clock is more involved than that of the usual perpendicular light clock.