B003CTEFLQ EBOK

by Michio Kaku

  What is interesting about the picture is that the ripples probably correspond to tiny quantum fluctuations in the big bang. According to the uncertainty principle, the big bang could not have been a perfectly smooth explosion, since quantum effects must have produced ripples of a certain size. This, in fact, was precisely what the Berkeley group found. (In fact, if they had not found these ripples, it would have been a great setback for the uncertainty principle.) These ripples not only showed that the uncertainty principle applied to the birth of the universe, but also gave scientists a plausible mechanism for the creation of our “lumpy universe.” When we look around us, we see that the galaxies are found in clusters, thereby giving the universe a rough texture. This lumpiness can possibly be easily explained as the ripples from the original big bang, which have been stretched as the universe expanded. Hence, when we see the clusters of galaxies in the heavens, we may be peering into the original ripples of the big bang left by the uncertainty principle.

  But perhaps the most spectacular rediscovery of Einstein’s work comes in the form of “dark energy.” As we saw earlier, he introduced the concept of the cosmological constant (or the energy of the vacuum) in 1917 in order to prevent the universe from expanding. (We recall that there are only two possible terms allowed by general covariance, the Ricci curvature and the volume of space-time, so the cosmological constant term cannot be easily dismissed.) He later called it his greatest blunder when Edwin Hubble showed that the universe is in fact expanding. Results found in 2000, however, reveal that Einstein was probably right after all: the cosmological constant not only exists, but dark energy probably makes up the largest source of matter/energy in the entire universe. By analyzing supernovae in distant galaxies, astronomers have been able to calculate the rate of expansion of the universe over billions of years. To their surprise, they found that the expansion of the universe, instead of slowing down as most had thought, is actually speeding up. Our universe is in a runaway mode and will eventually expand forever. Thus, we can now predict how our universe will die.

  Previously, some cosmologists believed that there might be enough matter in the universe to reverse the cosmic expansion, so that the universe might eventually contract and a blue shift would be seen in outer space. (Physicist Stephen Hawking even believed that time might reverse itself as the universe contracted and history might repeat itself in a backward fashion. This would mean that people would turn younger and jump into their mother’s womb, that people would dive backward from a swimming pool and land dry on the diving board, and frying eggs would leap into their unbroken shells. Hawking, however, has since admitted he made a mistake.) Eventually, the universe would implode on itself, creating the enormous heat of a “big crunch.” Others even speculated that the universe may then undergo another big bang, thereby creating an oscillating universe.

  However, all this has now been ruled out with the experimental result that the expansion of the universe is accelerating. The simplest explanation that seems to fit the data is to assume that there is an enormous amount of dark energy pervading the universe which acts like antigravity, pushing the galaxies apart. The greater the universe becomes, the more vacuum energy there is, which in turn pushes the galaxies even farther apart, creating an accelerating universe.

  This seems to vindicate one version of the “inflationary universe” idea, first proposed by MIT physicist Alan Guth, which is a modification of the original big bang theory of Friedmann and Lemaître. Roughly, in the inflationary picture there are two phases to the expansion. The first is a rapid, exponential expansion, when the universe was dominated by a large cosmological constant. Eventually, this exponential inflation terminates, and the expansion slows down to resemble the conventional expanding universe found by Friedmann and Lemaître. If correct, this means that the universe visible around us is just a pinpoint on a much larger space-time that represents the true universe. Recent experiments with balloons high in the atmosphere have also given credible evidence of inflation by showing that the universe seems to be approximately flat, which indicates how big it really is. We are like ants sitting on a huge balloon, thinking that our universe is flat only because we are so small.

  Dark energy also forces us to reappraise our true role and position in the universe. It was Copernicus who showed that there was nothing special about the position of humans in the solar system. The existence of dark matter shows that there is nothing special about the atoms that make up our world, since 90% of the matter in the universe is made of mysterious dark matter. Now, the result from the cosmological constant indicates that dark energy dwarfs dark matter, which in turn dwarfs the energy of the stars and galaxies. The cosmological constant, once reluctantly introduced by Einstein to stabilize the universe, is probably by far the largest source of energy in the universe. (In 2003, the WMAP satellite verified that 4% of the universe’s matter and energy is found in ordinary atoms, 23% in some form of unknown dark matter, and 73% of it in dark energy.)

