Time Dilation and Space Travel: Is Wikipedia example wrong?

[kornelma]

Quoting from Wikipedia:

"Time dilation would make it possible for passengers in a fast-moving vehicle to travel further into the future while aging very little, in that their great speed slows down the rate of passage of on-board time. That is, the ship's clock (and according to relativity, any human traveling with it) shows less elapsed time than the clocks of observers on Earth. For sufficiently high speeds the effect is dramatic. For example, one year of travel might correspond to ten years at home. Indeed, a constant 1 g acceleration would permit humans to travel through the entire known Universe in one human lifetime.[14] The space travellers could return to Earth billions of years in the future. A scenario based on this idea was presented in the novel Planet of the Apes by Pierre Boulle."

From my understanding of time dilation, this is an incorrect interpretation of its effects.
Observer A's clock on Earth would experience a slowing of the clock on Spaceship B (traveling close to speed of light) as it moves away from A. However, should B turn around and come back towards A with same speed, A would then experience that B's clock is speeding up the same amount. Hence, when spaceship lands, A and B clocks would show the same time.

This would make the notion of time travel into the future by boarding a fast spaceship that travels with speeds close to speed of light an impossibility.
Time dilation is not about actual slowing of the passing of time on an object traveling close to speed of light, but the about the slowing of THE EXPERIENCE of that time that a relatively stationary object has.

If that is the case, then roundtrips must cancel out this effect, making travel into the future a logical impossibility no matter what kind of propulsion we can invent for spaceships.

 

[Dale]

Hi kornelma, welcome to PF!

The wikipedia quote is correct.

However, should B turn around and come back towards A with same speed, A would then experience that B's clock is speeding up the same amount.

This is not correct. Time dilation depends only on the speed in an inertial frame, not on the direction.

I think that you are thinking of the Doppler effect where receeding objects are redshifted and approaching objects are blueshifted. The relativistic Doppler effect is slightly redder than the classical Doppler effect due to time dilation, but time dilation does not depend on direction.

 

[kornelma]

I understand about doppler effect.

What I'm questioning is that since speed is relative, somebody observing both A & B, could actually conclude that it was A that was speeding away from B and then returning...or that both A & B were speeding away from each other then back. With other words, A & B are interchangeable, so B could not travel into A's future...

 

[Dale]

A and B are not interchangeable. If they both carry accelerometers then one will measure a non-zero acceleration and the other will measure zero acceleration. Velocity is relative, but acceleration is not.

This is the standard "twin's paradox". Here is a very thorough FAQ:
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

 

[harrylin]

I understand about doppler effect.

What I'm questioning is that since speed is relative, somebody observing both A & B, could actually conclude that it was A that was speeding away from B and then returning...or that both A & B were speeding away from each other then back. With other words, A & B are interchangeable, so B could not travel into A's future...

Only uniform speed is relative like that. Basically you hit on the "twin paradox" issue: a change of velocity is "absolute" in the sense that it breaks the symmetry.

If you understand the Doppler effect then you can figure out for yourself that these are physically different situations: the effect of you changing velocity instantly changes your observation of the other's frequency, but not immediately the other's observation of your frequency.

 

[kcdodd]

Actually it is more simple then acceleration. Imagine two planets A and B separated by 1ly who have Einstein synchronized clocks. A spaceship traveling at a constant 0.99c in a straight line from planet A to planet B, passes planet A when the clock on the planet reads zero in both frames, and the clock on the spaceship synchronizes to zero. When the spaceship passes planet B, the clock on planet B reads a few days over 1yr in both frames. Yet the clock on board the spaceship reads a little under 2 months. Time dilation by itself does not account for this. The confusion results since planet B's clock should have ticked more slowly from the spaceship's perspective, and yet should be synchronized with planet A, so one might conclude that it should read less then the spaceship's clock, not more. The missing fact is that way back at planet A, planet B's clock appears to already be set ahead by about 10 months in the spaceships frame, a consequence of simultaneity being relative.