A really dull wormhole question...

[rajama]

Say we have a stable wormhole that can be used for transport and decide to move one mouth of this object some vast distance at relativistic speed - at say 0.866c to hang a figure on it – and we send a vehicle through from the ‘home’ mouth to the mouth that’s in transit…

 

Does the vehicle undergo a huge net acceleration in the direction of travel during its passage through the wormhole?

 

Related to this:

 

a) When the vehicle clears the ‘transit’ mouth, is its inertial frame relative to it the same as it was relative to the ‘home’ mouth?

 

b) Or does the vehicle – once clear of the transit mouth – get left behind by the transit mouth which is moving away at 0.866c – that is, the vehicle has same inertial frame it had back before it began the journey?

[rajama]

As usual, I couldn’t wait for a reply (only a day so far) and couldn’t find what I wanted at SFN or online (an afternoon and an evening) but did discover that a text I already had, a dusty copy of Lorentzian Wormholes by Matt Visser (1995) covered what I needed (half an hour).

 

Missing out most of the (still) impenetrable math, in addressing Morris & Thorne’s original paper the author notes on page 110:

 

“If time runs at different rates in the two asymptotically flat regions of the inter-universe wormhole, the associated intra-universe wormhole has a non-conservative gravitational field.”

 

So, one way to achieve a difference in time rate is to transit one of the mouths as described in my post – I assume the act of accelerating the transit mouth piles up a gravitational field in the throat. This then accelerates the vehicle during its journey to the transit mouth.

 

As for the two related questions, I could assume a) is correct as it would appear consistent.

 

Have fun.

[rajama]

or not…

 

In briefly exploring this non-conservative gravity field, the text examines the way energy might be extracted from a wormhole - in an analogous way to it being extracted from a black hole - but uses a mass near one of the mouths to slow time rather than a difference in inertial frame between the mouths. *

 

When I began this thread it I did consider the effect discussed may be due to a change in the structure of the transit mouth, having undergone acceleration, but the implication of the text is that the non-conservative field explored is solely due to the difference in time rates that are joined by the throat, and that the mouths remain unchanged (the effect is internal to the wormhole).

 

But this difference is produced by SR and it must be reciprocal: this will therefore act whichever way the wormhole is traversed, providing a net acceleration of the vehicle toward the mouth from which it will emerge… like crossing a valley from the top of the tallest hill, only to find the lesser hill on which you now stand is the taller of the two..?

 

I won’t add to this post as it’s turning into a book report…

 

* Just to note that I am aware these two objects do not have the same standing, a black hole being a problematic inevitability of unopposed gravity, a traversable wormhole being an example of GR engineering with exotic caveats.

 

Addendum to 9:18 posting: I think I get it…

 

The vehicle sees a greater tidal force in a wormhole of this kind, but can’t tell which way is up…

 

The throat of the wormhole has a similar role or standing as infinity outside the wormhole system… therefore when the transit mouth is ‘seen’ through the throat from the home mouth it has the same relativistic mass as it would ‘seen’ across normal space, in this example at 0.866c making its mass twice the rest mass of the two (identical) mouths.

 

This mass being due to the transit mouth’s relative speed, as the vehicle passes through the throat to rendezvous with the transit mouth, the field in the throat is transformed, effectively tilting it the other way… the two hills are equal in height, but the whole valley rocks.

 

Huh... still not entirely happy with the result. So it goes.