Wormhole Time Machine: As Time Goes On

[edgepflow]

Suppose a wormhole time machine is made by moving one mouth close to speed of light for a suitable time. Further suppose that immediately after the time machine is first completed, we have the following:

Time at Mouth 'A' ---> 2010
Time at Mouth 'B' ---> 2000

Now if 20 years go by, would the times be:

20 Yr Later Time at Mouth 'A' ---> 2010
20 Yr Later Time at Mouth 'B' ---> 2000

OR,

20 Yr Later Time at Mouth 'A' ---> 2010 + 20 = 2030
20 Yr Later Time at Mouth 'B' ---> 2000 + 20 = 2050 ?

 

[pervect]

In the usual case, the wormhole end travels at a high speed, comes back, and stops. I'm not quite sure what case you're envisioning.

I can give you a quick answer as to what I think you'll see in the case I described. If you look through the wormhole, and pass notes to the person on the other end, you'll see them age at the same rate as you do. At least, as long as there isn't any sort of gravitational potential difference between the two wormhole ends, that is. With no potential difference, there is no gravitational redshifting, so you'll see time pass at the same rate looking through the wormhole.

(Note: I've tried to make things simple here as far as explaining why there isn't any difference in aging when looking through the wormhole, rather than to be precise.)

You could even visit back and forth, through the wormhole, and they'd be the same age.

But when they take a round trip at relativistic speeds and come back, when you visit them, you being the "stay at home" twin, they'll be much younger than you.

Note that if they don't come back home and stop, you'll have the usual ambiguities of how to synchronize your clocks that you always get in relativity.

 

[edgepflow]

Thank you for the reply pervect.

Let me try to rephrase my question. After all motion of the wormhole mouths have stopped, and a time difference is established between the two mouths, do both mouths now move into the future with their time difference or do they stay in their original time?

 

[JesseM]

Thank you for the reply pervect.

Let me try to rephrase my question. After all motion of the wormhole mouths have stopped, and a time difference is established between the two mouths, do both mouths now move into the future with their time difference or do they stay in their original time?

Time does continue to go forward as normally. If there is a five-year difference, so that entering mouth A in 2010 causes you to exit mouth B in 2005, that means that if you enter mouth A in 2020, you'll exit mouth B in 2015, not 2005.