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Old 09-18-2003, 11:14 AM   #4 (permalink)
CSflim
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Location: Ireland
Quote:
Originally posted by TIO
CSfilm, the thing that has always bothered me about the twins paradox is not that the stationary one gets older. I've done enough physics to see that, and I'm quite comfortable with time dilation.
The thing is, it seems to assume that the Earth is an inertial FoR. I don't see why the twin in the spaceship doesn't see the earth accelerate away from him, then fly around a bit and come back. From his FoR, shouldn't the Earth twin be 49 years younger?

For a more intuitive scenario (in that it doesn't appeal to our intuition that the Earth is an inertial FoR), what if the twins were both in rockets, and they both flew away from each other and back? What if one flew off and the other didn't?
Velocity is relative, acceleration isn't.

If we look at a spaceship with a constant velocity moving across the sky, we can say either:
a)The spaceship is moving relative to the earth
or
b)The earth is moving relative to the spaceship.

Both are correct. As far as people on the earth are concerned, they are static.
As far as the people on the spaceship are concerned, THEY are static.
If you carry out any experiment on board the moving spaceship, you will get precisely the same results, had yo performed it on board the "stationary earth".

However, accelearation is quite a different thing to constant velocity.
Acceleration requires a FORCE. Constant velocity does not. There is no force of motion acting on the spaceship, nor is there a force of motion acting on the earth(^1).

If you are now to imagine a spaceship accelerating across the sky, you cannot make the claim that the spaceship is stationary, and it is the earth that is accelerating. The force of motion is acting on the spaceship.
This can be objectively proven. If you carry out experiemtns on board the accelerating spaceship, you will get different results to what you would have expecting to get assuming the spaceship was stationary.

A simple analogy can be made as so:
When you are on a train, which is moving smoothly and constantly, you don't feel anything strange. You can get up, and walk around as normal. Walking towards the front of the train, feels the same as walking to the back of the train. Exactly as you would expect given a stationary train.
Now imagine that the train decelerates very rapidly (i.e. brakes) if you are not in your seat, you will be thrown off your feet! Not what you expect to happen while on an umoving train!

Hope that helps you to understand the difference between acceleration and constant velocity, and presumably, you can now apply it to your knowledge of time dialation, to fully understand the twin "paradox".

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1: Not strictly true, there is a centripedal force acting on the earth (Gravity of the sun), which causes an angular acceleration. But the earth remains at a constant linear velocity, which is what matters in this argument.
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Last edited by CSflim; 09-18-2003 at 11:52 AM..
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