Relativity, Einstein, Discover Magazine and Constants

[WordMan]

@audilover

One thing that has always puzzled me about the space traveler case is why isn’t it symmetric. One of the basic underpinnings of relativity is the concept of, well, relativity. That is, why don’t things work both ways based on the reference frame you pick?

In the space traveler example, Dude gets in a rocket, heads towards Alpha Centauri at a high fraction of the speed of light. Then, he turns around and heads back home at a similarly high speed. Since he has been moving at a high rate of speed, the resulting time dilation causes thousands of years to have gone by on earth, while only handful of years have passed for Dude (considerably shorter than his lifespan.)

But, based on the whole notion of relativity, it is just as correct to say this: from the frame of reference of the traveler, the earth has moved away and returned at a high speed, while you (Dude the traveler) have remained still in your reference frame. So, given that all the roles are completely reversed, why doesn’t the time dilation happen the other way. Why doesn’t the earth return to see Dude long dead, while only a few years have passsed for the Earthlings? Or why don’t both points of view cancel out and cause the time to pass symmetrically (perhaps much longer than a simple *time time = distance / velocity * calculation would indicate) ?

I’ve always understood the notion of time dilation. Or maybe understood isn’t the right word. I’ve had it explained so much that I accept it as true without a fundamental understanding. I’m long past the point of trying to wrap my mind around the cause, and have moved on to simply accepting the results as dogma. But being an engineer, that bothers me. And my lack of a real understanding is probably what’s leading me to the paradox described above.

Anyone care to explain?

To my understanding, it is because Dude on the Earth is moving at a constant speed, and Dude the Traveller is changing his rate of speed - accelerating, decelerating, reversing and doing it all over again…and relativity is about inertia and/or not maintaining it…

[Chronos]

But, based on the whole notion of relativity, it is just as correct to say this: from the frame of reference of the traveler, the earth has moved away and returned at a high speed, while you (Dude the traveler) have remained still in your reference frame.

Ah, but which frame of reference of the traveller? The key is that there are three frames of reference in this problem, not two. You have the familiar Earth-based frame: In that frame, the square who stays on Earth is at rest, and Dude is travelling away and then back at high speed. So Square grows old and dies before Dude gets back. Then you have the frame of reference that Dude is in on his outbound voyage: To an observer who stays in that frame of reference, Dude starts off at rest while Square is zipping away, but then after a while Dude starts going even faster than Square, and catches up. Because Dude is going so much faster than Square, an observer in that frame would again see Square much older than Dude, at the time they meet again. And finally, you have the reference frame that Dude is in while returning, and again in that reference frame, you find the same result.