Hyperspace (42 page)

Anyone who has read H. G. Wells’s
The Time Machine
, however, may be disappointed with Thorne’s blueprint for a time machine. You do not sit in a chair in your living room, turn a few dials, see blinking lights, and witness the vast panorama of history, including destructive world wars, the rise and fall of great civilizations, or the fruits of futuristic scientific marvels.

One version of Thorne’s time machine consists of two chambers, each containing two parallel metal plates. The intense electric fields created between each pair of plates (larger than anything possible with today’s technology) rips the fabric of space-time, creating a hole in space that links the two chambers. One chamber is then placed in a rocket ship and is accelerated to near-light velocities, while the other chamber stays on the earth. Since a wormhole can connect two regions of space with different times, a clock in the first chamber ticks slower than a clock in the second chamber. Because time would pass at different rates at the two ends of the wormhole, anyone falling into one end of the wormhole would be instantly hurled into the past or the future.

Another time machine might look like the following. If exotic matter can be found and shaped like metal, then presumably the ideal shape would be a cylinder. A human stands in the center of the cylinder. The exotic matter then warps the space and time surrounding it, creating a wormhole that connects to a distant part of the universe in a different time. At the center of the vortex is the human, who then experiences no more than 1
g
of gravitational stress as he or she is then sucked into the wormhole and finds himself or herself on the other end of the universe.

On the surface, Thorne’s mathematical reasoning is impeccable. Einstein’s equations indeed show that wormhole solutions allow for time to pass at different rates on either side of the wormhole, so that time travel, in principle, is possible. The trick, of course, is to create the wormhole in the first place. As Thorne and his collaborators are quick to point out, the main problem is how to harness enough energy to create and maintain a wormhole with exotic matter.

Normally, one of the basic tenets of elementary physics is that all objects have positive energy. Vibrating molecules, moving cars, flying birds, and soaring rockets all have positive energy. (By definition, the empty vacuum of space has zero energy.) However, if we can produce objects with “negative energies” (that is, something that has an energy
content less than the vacuum), then we might be able to generate exotic configurations of space and time in which time is bent into a circle.

This rather simple concept goes by a complicated-sounding title: the
averaged weak energy condition
(AWEC). As Thorne is careful to point out, the AWEC must be violated; energy must become temporarily
negative
for time travel to be successful. However, negative energy has historically been anathema to relativists, who realize that negative energy would make possible antigravity and a host of other phenomena that have never been seen experimentally.

But Thorne is quick to point out that there is a way to obtain negative energy, and this is through quantum theory. In 1948, the Dutch physicist Henrik Casimir demonstrated that quantum theory can create negative energy: Just take two large, uncharged parallel metal plates. Ordinarily, common sense tells us that these two plates, because they are electrically neutral, have no force between them. But Casimir proved that the vacuum separating these two plates, because of the Heisenberg Uncertainty Principle, is actually teeming with activity, with trillions of particles and antiparticles constantly appearing and disappearing. They appear out of nowhere and disappear back into the vacuum. Because they are so fleeting, they are, for the most part, unobservable, and they do not violate any of the laws of physics. These “virtual particles” create a net attractive force between these two plates that Casimir predicted was measurable.

When Casimir first published his paper, it met with extreme skepticism. After all, how can two electrically neutral objects attract each other, thereby violating the usual laws of classical electricity? This was unheard of. However, in 1958 physicist M.J. Sparnaay observed this effect in the laboratory, exactly as Casimir had predicted. Since then, it has been christened the
Casimir effect
.

One way of harnessing the Casimir effect is to place two large conducting parallel plates at the entrance of each wormhole, thereby creating negative energy at each end. As Thorne and his colleagues conclude, “It may turn out that the average weak energy condition can never be violated, in which case there could be no such things as transversible wormholes, time travel, or a failure of causality. It’s premature to try to cross a bridge before you come to it.”
⁷

At present, the jury is still out on Thorne’s time machine. The decisive factor, all agree, is to have a fully quantized theory of gravity settle the matter once and for all. For example, Stephen Hawking has pointed out that the radiation emitted at the wormhole entrance will be quite large and will contribute back into the matter-energy content of Einstein’s equations. This feedback into Einstein’s equations will distort the
entrance to the wormhole, perhaps even closing it forever. Thorne, however, disagrees that the radiation will be sufficient to close the entrance.

This is where superstring theory comes in. Because superstring theory is a fully quantum-mechanical theory that includes Einstein’s theory of general relativity as a subset, it can be used to calculate corrections to the original wormhole theory. In principle, it will allow us to determine whether the AWEC condition is physically realizable, and whether the wormhole entrance stays open for time travelers to enjoy a trip to the past.

Hawking has expressed reservations about Thorne’s wormholes. However, this is ironic because Hawking himself has proposed a new theory of wormholes that is even more fantastic. Instead of connecting the present with the past, Hawking proposes to use wormholes to connect our universe with an infinite number of parallel universes!

[Nature is] not only queerer than we suppose, it is queerer than we can suppose.

