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Time Dilation - How does it know which Frame of Reference to age slower?

This has bugged me for years.

According to the theory of relativity, the faster an object moves, the slower time goes for that object, relative to a stationary observer.

However, it is my understanding that motion is necessarily relative to a frame of reference. If you have two objects in space moving away from each other at a combined velocity of 20mph, the rate at which each is moving is totally conditional on what frame of reference you specify.

  1. If object A is your frame of reference, than object A is moving at 0mph, and object B is moving at 20mph.
  2. If object B is your frame of reference, the opposite is true.
  3. If something else is your frame of reference, then the two objects will have some other two velocities, which, when summed, equal 20mph.

If this is true, how does physics know how much to slow down time for each object? It's as if they don't actually have set velocities.

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Related: physics.stackexchange.com/q/6147/2451 –  Qmechanic Mar 20 '12 at 15:45
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Welcome to Physics.SE! This looks like a pretty good match for the question that Qmechanic found and I'm going to close it for the nonce. @Nathan, if you the answers to that question don't help you can edit this one to be a specific follow on and flag it for moderator attention, we should be able to re-open if you make the distinction clear. –  dmckee Mar 20 '12 at 16:55
    
Thank you, @dmckee! I guess I'm just a bit out of my league here. Both the answers here and the answers on the linked-to thread don't really make sense to me, though @John Rennie's answer was much easier to follow than anything in the other question. =P –  Nathan Arthur Mar 20 '12 at 18:12
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marked as duplicate by Qmechanic, dmckee Mar 20 '12 at 16:56

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You're quite correct that motion is relative. I suspect that what is catching you out is that you think time must behave differently in frame A and frame B i.e. there is some absolute sense in which it's slower in the moving frame and faster in the stationary frame.

Suppose you're sitting in frame A watching me in frame B. As far as you are concerned you're stationary so time moves at the normal rate. However you see me moving, so you see time moving slowly for me.

But now look at it from my point of view. As far as I'm concerned I'm the stationary one, and you're the one who's moving. That means my time moves at the normal rate and I see your time running slowly.

This means the situation is symmetrical. Each of us sees our time move as normal and the other person's time slow down. Actually it has to be this way because if the situation wasn't symmetrical there would be a way to assign absolute motion i.e. one frame would be different to the other.

The third observer (I assume you mean he sees us both moving with equal but opposite velocities) see both your and my time slow down. Likewise we both see his time slow down.

In general you need to very careful with intuitive arguments about relativity, because it's unintuitive. The only safe way to work out what is going on is to use the Lorentz tranformation (http://en.wikipedia.org/wiki/Lorentz_transformation) to work out the difference between different frames.

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This might help: link –  Csources Aug 31 '12 at 19:35
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