Hyperspace (41 page)

Gödel’s solution could not be dismissed as the work of a crackpot because Gödel had used Einstein’s own field equations to find strange solutions in which time bent into a circle. Because Gödel had played by the rules and discovered a legitimate solution to his equations, Einstein was forced to take the evasive route and dismiss it because it did not fit the experimental data.

The weak spot in Gödel’s universe was the assumption that the gas and dust in the universe were slowly rotating. Experimentally, we do not see any rotation of the cosmic dust and gas in space. Our instruments have verified that the universe is expanding, but it does not appear to be rotating. Thus the Gödel universe can be safely ruled out. (This leaves us with the rather disturbing, although plausible, possibility that if our universe did rotate, as Gödel speculated, then CTCs and time travel would be physically possible.)

Einstein died in 1955, content that disturbing solutions to his equations could be swept under the rug for experimental reasons and that people could not meet their parents before they were born.

Then, in 1963, Ezra Newman, Theodore Unti, and Louis Tamburino discovered a new solution to Einstein’s equations that was even crazier than Gödel’s. Unlike the Gödel universe, their solution was not based on a rotating dust-filled universe. On the surface, it resembled a typical black hole.

As in the Gödel solution, their universe allowed for CTCs and time travel. Moreover, when going 360 degrees around the black hole, you would not wind up where you originally started. Instead, like living on a universe with a Riemann cut, you would wind up on another sheet of
the universe. The topology of a Newman-Unti-Tamburino universe might be compared to living on a spiral staircase. If we move 360 degrees around the staircase, we do not arrive at the same point at which we started, but on another landing of the staircase. Living in such a universe would surpass our worst nightmare, with common sense being completely thrown out the window. In fact, this bizarre universe was so pathological that it was quickly coined the NUT universe, after the initials of its creators.

At first, relativists dismissed the NUT solution in the same way they had dismissed the Gödel solution; that is, our universe didn’t seem to evolve in the way predicted by these solutions, so they were arbitrarily discarded for experimental reasons. However, as the decades went by, there was a flood of such bizarre solutions to Einstein’s equations that allowed for time travel. In the early 1970s, Frank J. Tipler at Tulane University in New Orleans reanalyzed an old solution to Einstein’s equations found by W.J. van Stockum in 1936, even before Gödel’s solution. This solution assumed the existence of an infinitely long, rotating cylinder. Surprisingly enough, Tipler was able to show that this solution also violated causality.

Even the Kerr solution (which represents the most physically realistic description of black holes in outer space) was shown to allow for time travel. Rocket ships that pass through the center of the Kerr black hole (assuming they are not crushed in the process) could violate causality.

Soon, physicists found that NUT-type singularities could be inserted into any black hole or expanding universe. In fact, it now became possible to cook up an infinite number of pathological solutions to Einstein’s equations. For example, every wormhole solution to Einstein’s equations could be shown to allow some form of time travel.

According to relativist Frank Tipler, “solutions to the field equations can be found which exhibit virtually any type of bizarre behavior.”
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Thus an explosion of pathological solutions to Einstein’s equations was discovered that certainly would have horrified Einstein had he still been alive.

Einstein’s equations, in some sense, were like a Trojan horse. On the surface, the horse looks like a perfectly acceptable gift, giving us the observed bending of starlight under gravity and a compelling explanation of the origin of the universe. However, inside lurk all sorts of strange demons and goblins, which allow for the possibility of interstellar travel through wormholes and time travel. The price we had to pay for peering into the darkest secrets of the universe was the potential downfall of some of our most commonly held beliefs about our world—that its space is simply connected and its history is unalterable.

But the question still remained: Could these CTCs be dismissed on purely experimental grounds, as Einstein did, or could someone show that they were theoretically possible and then actually build a time machine?

