# Time Shift in Wormholes

#### Jackson Tan

A typical device in (theoretical) time travel is a wormhole, and the usual method of inducing a time shift, i.e. the two mouths at different times, is to subject one mouth to relativistic time dilation.

However, I can't see why a relativistic boost will result in a time shift. It seems that time dilation will only cause the wormhole mouth to age slower, and not link it between two different times.

To illustrate this, suppose, at t = 0 years (Earth's clock), we have a wormhole sitting in our labs on Earth. We keep mouth A on Earth and accelerate mouth B at high speeds. At t = 10 years, B returns to Earth. Now, due to relativistic effects, when 10 years have passed on Earth, only 1 year has passed on B. But let's look at it from a point of view of someone on Earth. t = 0, mouth B leaves Earth; t = 10, mouth B returns. But how does this connect two different points in time? How can this guy use this wormhole as time travel?

Have I understood something wrongly about inducing time shifts in wormhole mouths?

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#### JesseM

Apparently it's just a feature of traversable wormholes in general relativity that time "threads" differently through the wormhole than outside it...you'd have to do a detailed GR analysis to prove this. But the idea is that if two clocks are synchronized next to one mouth and then one clock goes through the wormhole's throat and is placed next to the other mouth, and from then on each clock stays right next to its respective mouth, then if you're sitting next to one clock and you look through the wormhole's throat at the other clock, the time on both clocks will be the same (aside from a small delay due to the light taking some time to get to you). The time will continue to be the same when you look through the throat even if the two mouths are moved around next to one another so that an observer who looks at the two clocks from an external vantage point sees them as showing very different times.

#### Jackson Tan

Apparently it's just a feature of traversable wormholes in general relativity that time "threads" differently through the wormhole than outside it...you'd have to do a detailed GR analysis to prove this. But the idea is that if two clocks are synchronized next to one mouth and then one clock goes through the wormhole's throat and is placed next to the other mouth, and from then on each clock stays right next to its respective mouth, then if you're sitting next to one clock and you look through the wormhole's throat at the other clock, the time on both clocks will be the same (aside from a small delay due to the light taking some time to get to you). The time will continue to be the same when you look through the throat even if the two mouths are moved around next to one another so that an observer who looks at the two clocks from an external vantage point sees them as showing very different times.

Thanks for the reply (and sorry for my late response), but I'm not certain if it answers my question. My understanding of wormholes is that it is simply a metric that connects two different regions of spacetime (it doesn't even state if it's the same universe). The usual wormhole - the Morris-Thorne wormhole - requires something called exotic matter as a source for such a curvature. I can't see how a relativistic boost on this matter will induce a time shift on the wormhole.

Does anyone else have any idea?

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#### Jackson Tan

Alright, thanks for the input. I'll take a look into them when I have more time on my hands!

Cheers,
Jackson

#### Julian M

Hi -

I have a very similar problem with the MTW analysis because it seems to treat the wormhole mouth as an object in spacetime whereas it seems to me that it should be treated as a feature of spacetime, which treatment would I believe (without supporting math) obviate the creation of a time machine.

If you have access to the original MTW paper (here if you need a copy http://authors.library.caltech.edu/9262/) the wormhole mouth is shown moving in Minkowski spacetime whereas I believe that as per e.g. the Alcubierre Warp drive the only* way for one wormhole mouth to move is for the space(time) between it and the other mouth to be expanded, hence movement against a static "flat" background would be an inappropriate illustration.

[NB if you do look at the MTW paper, note that the wormhole mouth seems to undergo Lorentz contraction, for which no justification is immediately apparent to me; the other post referred to above is stage 1 of clarifying how such time machines could be created - I also have a problem with wormhole mouths having tractable mass/charge and the nature of their motion even if they could be moved.]

Should a wormhole mouth be moved in a pseudo (but sub-luminal) Alcubierre "warp bubble", there should be no time dilation within the flat region containing the "moving mouth" (or spaceship sitting within it) and no time machine should be created (otherwise the Alcubierre drive would not allow the right sort of FTL travel).

If I could get a handle on the lapse function for a sub-luminal "warp bubble" I might be able to work through the math... but I haven't/can't.

I'm still seeking clarification on this - I must be wrong, but I can't see why; I've done extensive literature searches, Matt Visser, Kip Thorne, Jim Al-Khalili etc. and they all agree so I must be wrong...but why? Their thought experiements all "work" if the wormhole mouth is an object in spacetime but that's not how I see it at the moment. Unfortunately I can't help feeling that my disagreement with such eminent authorities is prima facie evidence of either a) culpable ignorance or b) insanity and I'm not sure which I'm suffering from - but the more obvious the resolution of the issue the stupider I will feel though, I'm sure.

Julian

* I can think of another way, but if the stress-energy requirements of wormholes and the Alcubierre drive are bad, this is even worse.

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