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Wormholes and Time Machines

by John G. Cramer

Alternate View Column AV-33
Keywords: wormholes, general relativity, time machine, FTL
Published in the June-1989 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 11/21/88 and is copyrighted © 1988, John G. Cramer. All rights reserved.
No part may be reproduced in any form without the explicit permission of the author.

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Science fiction writers, to avoid undue delays in the story's plot-line, need a way of beating the speed-of-light speed limit of the universe. Most readers of this magazine are familiar with the gimmicks that have been used for faster-than light travel: warp drives, detours through hyperspace, matter-to-tachyon conversion, trans-spatial jumps, and dives past the singularity of a rotating black hole. But perhaps the faster-than light mechanism which has the best credentials in orthodox physics is the wormhole, also known as a Schwartzschild wormhole or an Einstein-Rosen bridge.

The wormhole idea comes from Einstein's theory of general relativity itself using "Schwartzschild geometry", a way of inscribing a space-time coordinate system on the highly curved space in the vicinity of a black hole. A wormhole is a funnel-shaped tunnel that can connect one complete universe with another or can connect two separated regions of the same universe. In the latter case it is a short path connecting two distant locations in space. Thus it the SF writer's dream, a spatial shortcut that a space traveler might use to bypass the speed-of-light barrier and travel almost instantaneously from one place to another within our universe.

However, there is a basic problem with wormholes as a transport system. Wormholes, as described by the equations of general relativity, are dismayingly unstable. In fact, any wormhole connection that happens to form between two points in space should pinch closed again so rapidly that neither material objects nor light-beam messages can pass across the wormhole "bridge" during its brief existence. Thus a wormhole, at least in its pristine form, is unsuitable for the instantaneous space transport that SF writers may have in mind.

Most physicists will find this result very satisfying, for it avoids a sumultaneity paradox. Einstein's special theory of relativity treats space-time in a very even-handed and symmetric way. It requires a complete equivalence of "inertial reference frames", space-time coordinate systems moving through space with any constant speed (including zero). These must be equivalent by any internal measurement that would single out one such frame as special. For example, no measurements made inside a spaceship traveling at near light-speed can show different results from similar measurements made when the ship was at rest in space. In special relativity "at rest in space" is a meaningless concept, since that condition is undetectable.

Thus, a semi-permanent wormhole would present a problem for special relativity not only because it would breach the light-speed barrier but also because the reference-frame symmetry would be broken. If a wormhole connection between separated regions of space existed only long enough to permit a message to be sent, it would seem that a reference-frame test could be made that would single out one reference frame as "preferred". Absolute space would be detected and defined.

The satisfying instability of wormholes has now been called into question. Last Fall a paper by Michael Morris, Kip Thorne, and Ulvi Yurtsever was published in the conservative and prestigious journal Physical Review Letters which changes all this. The authors describe how an "advanced civilization" might: (a) create a large wormhole; (b) stabilize it to prevent its re-collapse; and (c) convert it to a time machine, a device for traveling or at least communicating back and forth in time. This remarkable paper, which borders on science fiction in its approach, has a very serious purpose. There is presently no well-established theory that can accommodate both quantum mechanics and the physics of strong gravitational fields within the same mathematical framework. The paper of Morris, Thorne, and Yurtsever is a vehicle for guessing, in a rather unorthodox way, what restrictions a proper theory of quantum gravity might place on the physics of wormholes. The authors demonstrate that general relativity contains within its framework mechanisms that appear to permit both faster-than-light travel and time travel. If these physical calamities are to be averted, the authors argue, it can only be done through a proper theory of quantum gravity.

To devotees of science fiction, however, these aren't calamities at all but delightful prospects. So let's discuss how Morris, Thorne, and Yurtsever propose to create a stable wormhole, with the idea that someday we may be able to build one (or at least write a good story about it). Empty space, when examined with quantum theory on a sufficiently small distance scale, is not empty at all. Even at nuclear dimensions (10-13 cm) empty space is filled with particle-antiparticle pairs that are continually flashing into a brief existence, bankrolled on the credit of borrowed mass-energy, only to wink out of existence again as the law of conservation of energy reasserts itself. If the length-scale is contracted to a size appropriate to quantum gravity (10-33 cm) this quantum fireworks intensifies to a "quantum foam" of violent fluctuations in the topology and geometry of space itself. Quantum black holes form and vanish in a span of time of 10-23 seconds; highly curved and convoluted regions of space in ant physically allowed configuration have a similarly brief existence. In this environment Morris, Thorne, and Yurtsever speculate, it my be possible for a civilization considerably more advanced than ours, by "pulling a wormhole out of the quantum foam and enlarging it to classical size" to create a connection between two nearby points in space. This would use the well-known quantum mechanical process called "tunneling", a jump from one allowed energy state to another across a barrier of intermediate states that are forbidden by energy conservation.

