by Michio Kaku
Actually, even more bizarre types of solutions to Einstein’s equations can be found. Einstein’s equations state that if you are given a certain amount of mass or energy, you can compute the warping of space-time that the mass or energy will generate (in the same way that if you throw a rock into a pond, you can calculate the ripples that it will create). But you can also run the equations backward. You can start with a bizarre space-time, the kind found in episodes of The Twilight Zone. (In these universes, for example, you can open up a door and find yourself on the moon. You can run around a tree and find yourself backward in time, with your heart on the right side of your body.) Then you calculate the distribution of matter and energy associated with that particular space-time. (This means that if you are given a bizarre collection of waves on the surface of a pond, you can work backward and calculate the distribution of rocks necessary to produce these waves). This was, in fact, the way in which Alcubierre derived his equations. He began with a space-time consistent with going faster than light, and then he worked backward and calculated the energy necessary to produce it.
WORMHOLES AND BLACK HOLES
Besides stretching space, the second possible way to break the light barrier is by ripping space, via wormholes, passageways that connect two universes. In fiction, the first mention of a wormhole came from Oxford mathematician Charles Dodgson, who wrote Through the Looking Glass under the pen name Lewis Carroll. The Looking Glass of Alice is the wormhole, connecting the countryside of Oxford with the magical world of Wonderland. By placing her hand through the Looking Glass, Alice can be transported instantly from one universe to the next. Mathematicians call these “multiply connected spaces.”
The concept of wormholes in physics dates back to 1916, one year after Einstein published his epic general theory of relativity. Physicist Karl Schwarzschild, then serving in the Kaiser’s army, was able to solve Einstein’s equations exactly for the case of a single pointlike star. Far from the star, its gravitational field was very similar to that of an ordinary star, and in fact Einstein used Schwarzschild’s solution to calculate the deflection of light around a star. Schwarzschild’s solution had an immediate and profound impact on astronomy, and even today it is one of the best-known solutions of Einstein’s equations. For generations, physicists used the gravitational field around this pointlike star as an approximation to the field around a real star, which has a finite diameter.
But if you took this pointlike solution seriously, then lurking at the center of it was a monstrous pointlike object that has shocked and amazed physicists for almost a century—a black hole. Schwarzschild’s solution for the gravity of a pointlike star was like a Trojan Horse. On the outside it looked like a gift from heaven, but on the inside there lurked all sorts of demons and ghosts. But if you accepted one, you had to accept the other. Schwarzschild’s solution showed that as you approached this pointlike star, bizarre things happened. Surrounding the star was an invisible sphere (called the “event horizon”) that was a point of no return. Everything checked in, but nothing could check out, like a Roach Motel. Once you passed through the event horizon, you never came back. (Once inside the event horizon, you would have to travel faster than light to escape back outside the event horizon, and that would be impossible.)
As you approached the event horizon, your atoms would be stretched by tidal forces. The gravity felt by your feet would be much greater than the gravity felt by your head, so you would be “spaghettified” and then ripped apart. Similarly, the atoms of your body would also be stretched and torn apart by gravity.
To an outside observer watching you approach the event horizon, it would appear that you were slowing down in time. In fact, as you hit the event horizon, it would appear that time had stopped!
Furthermore, as you fell past the event horizon, you would see light that has been trapped and circulating around this black hole for billions of years. It would seem as if you were watching a motion picture film, detailing the entire history of the black hole, going back to its very origin.
And finally, if you could fall straight through to the black hole, there would be another universe on the other side. This is called the Einstein-Rosen Bridge, first introduced by Einstein in 1935; it is now called a wormhole.
Einstein and other physicists believed a star could never evolve naturally into such a monstrous object. In fact, in 1939 Einstein published a paper showing that a circulating mass of gas and dust will never condense into such a black hole. So although there was a wormhole lurking in the center of a black hole, he was confident that such a strange object could never form by natural means. In fact, astrophysicist Arthur Eddington once said that there should “be a law of nature to prevent a star from behaving in this absurd way.” In other words, the black hole was indeed a legitimate solution of Einstein’s equations, but there was no known mechanism that could form one by natural means.
All this changed with the advent of a paper by J. Robert Oppenheimer and his student Hartland Snyder, written that same year, showing that black holes can indeed be formed by natural means. They assumed that a dying star had used up its nuclear fuel and then collapsed under gravity, so that it imploded under its own weight. If gravity could compress the star to within its event horizon, then nothing known to science could prevent gravity from squeezing the star to a point-particle, the black hole. (This implosion method may have given Oppenheimer the clue for building the Nagasaki bomb just a few years later, which depends on imploding a sphere of plutonium.)
The next breakthrough came in 1963, when New Zealand mathematician Roy Kerr examined perhaps the most realistic example of a black hole. Objects spin faster as they shrink, in much the same way that skaters spin faster when they bring in their arms close to their body. As a result black holes should be spinning at fantastic rates.
