Confused over Lenght Contraction.

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• March 24th, 2011, 03:37 PM
kojax
Confused over Lenght Contraction.
The lack of a reference frame makes length contraction incredibly crazy. If two objects are moving toward each other, there's no way to say that one is moving slower and the other is moving faster. We can't say that because there is no absolute reference frame. Each is measuring the others' speed relative to itself.

If there were an absolute reference frame, and both were moving in the same direction, but one were moving faster than the other, we would observe that the faster moving object had its length contracted more than the slower moving object. But if they were both moving at the same speed in opposite directions relative to that absolute frame, then their lengths would both be contracted by the same amounts, and they would both observe each other to be their normal length. ....but of course there is no absolute reference frame.

Since we don't have an absolute reference frame, my question is: what does object #1 observe object #2's length to be? Does the distance between them also appear to conform to this observation, or does the fact the distance is changing make things complicated?
• March 24th, 2011, 04:32 PM
mathman
Length contraction, as well as effect on mass and time, is defined by the reference frame. Essentially, define yourself as a "rest" frame, then any object moving with respect to you will be seen by you to have a length contraction. An observer in the moving frame will see objects in your frame undergoing a similar length contraction.
• March 24th, 2011, 04:40 PM
Janus
Re: Confused over Lenght Contraction.
Quote:

Originally Posted by kojax

Since we don't have an absolute reference frame, my question is: what does object #1 observe object #2's length to be?

length contracted by the factor determined by their relative velocity to each other. Note that you can find this relative velocity by using the additions of velocities theorem:

Thus if observer 1 is moving at 0.5c in one direction relative to some reference frame and observer 2 is moving at 0.5c in the opposite direction relative to the same frame, then observer 2 is moving at 0.8c relative to observer 1 and is length contracted by a factor of 0.6.
Quote:

Does the distance between them also appear to conform to this observation, or does the fact the distance is changing make things complicated?
The distance between them for each observer is just a matter of their relative velocity and the difference in time between the moment they meet and when you measure want to know the distance. In other words, if they meet when observer 1's clock reads any given time, then 1 sec earlier or later they will be 0.8 light seconds apart according to his clock.