In June 1988, three physicists (Kip Thorne and Michael Morris at the California Institute of Technology and Ulvi Yurtsever at the University of Michigan) made the first serious proposal for a time machine. They convinced the editors of
Physical Review Letters
, one of the most distinguished publications in the world, that their work merited serious consideration. (Over the decades, scores of crackpot proposals for time travel have been submitted to mainstream physics journals, but all have been rejected because they were not based on sound physical principles or Einstein’s equations.) Like experienced scientists, they presented their arguments in accepted field theoretical language and then carefully explained where their weakest assumptions were.

To overcome the skepticism of the scientific community, Thorne and his colleagues realized that they would have to overcome the standard objections to using wormholes as time machines. First, as mentioned earlier, Einstein himself realized that the gravitational forces at the center of a black hole would be so enormous that any spacecraft would be torn apart. Although wormholes were mathematically possible, they were, in practice, useless.

Second, wormholes might be unstable. One could show that small disturbances in wormholes would cause the Einstein-Rosen bridge to collapse. Thus a spaceship’s presence inside a black hole would be sufficient to cause a disturbance that would close the entrance to the wormhole.

Third, one would have to go faster than the speed of light actually to penetrate the wormhole to the other side.

Fourth, quantum effects would be so large that the wormhole might close by itself. For example, the intense radiation emitted by the entrance to the black hole not only would kill anyone who tried to enter the black hole, but also might close the entrance.

Fifth, time slows down in a wormhole and comes to a complete stop at the center. Thus wormholes have the undesirable feature that as seen by someone on the earth, a space traveler appears to slow down and come to a total halt at the center of the black hole. The space traveler looks like he or she is frozen in time. In other words, it takes an infinite
amount of time for a space traveler to go through a wormhole. Assuming, for the moment, that one could somehow go through the center of the wormhole and return to earth, the distortion of time would still be so great that millions or even billions of years may have passed on the earth.

For all these reasons, the wormhole solutions were never taken seriously.

Thorne is a serious cosmologist, one who might normally view time machines with extreme skepticism or even derision. However, Thorne was gradually drawn into this quest in the most curious way. In the summer of 1985, Carl Sagan sent to Thorne the prepublication draft of his next book, a novel called
Contact
, which seriously explores the scientific and political questions surrounding an epoch-making event: making contact with the first extraterrestrial life in outer space. Every scientist pondering the question of life in outer space must confront the question of how to break the light barrier. Since Einstein’s special theory of relativity explicitly forbids travel faster than the speed of light, traveling to the distant stars in a conventional spaceship may take thousands of years, thereby making interstellar travel impractical. Since Sagan wanted to make his book as scientifically accurate as possible, he wrote to Thorne asking whether there was any scientifically acceptable way of evading the light barrier.

Sagan’s request piqued Thorne’s intellectual curiosity. Here was an honest, scientifically relevant request made by one scientist to another that demanded a serious reply. Fortunately, because of the unorthodox nature of the request, Thorne and his colleagues approached the question in a most unusual way: They worked
backward
. Normally, physicists start with a certain known astronomical object (a neutron star, a black hole, the Big Bang) and then solve Einstein’s equations to find the curvature of the surrounding space. The essence of Einstein’s equations, we recall, is that the matter and energy content of an object determines the amount of curvature in the surrounding space and time. Proceeding in this way, we are guaranteed to find solutions to Einstein’s equations for astronomically relevant objects that we expect to find in outer space.

However, because of Sagan’s strange request, Thorne and his colleagues approached the question backward. They started with a rough idea of what they wanted to find. They wanted a solution to Einstein’s equations in which a space traveler would not be torn apart by the tidal effects of the intense gravitational field. They wanted a wormhole that would be stable and not suddenly close up in the middle of the trip. They wanted a wormhole in which the time it takes for a round trip
would be measured in days, not millions or billions of earth years, and so on. In fact, their guiding principle was that they wanted a time traveler to have a reasonably comfortable ride back through time after entering the wormhole. Once they decided what their wormhole would look like, then, and only then, did they begin to calculate the amount of energy necessary to create such a wormhole.