Kerr found that a spinning black hole would not collapse into a pointlike star, as Schwarzschild assumed, but would collapse into a spinning ring. Anyone unfortunate enough to hit the ring would perish; but someone falling into the ring would not die, but would actually fall through. But instead of winding up on the other side of the ring, he or she would pass through the Einstein-Rosen Bridge and wind up in another universe. In other words, the spinning black hole is the rim of Alice’s Looking Glass.
If he or she were to move around the spinning ring a second time, he or she would enter yet another universe. In fact, repeated entry into the spinning ring would put a person in different parallel universes, much like hitting the “up” button on an elevator. In principle, there could be an infinite number of universes, each stacked on top of each other. “Pass through this magic ring and—presto!—you’re in a completely different universe where radius and mass are negative!” Kerr wrote.
There is an important catch, however. Black holes are examples of “nontransversable wormholes” that is, passing through the event horizon is a one-way trip. Once you pass through the event horizon and the Kerr ring, you cannot go backward through the ring and out through the event horizon.
But in 1988 Kip Thorne and colleagues at Cal Tech found an example of a transversable wormhole, that is, one through which you could pass freely back and forth. In fact, for one solution, the travel through a wormhole would be no worse than riding on an airplane.
Normally gravity would crush the throat of the wormhole, destroying the astronauts trying to reach the other side. That is one reason that faster-than-light travel through a wormhole is not possible. But the repulsive force of negative energy or negative mass could conceivably keep the throat open sufficiently long to allow astronauts a clear passage. In other words, negative mass or energy is essential for both the Alcubierre drive and the wormhole solution.
In the last few years an astonishing number of exact solutions have been found to Einstein’s equations that allow for wormholes. But do wormholes really exist, or are they just a figment of mathematics? There are several major problems facing wormholes.
First, to create the violent distort
ions of space and time necessary to travel through a wormhole, one would need fabulous amounts of positive and negative matter, on the order of a huge star or a black hole. Matthew Visser, a physicist at Washington University, estimates that the amount of negative energy you would need to open up a 1-meter wormhole is comparable to the mass of Jupiter, except that it would need to be negative. He says, “You need about minus one Jupiter mass to do the job. Just manipulating a positive Jupiter mass of energy is already pretty freaky, well beyond our capabilities into the foreseeable future.”
Kip Thorne of the California Institute of Technology speculates that “it will turn out that the laws of physics do allow sufficient exotic matter in wormholes of human size to hold the wormhole open. But it will also turn out that the technology for making wormholes and holding them open is unimaginably far beyond the capabilities of our human civilization.”
Second, we do not know how stable these wormholes would be. The radiation generated by these wormholes might kill anyone who enters. Or perhaps the wormholes would not be stable at all, closing as soon as one entered them.
Third, light beams falling into the black hole would be blue shifted; that is, they would attain greater and greater energy as they came close to the event horizon. In fact, at the event horizon itself, light is technically infinitely blue shifted, so the radiation from this infalling energy could kill anyone in a rocket.
Let us discuss these problems in some detail. One problem is to amass enough energy to rip the fabric of space and time. The simplest way to do this is to compress an object until it becomes smaller than its “event horizon.” For the sun, this means compressing it down to about 2 miles in diameter, whereupon it will collapse into a black hole. (The Sun’s gravity is too weak to compress it naturally down to 2 miles, so our sun will never become a black hole. In principle, this means that anything, even you, can become a black hole if you were sufficiently compressed. This would mean compressing all the atoms of your body to smaller than subatomic distances—a feat that is beyond the capabilities of modern science.)
A more practical approach would be to assemble a battery of laser beams to fire an intense beam at a specific spot. Or to build a huge atom smasher to create two beams, which would then collide with each other at fantastic energies, sufficient to create a small tear in the fabric of space-time.
PLANCK ENERGY AND PARTICLE ACCELERATORS
One can calculate the energy necessary to create an instability in space and time: it is of the order of the Planck energy, or 1019 billion electron volts. This is truly an unimaginably large number, a quadrillion times larger than the energy attainable with today’s most powerful machine, the Large Hadron Collider (LHC), located outside Geneva, Switzerland. The LHC is capable of swinging protons in a large “doughnut” until they reach energies of trillions of electron volts, energies not seen since the big bang. But even this monster of a machine falls far short of producing energy anywhere near the Planck energy.
The next particle accelerator after the LHC will be the International Linear Collider (ILC). Instead of bending the path of subatomic particles into a circle, the ILC will shoot them down a straight path. Energy will be injected as the particles move along this path, until they attain unimaginably large energies. Then a beam of electrons will collide with antielectrons, creating a huge burst of energy. The ILC will be 30 to 40 kilometers long, or ten times the length of the Stanford Linear Accelerator, currently the largest linear accelerator. If all goes well, the ILC is due to be completed sometime in the next decade.
The energy produced by the ILC will be .5 to 1.0 trillion electron volts—less than the 14 trillion electron volts of the LHC, but this is deceptive. (In the LHC, the collisions between the protons take place between the constituent quarks making up the proton. Hence the collisions involving the quarks are less than 14 trillion electron volts. That is why the ILC will produce collision energies larger than those of the LHC.) Also, because the electron has no known constituent, the dynamics of the collisions between electron and antielectron are simpler and cleaner.
