Joined: 21 May 2011
|Posted: Sat May 21, 2011 5:54 pm Post subject: Understanding Light Clocks
|The following is original, not homework, written to describe the problem I'm having with the Light Clock thought experiment.
The following experiment is performed separately by both Jim and Steve: A light clock in which light bounces horizontally is set into vertical motion and observed. Jim and Steve agree on both the distance and time for which to measure the experiment, but use different speeds for the light clock. The image below describes their observations.
Now they try to reconcile their results. Steve notices two things: first, that postulating time dilation would make the number of 'bounces' in their data agree, and second, that length contraction was necessary to make their 'slopes' agree. The ratio of the slopes in their data was equal to the ratio of the length contraction in their experiments, and the ratio of the number of bumps in their data was equal to the ratio of the time dilation in their experiments.
Now equipped with the values for both time dilation and length contraction, they each perform the same experiment, only this time the light in the light clocks bounces vertically. They use the same speeds, times, and distances that were used in the first experiment. This time, they were unable to reconcile their results. Steve noticed the following: the light took longer to reach the next 'bounce' when moving away from the observer than it did when it was moving towards the observer. He also noticed that Jim's data could not be stretched or shrunk to match his results.
(vertical position V time)
The problem was the following: Jim's data had longer upward distance and shorter downward distance than Steve's. So shrinking Jim's data would reconcile their upward distances, but not their downward distances, and stretching Jim's data would reconcile their downward distances, but not their upward distances.
What was the error in their reasoning? How can their data be reconciled?
I am assuming time dilations and length contractions occur consistently. The presence of the light clocks should aid in figuring out how time and space are effected, but the effects themselves do not depend on the orientation of the clocks, or their presence.
Also, please note that I'm not good at physics. There are probably other ways to set up the experiment to make things more clear, but please try to stick as closely as you can to what I've described. I ask this because what I've written is the best way I've found to understand this material. Starting from a completely different approach, I would still feel uncertain/confused until I found the errors in what I've already written.
Thank you for your help, it is much appreciated.