From their unorthodox point of view, they did not particularly care if the energy requirements were well beyond twentieth-century science. To them, it was an engineering problem for some future civilization actually to construct the time machine. They wanted to prove that it was scientifically feasible, not that it was economical or within the bounds of present-day earth science:

Normally, theoretical physicists ask, “What are the laws of physics?” and/or “What do those laws predict about the Universe?” In this Letter, we ask, instead, “What constraints do the laws of physics place on the activities of an arbitrarily advanced civilization?” This will lead to some intriguing queries about the laws themselves. We begin by asking whether the laws of physics permit an arbitrarily advanced civilization to construct and maintain wormholes for interstellar travel.
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The key phrase, of course, is “arbitrarily advanced civilization.” The laws of physics tell us what is possible, not what is practical. The laws of physics are independent of what it might cost to test them. Thus what is theoretically possible may exceed the gross national product of the planet earth. Thorne and his colleagues were careful to state that this mythical civilization that can harness the power of wormholes must be “arbitrarily advanced”—that is, capable of performing all experiments that are possible (even if they are not practical for earthlings).

Much to their delight, with remarkable ease they soon found a surprisingly simple solution that satisfied all their rigid constraints. It was
not
a typical black hole solution at all, so they didn’t have to worry about all the problems of being ripped apart by a collapsed star. They christened their solution the “transversible wormhole,” to distinguish it from the other wormhole solutions that are not transversible by spaceship. They were so excited by their solution that they wrote back to Sagan, who then incorporated some of their ideas in his novel. In fact, they were so surprised by the simplicity of their solution that they were convinced that a beginning graduate student in physics would be able to understand their solution. In the autumn of 1985, on the final exam in a course on general relativity given at Caltech, Thorne gave the worm-hole
solution to the students without telling them what it was, and they were asked to deduce its physical properties. (Most students gave detailed mathematical analyses of the solution, but they failed to grasp that they were looking at a solution that permitted time travel.)

If the students had been a bit more observant on that final exam, they would have been able to deduce some rather astonishing properties of the wormhole. In fact, they would have found that a trip through this transversible wormhole would be as comfortable as a trip on an airplane. The maximum gravitational forces experienced by the travelers would not exceed 1
g
. In other words, their apparent weight would not exceed their weight on the earth. Furthermore, the travelers would never have to worry about the entrance of the wormhole closing up during the journey. Thorne’s wormhole is, in fact, permanently open. Instead of taking a million or a billion years, a trip through the transversible worm-hole would be manageable. Morris and Thorne write that “the trip will be fully comfortable and will require a total of about 200 days,” or less.
⁵

So far, Thorne notes that the time paradoxes that one usually encounters in the movies are not to be found: “From exposure to science fiction scenarios (for example, those in which one goes back in time and kills oneself) one might expect CTCs to give rise to initial trajectories with zero multiplicities” (that is, trajectories that are impossible).
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However, he has shown that the CTCs that appear in his worm-hole seem to
fulfill
the past, rather than change it or initiate time paradoxes.

Finally, in presenting these surprising results to the scientific community, Thorne wrote, “A new class of solutions of the Einstein field equations is presented, which describe wormholes that, in principle, could be traversed by human beings.”

There is, of course, a catch to all this, which is one reason why we do not have time machines today. The last step in Thorne’s calculation was to deduce the precise nature of the matter and energy necessary to create this marvelous transversible wormhole. Thorne and his colleagues found that at the center of the wormhole, there must be an “exotic” form of matter that has unusual properties. Thorne is quick to point out that this “exotic” form of matter, although unusual, does not seem to violate any of the known laws of physics. He cautions that, at some future point, scientists may prove that exotic matter does not exist. However, at present, exotic matter seems to be a perfectly acceptable form of matter
if
one has access to sufficiently advanced technology. Thorne writes confidently that “from a single wormhole an arbitrarily advanced civilization can construct a machine for backward time travel.”