To stabilize the wormhole pulled from the quantum foam, preventing its immediate recollapse, Morris, Thorne, and Yurtsever propose to use an electric field of such enormous strength that it creates enough energy in the mouth of the wormhole to force it to remain open. They suggest that this might be accomplished by placing a pair of spheres with equal electric charges at the two spatial entrances of the wormhole. The spheres would be held in place by a delicate balance, the force of their gravitational attraction just offsetting the force of their electrical repulsion. Such a system might be very small, an atom-scale opening permitting the passage of only a few photons at a time, or it might be large enough to pass a large vehicle.

Having produced this stabilized wormhole the engineering can begin. The size of the connection can be enlarged or contracted depending on energy considerations. The two portal ends of the wormhole connection can be separated from each other. For example, a portal placed aboard a space ship might be carried to some location many light years away. Such a trip might require a long time, but during the trip and afterwards instantaneous communication and transport through the wormhole would be available. The ship could even be supplied with fuel and provisions through the portal. A similar scenario has already been described in Poul Anderson's The Enemy Stars, in which starships were required to travel at sub-light speeds, but they carried onboard matter transmitters that permitted instantaneous transmission of crew and supplies from Earth.

This brings us to the last point of the Morris, Thorne, and Yurtsever paper, the construction of a time machine. Suppose that initially a wormhole establishes a connection between two spatial points A and B that have no motion with respect to each other and are simultaneous in time. By "simultaneous", a slippery concept in relativity, we mean that an observer at A who determines a clock reading at B would get the same reading via normal space (by light beam signals corrected for transit time, for example) as he would through the wormhole.

Now suppose, in the spirit of the Twin Paradox of special relativity, that portal B is placed aboard a space ship while portal A remains on Earth. The ship carrying B, say, accelerates rapidly to 86.6% of light speed and travels a distance of one light-year, then reverses its course and returns to Earth at the same speed. On its arrival portals A and B are placed near one another. At 86.6% of the velocity of light any clock aboard the ship will run at just half the speed of a similar clock on Earth due to relativistic time dilation. Therefore at the end of the trip the ship's clock will be one year slow, as compared to an identical clock that remained on Earth. And, as Morris, Thorne, and Yurtsever point out, portal B will also be one year slow as compared with portal A. Now a message sent through B to A will emerge one year in the future of B, and a message sent through A to B will emerge one year in the past of A! Similarly a traveler making the same trips through the wormhole will travel one year into the future or the past. The wormhole connection through space has been transformed to a connection through time, a wormhole time machine.

Does this device, embodying faster-than-light space travel as well as time travel, demonstrate that special relativity is wrong? Does it show that Einstein's speed limit had been defeated? Not at all. The restrictions usually associated with special relativity implicitly assume that no time travel is possible. Clearly one could travel, in effect, at an infinite velocity by traveling from one place to another at some sub-light velocity and then on arrival traveling backwards in time to the instant of departure. To put it another way, the simultaneity measurements prohibited by special relativity must lead to a definite and unambiguous determination of the simultaneous readings of two clocks separated in space. The clock-comparisons made possible by wormholes are not definite, because one clock could be in the future of the other, displaced by any time interval produced by the travel histories of the portals. Special relativity, which after all is embedded in the theory of general relativity that produced these revelations about wormhole physics, is preserved.

The law of physics that would be destroyed by the construction of a wormhole space-time connection is causality, the mysterious principle that prohibits communication backwards in time, that requires a cause to precede its effects in time sequence in all space-time reference frames. Causality as a law of the universe would not survive even a two-way communications link across time, let alone a portal permitting trans-time matter transmission.

The principal purpose of Morris, Thorne, and Yurtsever in discussing what an advanced civilization might do with wormholes, as mentioned above, is to demonstrate in effect that if causality is to be preserved as a law of physics, it must be saved at the quantum level. Quantum gravity, a theory-to-be which has not yet been developed, must impose some new physical limitations that make impossible the production of stable wormholes by the Morris-Thorne-Yurtsever scenario. General relativity, our present theory of gravity, prohibits neither faster-than-light space travel nor time travel with wormholes, but it does require that the two go together. Writers of hard SF should have fun with that one!

REFERENCES:

Schwartzschild Wormholes:
Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler, Gravitation, pp. 836-840, W. H. Freeman and Company, San Francisco (1973).

Wormholes & Time Machines:
Michael S. Morris, Kip S. Thorne, and Ulvi Yurtsever, Physical Review Letters 61, 1446 (1988).


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