  Another strange prediction of general relativity is the black hole, which was considered science fiction when Schwarzschild reintroduced the concept of dark stars back in 1916. However, the Hubble Space Telescope and the Very Large Array Radio Telescope have now verified the existence of over fifty black holes, mainly lurking in the heart of large galaxies. In fact, many astronomers now believe that perhaps half of all the trillions of galaxies in the heavens have black holes at their center.

  Einstein realized the problem with identifying these exotic creatures: by definition, they are invisible since light itself cannot escape, and hence extremely difficult to see in nature. The Hubble Space Telescope, peering into the hearts of distant quasars and galaxies, has now taken spectacular photographs of the spinning disk surrounding the black holes located in the heart of distant galaxies, such as M-87 and NGC-4258. In fact, one can clock some of this matter revolving around the black hole at about a million miles per hour. The most detailed Hubble photographs show that there is a dot at the very center of the black hole, about a single light-year across, which is powerful enough to spin an entire galaxy about 100,000 light-years across. After years of speculation, it was finally shown in 2002 that there is a black hole lurking in our own backyard, the Milky Way galaxy, which weighs the same as about 2 million suns. Thus, our moon revolves around the earth, the earth revolves around the sun, and the sun revolves around a black hole.

  According to the work of Michell and Laplace in the eighteenth century, the mass of a dark star or black hole is proportional to its radius. Thus, the black hole at the center of our galaxy is roughly a tenth of the radius of the orbit of Mercury. It is astonishing that an object that small can affect the dynamics of our entire galaxy. In 2001, astronomers using the Einstein lens effect announced that a wandering black hole was discovered moving within the Milky Way galaxy. As the black hole moved, it distorted the surrounding starlight. By tracing the movement of this light distortion, astronomers could calculate its trajectory across the heavens. (Any wandering black hole approaching the earth could have catastrophic consequences. It would eat up the entire solar system and not even burp.)

  In 1963, research in black holes received a boost when New Zealand mathematician Roy Kerr generalized Schwarzschild’s black hole to include spinning black holes. Since everything in the universe seems to be spinning, and because objects spin faster when they collapse, it was natural to assume that any realistic black hole would be spinning at a fantastic rate. Much to everyone’s surprise, Kerr found an exact solution of Einstein’s equations in which a star collapsed into a spinning ring. Gravity would try to collapse the ring, but centrifugal effects could become sufficiently strong to counteract gravity, and the spinning ring would be stable. What most puzzled relativists was that if you fell through the ring, you would not be crushed to death. Gravity was actually large but finite at the center, so you could in principle fall straight through the ring, into another universe. A journey through the Einstein-Rosen bridge would not necessarily be a
lethal one. If the ring were large enough, one might enter the parallel universe safely.

  Physicists immediately began to pick apart what might happen if you fell into a Kerr black hole. An encounter with such a black hole would certainly be an unforgettable experience. In principle, it might give us a shortcut to the stars, transporting us instantly into another part of the galaxy, or perhaps another universe entirely. As you approached the Kerr black hole, you would pass through the event horizon so you would never be able to go back to where you started (unless there was another Kerr black hole that connected the parallel universe back to our universe, making a roundtrip possible). Also, there were problems with stability. One could show that if you fell through the Einstein-Rosen bridge, the distortions of space-time that you created might force the Kerr black hole to close up, making a complete journey through the bridge impossible.

  As strange as the idea of a Kerr black hole was, acting as a gateway or portal between two universes, it could not be dismissed on physical grounds because black holes are indeed spinning very rapidly. However, it soon became apparent that these black holes not only connected two distant points in space, but also connected two times as well, acting as time machines.

  When Gödel found the first time travel solution of Einstein’s equations in 1949, it was considered a novelty, an isolated aberration of the equations. Since then, however, scores of time travel solutions have now been discovered in Einstein’s equations. For example, it was discovered that an old solution, discovered by W. J. van Stockum in 1936, actually allowed for time travel. The van Stockum solution consisted of an infinite cylinder spinning rapidly around its axis, like the spinning pole found in old barbershops. If you journeyed around the spinning cylinder, then you might be able to return to the original spot before you left, much like the Gödel solution of 1949. Although this solution is intriguing, the problem is that the cylinder has to be infinite in length. A finite spinning cylinder will apparently not work. In principle, therefore, both the Gödel and the van Stockum solution can be ruled out on physical grounds.

