Hyperspace (39 page)

The wind now changes direction, and the hat is carried in the other
direction. We stick our other hand into the window, but from the other side. We are now in an awkward position. Both our hands are sticking into the window, but from different sides. But we can’t see our fingers. Instead, it appears to us that both hands have disappeared.

Figure 10.4. If we insert our hands into the window from two different directions, then it appears as though our hands have disappeared. We have a body, but no hands. In the alternative universe, two hands have emerged from either side of the window but they are not attached to a body
.

How does this appear to the dinosaurs? They see two wiggling, tiny hands dangling from the window, from either side. But there is no body (
Figure 10.4
).

This example illustrates some of the delicious distortions of space and time that one can invent with multiply connected spaces.

It seems remarkable that such a simple idea—that higher dimensions can unify space with time, and that a “force” can be explained by the warping of that space-time—would lead to such a rich diversity of physical consequences. However, with the wormhole and multiply connected spaces, we are probing the very limits of Einstein’s theory of general relativity. In fact, the amount of matter-energy necessary to create a wormhole or dimensional gateway is so large that we expect quantum effects to dominate. Quantum corrections, in turn, may actually close the opening of the wormhole, making travel through the gateway impossible.

Since neither quantum theory nor relativity is powerful enough to settle this question, we will have to wait until the ten-dimensional theory is completed to decide whether these wormholes are physically relevant or just another crazy idea. However, before we discuss the question of quantum corrections and the ten-dimensional theory, let us now pause and consider perhaps the most bizarre consequence of wormholes. Just as physicists can show that wormholes allow for multiply connected spaces, we can also show that they allow for time travel as well.

Let us now consider perhaps the most fascinating, and speculative, consequence of multiply connected universes: building a time machine.

People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion.

Albert Einstein

CAN we go backward in time?

Like the protagonist in H. G. Wells’s
The Time Machine
, can we spin the dial of a machine and leap hundreds of thousands of years to the year 802,701? Or, like Michael J. Fox, can we hop into our plutonium-fired cars and go back to the future?

The possibility of time travel opens up a vast world of interesting possibilities. Like Kathleen Turner in
Peggy Sue Got Married
, everyone harbors a secret wish somehow to relive the past and correct some small but vital mistake in one’s life. In Robert Frost’s poem “The Road Not Taken,” we wonder what might have happened, at key junctures in our lives, if we had made different choices and taken another path. With time travel, we could go back to our youth and erase embarrassing events from our past, choose a different mate, or enter different careers; or we could even change the outcome of key historical events and alter the fate of humanity.

For example, in the climax of
Superman
, our hero is emotionally devastated when an earthquake ravages most of California and crushes his
lover under hundreds of tons of rock and debris. Mourning her horrible death, he is so overcome by anguish that he rockets into space and violates his oath not to tamper with the course of human history. He increases his velocity until he shatters the light barrier, disrupting the fabric of space and time. By traveling at the speed of light, he forces time to slow down, then to stop, and finally to go backward, to a time before Lois Lane was crushed to death.

This trick, however, is clearly not possible. Although time does slow down when you increase your velocity, you cannot go faster than the speed of light (and hence make time go backward) because special relativity states that your mass would become infinite in the process. Thus the faster-than-light travel method preferred by most science-fiction writers contradicts the special theory of relativity.

Einstein himself was well aware of this impossibility, as was A. H. R. Buller when he published the following limerick in
Punch:

There was a young lady girl named Bright,
Whose speed was far faster than light,
She traveled one day,
In a relative way,
And returned on the previous night.

Most scientists, who have not seriously studied Einstein’s equations, dismiss time travel as poppycock, with as much validity as lurid accounts of kidnappings by space aliens. However, the situation is actually quite complex.

To resolve the question, we must leave the simpler theory of special relativity, which forbids time travel, and embrace the full power of the
general
theory of relativity, which may permit it. General relativity has much wider validity than special relativity. While special relativity describes only objects moving at constant velocity far away from any stars, the general theory of relativity is much more powerful, capable of describing rockets accelerating near supermassive stars and black holes. The general theory therefore supplants some of the simpler conclusions of the special theory. For any physicist who has seriously analyzed the mathematics of time travel within Einstein’s general theory of relativity, the final conclusion is, surprisingly enough, far from clear.

Proponents of time travel point out that Einstein’s equations for general relativity do allow some forms of time travel. They acknowledge, however, that the energies necessary to twist time into a circle are so great that Einstein’s equations break down. In the physically interesting
region where time travel becomes a serious possibility, quantum theory takes over from general relativity.

Einstein’s equations, we recall, state that the curvature or bending of space and time is determined by the matter-energy content of the universe. It is, in fact, possible to find configurations of matter-energy powerful enough to force the bending of time and allow for time travel. However, the concentrations of matter-energy necessary to bend time backward are so vast that general relativity breaks down and quantum corrections begin to dominate over relativity. Thus the final verdict on time travel cannot be answered within the framework of Einstein’s equations, which break down in extremely large gravitational fields, where we expect quantum theory to become dominant.

