# Relativistic time dilation / length contraction [duplicate]

I follow that time dilates / distance contracts as you move faster, but sees anomalies in what happens when you slow down again. The time changes are supposedly permanent, with an identical twin ageing a lot more than the twin brother in a rocket accelerating to relativistic speeds... The problem is: Suppose we send the one twin (call him the astronaut-brother) up in a rocket, circling the earth for a day, going close enough to light-speed so that supposedly fifty years pass for the ground-logged twin. Now the rocket slows down and lands. The astronaut brother supposedly finds his brother fifty years older than himself!

BUT we know during this process only one day passed for the observer (ground-logged brother). I don't see how the astronaut-brother can possibly find his twin, tens of years older in this scenario, once they're reconciled back in the same time frame?

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• Your "paradox" has nothing to do with relativity and everything to do with the fact that you made two contradictory assumptions -- "fifty years pass for the ground-logged twin" and "only one day passed for the ground-logged brother". Here's a simpler version of the same paradox: I drove to the store this morning. Over the course of that drive, ten minutes passed on my watch. BUT it's also true that over the course of that drive, twenty minutes passed on my watch. How can I possibly reconcile those facts? – WillO Sep 28 '17 at 14:46

It is the other way around. If you assume that the rocket circles for one Earth day (i.e. until Earth has finished one 360° rotation), then the time that passes for the brother on Earth is exactly one day. However, the astronaut-brother experiences time dilation, and the trip only takes a very short amount of time from his point of view.

(This goes to show that, with these problems, one has to take great care to be precise. You said "circling for a day" without specifying how you measure "one day". I assumed that "one day" means one rotation of the Earth.
If on the other hand "one day" is measured by a clock on the space ship, then Earth will rotate around the sun many times during that "day" and the brother on ground ages accordingly.)

This is a variation of the famous "twin paradox". It is a nice example to show the new ideas that relativity forces.

The paradox is resolved with one word: acceleration.

Both twins suffer time dilation and see each other older than at rest. That's what looks so disturbing. The thing is that they cannot see each other again unless one of them goes back, for which acceleration is needed, and that breaks everything up, it can even invert efects.

In your example, a circular motion is accelerated, so Special Relativity doesn't apply. That's the thing.

• If you downvote a question, please add a comment and explain why. I'll be pleased to correct any mistakes and it will help the asker and any reader. – FGSUZ Sep 29 '17 at 18:49