But realistically, the ILC, too, falls far short of being able to open up a hole in space-time. For that, you would need an accelerator a quadrillion times more powerful. For our Type 0 civilization, which uses dead plants for fuel (e.g., oil and coal), this technology is far beyond anything we can muster. But it may become possible for a Type III civilization.
Remember, a Type III civilization, which is galactic in its use of energy, consumes 10 billion times more energy than a Type II civilization, whose consumption is based on the energy of a single star. And a Type II civilization in turn consumes 10 billion times more energy than a Type I civilization, whose consumption is based on the energy of a single planet. In one hundred to two hundred years, our feeble Type 0 civilization will reach Type I status.
Given that projection, we are a long, long way from being able to achieve the Planck energy. Many physicists believe that at extremely tiny distances, at the Planck distance of 10-33 centimeters, space is not empty or smooth but becomes “foamy” it is frothing with tiny bubbles that constantly pop into existence, collide with other bubbles, and then vanish back into the vacuum. These bubbles that dart in and out of the vacuum are “virtual universes,” very similar to the virtual particles of electrons and antielectrons that pop into existence and then disappear.
Normally, this quantum space-time “foam” is completely invisible to us. These bubbles form at such tiny distances that we cannot observe them. But quantum physics suggests that if we concentrate enough energy at a single point, until we reach the Planck energy, these bubbles can become large. Then we would see space-time frothing with tiny bubbles, each bubble a wormhole connected to a “baby universe.”
In the past these baby universes were considered an intellectual curiosity, a strange consequence of pure mathematics. But now physicists are seriously thinking that our universe might have originally started off as one of these baby universes.
Such thinking is sheer speculation, but the laws of physics allow for the possibility of opening a hole in space by concentrating enough energy at a single point, until we access the space-time foam and wormholes emerge connecting our universe to a baby universe.
Achieving a hole in space would, of course, require major breakthroughs in our technology, but again, it might be possible for a Type III civilization. For example, there have been promising developments in something called a “Wakefield tabletop accelerator.” Remarkably, this atom smasher is so small that it can be placed on top of a table yet generate billions of electron volts of energy. The Wakefield tabletop accelerator works by firing lasers onto charged particles, which then ride on the energy of that laser. Experiments done at the Stanford Linear Accelerator Center, the Rutherford Appleton Laboratory in England, and the École Polytechnique in Paris show that enormous accelerations are possible over small distances using laser beams and plasma to inject energy.
Yet another breakthrough was made in 2007, when physicists and engineers at the Stanford Linear Accelerator Center, UCLA, and USC demonstrated that you can double the energy of a huge particle accelerator in just 1 meter. They started with a beam of electrons that are fired down a 2-mile-long tube in Stanford, reaching an energy of 42 billion electron volts. Then these high-energy electrons were sent through an “afterburner,” which consisted of a plasma chamber only 88 centimeters long, where the electrons pick up an additional 42 billion electron volts, doubling their energy. (The plasma chamber is filled with lithium gas. As the electrons pass through the gas, they create a plasma wave that creates a wake. This wake in turn flows to the back of the electron beam and then shoves it forward, giving it an extra boost.) In this stunning achievement, the physicists improved by a factor of three thousand the previous record for the amount of energy per meter they could accelerate an electron beam. By adding such “afterburners” to existing accelerators, one might in principle double their energy, almost for free.
Today the world
record for a Wakefield tabletop accelerator is 200 billion electron volts per meter. There are numerous problems scaling this result to longer distances (such as maintaining the stability of the beam as laser power is pumped into it). But assuming that we could maintain a power level of 200 billion electron volts per meter, this means that an accelerator capable of reaching the Planck energy would have to be 10 light-years long. This is well within the capability of a Type III civilization.
Wormholes and stretched space may give us the most realistic way of breaking the light barrier. But it is not known if these technologies are stable; if they are, it would still take a fabulous amount of energy, positive or negative, to make them work.
Perhaps an advanced Type III civilization might already have this technology. It might be millennia before we can even think about harnessing power on this scale. Because there is still controversy over the fundamental laws governing the fabric of space-time at the quantum level, I would classify this as a Class II impossibility.
12: TIME TRAVEL
If time travel is possible, then where are the tourists from the future?
—STEPHEN HAWKING
“[Time travel] is against reason,” said Filby.
“What reason?” said the Time Traveler.
—H. G. WELLS
In the novel Janus Equation, writer G. Spruill explored one of the harrowing problems with time travel. In this tale a brilliant mathematician whose goal is to discover the secret of time travel meets a strange, beautiful woman, and they become lovers, although he knows nothing about her past. He becomes intrigued about finding out her true identity. Eventually he discovers that she once had plastic surgery to change her features. And that she had a sex change operation. Finally, he discovers that “she” is actually a time traveler from the future, and that “she” is actually himself, but from the future. This means that he made love to himself. And one is left wondering, what would have happened if they had had a child? And if this child went back into the past, to grow up to become the mathematician at the beginning of the story, then is it possible to be your own mother and father and son and daughter?