This is where the hyperspace theory can settle the question. Because both quantum theory and Einstein’s theory of gravity are united in ten-dimensional space, we expect that the question of time travel will be settled decisively by the hyperspace theory. As in the case of wormholes and dimensional windows, the final chapter will be written when we incorporate the full power of the hyperspace theory.

Let us now describe the controversy surrounding time travel and the delicious paradoxes that inevitably arise.

Science-fiction writers have often wondered what might happen if a single individual went back in time. Many of these stories, on the surface, appear plausible. But imagine the chaos that would arise if time machines were as common as automobiles, with tens of millions of them commercially available. Havoc would soon break loose, tearing at the fabric of our universe. Millions of people would go back in time to meddle with their own past and the past of others, rewriting history in the process. A few might even go back in time armed with guns to shoot down the parents of their enemies before they were born. It would thus be impossible to take a simple census to see how many people there were at any given time.

If time travel is possible, then the laws of causality crumble. In fact, all of history as we know it might collapse as well. Imagine the chaos caused by thousands of people going back in time to alter key events that changed the course of history. All of a sudden, the audience at Ford’s Theater would be crammed with people from the future bickering among themselves to see who would have the honor of preventing
Lincoln’s assassination. The landing at Normandy would be botched as thousands of thrill seekers with cameras arrived to take pictures.

The key battlefields of history would be changed beyond recognition. Consider Alexander the Great’s decisive victory over the Persians, led by Darius III, in 331
B.C.
at the Battle of Gaugamela. This battle led to the collapse of the Persian forces and ended their rivalry with the West, which helped allow the flourishing of Western civilization and culture over the world for the next 1,000 years. But consider what would happen if a small band of armed mercenaries equipped with small rockets and modern artillery were to enter the battle. The slightest display of modern firepower would rout Alexander’s terrified soldiers. This meddling in the past would cripple the expansion of Western influence in the world.

Time travel would mean that any historical event could never be completely resolved. History books could never be written. Some diehard would always be trying to assassinate General Ulysses S. Grant or give the secret of the atomic bomb to the Germans in the 1930s.

What would happen if history could be rewritten as casually as erasing a blackboard? Our past would be like the shifting sands at the seashore, constantly blown this way or that by the slightest breeze. History would be constantly changing every time someone spun the dial of a time machine and blundered his or her way into the past. History, as we know it, would be impossible. It would cease to exist.

Most scientists obviously do not relish this unpleasant possibility. Not only would it be impossible for historians to make any sense out of “history,” but genuine paradoxes immediately arise whenever we enter the past or future. Cosmologist Stephen Hawking, in fact, has used this situation to provide “experimental” evidence that time travel is not possible. He believes that time travel is not possible by “the fact that we have not been invaded by hoardes of tourists from the future.”

To understand the problems with time travel, it is first necessary to classify the various paradoxes. In general, most can be broken down into one of two principal types:

1. Meeting your parents before you are born

2. The man with no past

The first type of time travel does the most damage to the fabric of space-time because it alters previously recorded events. For example, remember that in
Back to the Future
, our young hero goes back in time and meets his mother as a young girl, just before she falls in love with his father. To his shock and dismay, he finds that he has inadvertently prevented the fateful encounter between his parents. To make matters worse, his young mother has now become amorously attracted to him! If he unwittingly prevents his mother and father from falling in love and is unable to divert his mother’s misplaced affections, he will disappear because his birth will never happen.

The second paradox involves events without any beginning. For example, let’s say that an impoverished, struggling inventor is trying to construct the world’s first time machine in his cluttered basement. Out of nowhere, a wealthy, elderly gentleman appears and offers him ample funds and the complex equations and circuitry to make a time machine. The inventor subsequently enriches himself with the knowledge of time travel, knowing beforehand exactly when stock-market booms and busts will occur before they happen. He makes a fortune betting on the stock market, horse races, and other events. Decades later, as a wealthy, aging man, he goes back in time to fulfill his destiny. He meets himself as a young man working in his basement, and gives his younger self the secret of time travel and the money to exploit it. The question is: Where did the idea of time travel come from?

Perhaps the craziest of these time travel paradoxes of the second type was cooked up by Robert Heinlein in his classic short story “All You Zombies—.”

A baby girl is mysteriously dropped off at an orphanage in Cleveland in 1945. “Jane” grows up lonely and dejected, not knowing who her parents are, until one day in 1963 she is strangely attracted to a drifter. She falls in love with him. But just when things are finally looking up for Jane, a series of disasters strike. First, she becomes pregnant by the drifter, who then disappears. Second, during the complicated delivery, doctors find that Jane has both sets of sex organs, and to save her life, they are forced to surgically convert “her” to a “him.” Finally, a mysterious stranger kidnaps her baby from the delivery room.