Re: Musings On Wormholes

On Feb 2, 8:52 pm, George W Harris <ghar...@xxxxxxxxxxxxxx> wrote:
Also, if both mouths of the wormhole are in the
same vicinity, they will both undergo an acceleration of
magnitude G*m/d^2 (where G is the gravitational
constant, m is the mass of each wormhole (positve for
one, negative for the other), and d is the distance
between them) and the vector pointing from the
negative-mass wormhole to the positive-mass wormhole.
This acceleration will be constant, so they will quickly
reach relativistic velocities.

If they are not of exactly equal mass, one will experience a greater
acceleration than the other and the mouths will separate. Even if
they are of equal mass, the arrangement will be unstable with respect
to any external perturbation. This can be seen by considering both
wormholes as a single zero mass object. Any outside force will lead
to an infinite acceleration on the net body. Since each mouth has a
finite mass, this means that there must be an infinite force acting
between the two mouths, which will necessarily overcome anything
keeping the mouths from drifting apart (or together). This will lead
to the wormhole mouths acquiring separate trajectories where, unless
they collide, the gravitational acceleration will quickly become
minuscule (what happens if they collide is an interesting and, at this
point in our knowledge of wormholes, unanswerable, question).

For my own sanity, in my settings I assume that wormholes destabilize
and collapse if the mass difference between the mouths gets too large,
preventing the mass of either mouth from ever becoming negative.
While there is no reason this should occur using a general
relativistic description of wormholes alone, it seems that quantum
effects will be necessary to support wormholes by providing the
negative energy fluctuations that allow stable wormhole geometries.
Quantum mechanics places certain restrictions on the magnitude,
duration, and extent of negative energy regions that seems to forbid
isolated regions of space with a net negative energy. This suggests
that negative mass wormhole mouths are, in fact impossible, although
the argument I gave is by no means rigorous.

Luke
.

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