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Squeezing the Vacuum

by John G. Cramer

Alternate View Column AV-53
Keywords: natural wormholes negative energy squeezed vacuum black hole

Published in the July-1992 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 12/22/91 and is copyrighted ©1991 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
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This column is about a new development in the theory of wormholes. At Vanderbilt University, David Hochberg and Thomas W. Kephart have discovered that gravity itself can produce regions of negative energy. Within these regions, we may conjecture, stable wormholes may form naturally, particularly during the early Big Bang. A wormhole is a geometrical shortcut in curved space-time with the topology of a cup handle which, in principle, allows movement from one point in space-time to another without the necessity of traversing the intervening space-time interval. This provides a physical basis for two traditional gimmicks of science fiction: faster-than-light travel and time travel into the past and the future.

But any such wormholes, it had seemed, would have to be made and operated by a technological civilization far in advance of ours. With the new work, however, there is a plausible mechanism for the formation of stable natural wormholes. We'll discuss this after a brief summary of the status of wormhole physics.

My column "Wormholes and Time Machines" [Analog-June-1989] described the breakthrough work on wormholes by Kip Thorne and his group at Caltech. At the time, Thorne, Morris, and Yurtsever (TMY) had just published two papers demonstrating the possibility of stable wormholes and presenting a new class of wormhole solutions to Einstein's field equations. They used these to argue that a sufficiently advanced civilization might stabilize a wormhole and use it both for faster-than-light travel and for travel backwards and forwards in time.

It has long been known that lorentzian wormholes (the kind discussed here, as distinguished from the unrelated euclidian wormholes that Stephen Hawking, Sidney Coleman, and others conjure with in quantum gravity studies), are intrinsically unstable in field-free space and will snap shut so quickly that one cannot pass even a single photon through. What TMY discovered is that a lorentzian wormhole can be stabilized by creating a zone of negative energy in the wormhole throat, the place where it has maximum space-time curvature. They suggested creating the needed negative energy region by using a "parallel plate capacitor" made with a pair of superconducting spheres carrying huge electrical charges and separated by a very small gap, employing the Casimir effect [see my column "FTL Photons" in the Mid-December-1990 issue of Analog] to make the zone of negative energy by suppressing electromagnetic fluctuations of the vacuum and reducing the vacuum energy to a value less than zero. In the TMY scenario, the hypothetical advanced civilization (one that could convert whole suns to mass-energy for civil engineering projects) would extract from the "quantum foam" one of the many wormholes that wink into and out of existence at ultra-small distance scales, expand the selected wormhole to macroscopic dimensions by adding energy, and stabilize it by placing the two charged superconducting spheres in the wormhole mouths (or portals). The portals could then be transported to widely separated regions of space to provide FTL communication and travel.

TMY pointed out that if one wormhole portal was accelerated to a velocity near that of light, kept at that speed for a year, and then decelerated and brought back to stand in the laboratory beside to its stay-at-home portal twin, the pair of portals would constitute a time machine that could be used for two-way communication and transport one year into the future or one year into the past.

My second wormhole column ,"More about Wormholes - To the Stars in No Time" [Analog-May-1990] elaborated on some of the remarkable properties of wormholes when used for faster than light travel. The time travel and space travel aspects of a wormhole could combine under some scenarios to produce a near-zero waiting time for sending an accelerated mini-wormhole to a selected star system, expanding it into a useful portal for material objects, and using it for FTL transport.

However, lorentzian wormholes have their problems. The TMY scheme, while valuable as establishing an in-principle method of stabilizing wormholes, would be very difficult to implement in practice, even by the hypothetical advanced civilization. The two superconducting spheres must be suspended with a very narrow separation, without external supports to hold them up or precisely position them, in a delicate balance between gravitational and Casimir forces pulling them together and electrical repulsion of their charges pushing them apart. The electrical charges needed for the two spheres are so large that there would probably be violent electrical discharges to the surroundings or the FTL traveler.

As a device for time travel or FTL travel in SF stories, wormholes have a number of limitations that may get in the way of the plot. For example, (1) the wormholes must be created by a civilization with technological capabilities that far exceed ours, (2) they cannot be used for FTL travel to some selected destination until a wormhole portal is sent there at sub-light speed, and (3) they cannot be used for time travel to a time before the wormhole was created. Fortunately the new results provide a fix for all of these problems, at least at the level of SF writing.

As it turns out, wormholes may come prefabricated by nature. Hochberg and Kephart have discovered that gravity itself can produce regions of "squeezed vacuum" characterized by negative energy within which natural wormholes might form. To understand this new result we will need to discuss the "squeezing" of quantum mechanical states.

In quantum mechanics, Heisenberg's uncertainty principle, for certain "conjugate" pairs of measurable quantities (examples are position and momentum or energy and time), requires that the product of the uncertainties of the two quantities can never be less than an irreducible minimum value given by Planck's constant divided by 2 pi. If we try to measure the position of an electron with extreme precision, for example, we find that this can only be done at the expense of the measured momentum of the same electron, which becomes very uncertain as a result of the position measurement.

There is also another way in which measurements are limited by quantum mechanics. It's called zitterbewegung or zero-point motion. Imagine a classical (i.e., non-quantum-mechanical) system that can oscillate, for example a pendulum that is swinging back and forth. The pendulum can have large swings with lots of energy or small swings for less energy. But the pendulum has a minimum energy of zero when the swinging stops and the weight hangs straight down.