J. B. S. Haldane

COSMOLOGIST Stephen Hawking is one of the most tragic figures in science. Dying of an incurable, degenerative disease, he has relentlessly pursued his research activities in the face of almost insurmountable obstacles. Although he has lost control of his hands, legs, tongue, and finally his vocal cords, he has spearheaded new avenues of research while confined to a wheelchair. Any lesser physicist would have long ago given up the struggle to tackle the great problems of science.

Unable to grasp a pencil or pen, he performs all his calculations in his head, occasionally aided by an assistant. Bereft of vocal cords, he uses mechanical devices to communicate with the outside world. But he not only maintains a vigorous research program, but still took time to write a best-selling book,
A Brief History of Time
, and to lecture around the world.

I once visited Hawking in his home just outside Cambridge University when I was invited to speak at a physics conference he was organizing. Walking through his living room, I was surprised by the impressive array of ingenious gadgets that he uses to continue his research. For example, I saw on his desk a device much like those used by musicians to hold music sheets. This one, however, was much more elaborate and had the ability to grab each page and carefully turn it for reading a book. (I shivered to ponder, as I think many physicists have, whether I would
have the stamina and sheer willpower to continue research without arms, legs, or a voice even if I had the finest mechanical aids available.)

Hawking is the Lucasian Professor of Physics at Cambridge University, the same chair held by Isaac Newton. And like his illustrious predecessor, Hawking has embarked on the greatest quest of the century, the final unification of Einstein’s theory of gravity and quantum theory. As a result, he, too, has marveled at the elegant, self-consistency of the ten-dimensional theory, and in fact closes his best-selling book with a discussion of it.

Hawking no longer spends the bulk of his creative energy on the field that made him world-famous—black holes—which are by now passé. He is hunting bigger game—the unified field theory. String theory, we recall, began as a quantum theory and then later absorbed Einstein’s theory of gravity. Hawking, starting as a pure classical relativist rather than a quantum theorist, approaches the problem from the other point of view. He and his colleague James Hartle start with Einstein’s classical universe, and then quantize the entire universe!

Hawking is one of the founders of a new scientific discipline, called
quantum cosmology
. At first, this seems like a contradiction in terms. The word
quantum
applies to the infinitesimally small world of quarks and neutrinos, while
cosmology
signifies the almost limitless expanse of outer space. However, Hawking and others now believe that the ultimate questions of cosmology can be answered only by quantum theory. Hawking takes quantum cosmology to its ultimate quantum conclusion, allowing the existence of infinite numbers of parallel universes.

The starting point of quantum theory, we recall, is a wave function that describes all the various possible states of a particle. For example, imagine a large, irregular thundercloud that fills up the sky. The darker the thundercloud, the greater the concentration of water vapor and dust at that point. Thus by simply looking at a thundercloud, we can rapidly estimate the probability of finding large concentrations of water and dust in certain parts of the sky.

The thundercloud may be compared to a single electron’s wave function. Like a thundercloud, it fills up all space. Likewise, the greater its value at a point, the greater the probability of finding the electron there. Similarly, wave functions can be associated with large objects, like people.
As I sit in my chair in Princeton, I know that I have a Schödinger probability wave function. If I could somehow see my own wave function, it would resemble a cloud very much in the shape of my body. However, some of the cloud would spread out over all space, out to Mars and even beyond the solar system, although it would be vanishingly small there. This means that there is very large likelihood that I am, in fact, sitting in my chair and not on the planet Mars. Although part of my wave function has spread even beyond the Milky Way galaxy, there is only an infinitesimal chance that I am sitting in another galaxy.

Hawking’s new idea was to treat the entire universe as though it were a quantum particle. By repeating some simple steps, we are led to some eye-opening conclusions.

We begin with a wave function describing the
set of all possible universes
. This means that the starting point of Hawking’s theory must be an infinite set of parallel universes, the
wave function of the universe
. Hawking’s rather simple analysis, replacing the word
particle
with
universe
, has led to a conceptual revolution in our thinking about cosmology.

According to this picture, the wave function of the universe spreads out over all possible universes. The wave function is assumed to be quite large near our own universe, so there is a good chance that our universe is the correct one, as we expect. However, the wave function spreads out over all other universes, even those that are lifeless and incompatible with the familiar laws of physics. Since the wave function is supposedly vanishingly small for these other universes, we do not expect that our universe will make a quantum leap to them in the near future.

The goal facing quantum cosmologists is to verify this conjecture mathematically, to show that the wave function of the universe is large for our present universe and vanishingly small for other universes. This would then prove that our familiar universe is in some sense unique and also stable. (At present, quantum cosmologists are unable to solve this important problem.)

If we take Hawking seriously, it means that we must begin our analysis with an infinite number of all possible universes, coexisting with one another. To put it bluntly, the definition of the word
universe
is no longer “all that exists.” It now means “all that can exist.” For example, in
Figure 12.1
we see how the wave function of the universe can spread out over several possible universes, with our universe being the most likely one but certainly not the only one. Hawking’s quantum cosmology also assumes that the wave function of the universe allows these universes to collide. Wormholes can develop and link these universes. However, these wormholes are not like the ones we encountered in the previous
chapters, which connect different parts of three-dimensional space with itself—these wormholes connect different universes with one another.