The quantum mechanical equivalent of the oscillating pendulum is has an important difference at zero energy. It cannot swing just any old way it wants. Instead it is allowed to swing only in certain "states" or modes of swinging. The swing or oscillation modes are quantized, and the energy of the system can be changed only in quantum jumps that take the quantum pendulum system from one oscillation mode to another. For our purposes the really interesting aspect of the quantum oscillator is that it cannot stop. Its lowest allowed energy state does not correspond to zero energy, but to half the energy gap to the next allowed state. So even the zero-energy system can never be at rest. Even when all possible energy is removed, it remains is a state called zero-point motion, the motion that it retains when all removable energy is gone.

In a more complex quantum system containing many semi-independent quantum oscillators, the zero-point motion represents a quantum noise that is superimposed on any measurement of the system. If an attempt is made to cool the system by removing the heat energy, the zero-point motion represents a rock bottom, a limit below which straightforward cooling cannot go.

There is a trick, however, for making the system colder. In quantum mechanics the energy and the frequency of a quantum oscillator system are interchangeable, differing only by a constant multiplier. Further, in the context of Heisenberg's uncertainty principle, the conjugate variable to the frequency is the phase, in other words, the starting angle for an individual quantum oscillation. Phase is difficult to measure and is usually ignored in characterizing complex quantum systems. However, it has its uses. Recently it has been realized that in many quantum systems the limits to measurement precision imposed by zero-point motion can be breached by converting frequency noise into phase noise, keeping the product within the limits dictated by the uncertainty principle while reducing the variations in frequency (and therefore energy). If this technique is applied to a light beam, the result is called "squeezed light". Recent work in quantum optics using squeezed light has demonstrated that old measurement noise limits considered unbreachable can now be surpassed with ease.

The squeezing effect investigated by Hochberg and Kephart, however, was not for light but for the vacuum itself. The theory of quantum electrodynamics tells us that the vacuum, (i.e., empty space) when examined on very small distance scales is not empty at all; it seethes with a kind of fireworks called vacuum fluctuations. Pairs of "virtual" (energy non-conserving) particles of many kinds continually wink into existence, live briefly on the energy credit extended by Heisenberg's uncertainty principle, and then annihilate and vanish when the bill for their energy debts falls due a few picoseconds or femtoseconds later. These vacuum fluctuations can be squeezed in the same way that light beams or systems of atoms can be squeezed, and the result is a vacuum that has an energy less than zero, in other words, a region of negative energy of just the king needed for wormhole stabilization.

Hochberg and Kephart used a technique of general relativity called a Rindler transformation to show that over a period of time the vacuum in the presence of a gravitational field is squeezed. They found that near compact gravitational objects like black holes, substantial squeezing of vacuum fluctuations occurs at all wavelengths greater than about the Schwarzschild radius of the object.

For a solar-mass black hole such as might be found somewhere in our galaxy, this squeeze effect is not very interesting because only wavelengths greater than 5 km (long wavelength radio waves) are affected. However, the early stages of the Big Bang created a very large number of quantum black holes with masses corresponding to the Planck mass (about 10-8 kg). Near such quantum black holes, all wavelengths greater than the Planck length (about 10-33 cm) would be squeezed, in other words, all wavelengths of interest for vacuum fluctuations. This creates a significant zone of negative energy of just the kind that might stabilize a small wormhole.

There are two important consequences of these results of Hochberg and Kephart . First, in the TMY work on lorentzian wormholes it was found necessary to violate the weak energy condition. The weak energy condition does not have the status of a physical law, but it is a condition that holds in normal situations. There were speculations that its violation might be in conflict with quantum gravity, making stable lorentzian wormholes impossible. This is apparently incorrect. Hochberg and Kephart have now demonstrated that the natural and inevitable squeezing of the vacuum as it evolves in a strong gravitational field is in violation of the weak energy condition. This places the TMY work on a more secure foundation.

But from the point of view of SF, there is another consequence of squeezed vacuum that is more important. It appears that in the early universe and perhaps in other energy-rich environments the conditions are right for producing natural self-stabilizing wormholes (without the need to invoke TMY's advanced civilization to create them). Such wormholes, created in the Big Bang during the inflationary phase and afterwards, might be around today, spanning small or vast distances in space and waiting only to be found and expanded to a usable size. They might even connect one bubble-universe with another from which it is otherwise completely isolated.

Further, if such wormhole remnants of the Big Bang do exist, it is unlikely that the two separated ends of the wormhole could have had exactly the same history of velocity, acceleration, and relativistic time dilation, and so there will almost inevitably be a difference in the positions in time as well as in space for the two wormhole portals. Therefore, if such natural wormholes with their portal ends not too far apart could be found and expanded, they could be used for time travel.

Of course, as we say when writing funding proposals in science, more work needs to be done. The detailed stability and time evolution of small wormholes formed in the negative energy zone of a quantum black hole needs to be intensively investigated. Nevertheless, with the work of Hochberg and Kephart we have a plausible scenario for naturally occurring wormholes that can provide FTL travel and time travel that can be used in a thousand SF stories. For the purposes of SF, that's all we need.


Wormholes, FTL, & Time Machines:
Michael S. Morris, Kip S. Thorne, and Ulvi Yurtsever, Physical Review Letters 61, 1446 (1988);
Michael S. Morris, and Kip S. Thorne, American Journal of Physics 56, 395 (1988).

Wormholes and Squeezed Vacuum:
David Hochberg and Thomas W. Kephart, Physics Letters B 268, 377 (1991).

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