  In 1988, Kip Thorne and his colleagues at Caltech found yet another solution of Einstein’s equations that admits time travel via a wormhole. They were able to solve the problem of the one-way trip through the event horizon by showing that a new type of wormhole was completely transversable. In fact, they have calculated that a trip through such a time machine may be as comfortable as a plane ride.

  The key to all these time machines is the matter or energy that warps space-time onto itself. To bend time into a pretzel, one needs a fantastic amount of energy, far beyond anything known to modern science. For the Thorne time machine, one needs negative matter or negative energy. No one has ever seen negative matter before. In fact, if you had a piece of it in your hand, it would fall up, not down. Searches for negative matter have proved fruitless. If any existed on the earth billions of years ago, it would have fallen up into outer space, to be lost forever. Negative energy, on the other hand, actually exists in the form of the Casimir effect. If we take two neutral parallel metal plates, we know that they are uncharged and hence are not attracted or repelled toward each other. They should remain at rest. However, in 1948 Henrik Casimir demonstrated a curious quantum effect, demonstrating that the two parallel plates will actually attract each other by a small but nonzero force, which has actually been measured in the laboratory.

  Thus a Thorne time machine can be built as follows: Take two sets of parallel metal plates. Because of the Casimir effect, the region between each set of plates will have negative energy. According to Einstein’s theory, the presence of negative energy will open up tiny holes or bubbles in space-time (smaller than a subatomic particle) inside this region. Now assume, for the sake of argument, that an advanced civilization far ahead of ours can somehow manipulate these holes, grab one from each pair of plates, and then stretch them until a long tube or wormhole connects the two sets of plates. (Linking these two sets of parallel plates with a wormhole is far beyond anything possible with today’s technology.) Now send one pair of plates on a rocket that is traveling near the speed of light, so that time slows down aboard the rocket ship. As we discussed earlier, clocks on the rocket run slower than clocks on Earth. If you jump into the hole within the parallel plates sitting on Earth, you will be sucked through the wormhole connecting the two plates and find yourself on the rocket back in the past, at a different point in space and time.

  Since then, the field of time machines (or more properly “closed time like curves”) has become a lively area of physics, with scores of papers published with different designs, all of them based on Einstein’s theory. Not every physicist has been amused, though. Hawking, for one, did not like the idea of time travel. He said, tongue-in-cheek, that if time travel were possible, we would be flooded with tourists from the future, which we don’t see. If time machines were commonplace, then history would be impossible to write, changing anytime someone spun the dial of their time machine. Hawking has declared that he wants to make the world safe for historians. However, in T. H. White’s The Once and Future King, there is a society of ants that obeys the dictum, “Everything not forbidden is compulsory.” Physicists take this law to heart, so Hawking was forced to postulate the “chronology protection conjecture,” which bans time machines by fiat. (Hawking has since given up trying to prove this conjecture. He now maintains that time machines, although theoretically possible, are not practical.)

  These time machines apparently obey the laws of physics, as we currently know them. The trick, of course, is to somehow access these tremendous energies (available only to “sufficiently advanced civilizations”) and show that these wormholes are in fact stable against quantum corrections and don’t explode or close up as soon as you enter one.

  It should also be mentioned that time paradoxes (such as killing your parents before you are born) might be resolved with time machines. Because Einstein’s theory is based on smooth, curved Riemann surfaces, we do not simply disappear when we enter the past and create a time paradox. There are two possible resolutions of time travel paradoxes. First, if the river of time can have whirlpools, then perhaps we simply fulfill the past when we enter the time machine. This means that time travel is possible, but we cannot alter the past, merely complete it. It was meant to be that we would enter the time machine. This view is held by Russian cosmologist Igor Novikov, who says, “We cannot send a time traveler back to the Garden of Eden to ask Eve not to pick the apple from the tree.” Second, the river of time itself may fork into two rivers; that is, a parallel universe may open up. Thus, if you shoot your parents before you are born, you have only killed people who are genetically identical to your parents but are not really your parents at all. Your own parents indeed gave birth to you and made your body possible. What has happened is that you have jumped between our universe and another universe, so all time paradoxes are resolved.

  But the theory closest to Einstein’s heart was his unified field theory. Einstein remarked to Helen Dukas that perhaps in a hundred years, physicists will understand what he was doing. He was wrong. In less than fifty years, there has been a resurgence of interest in the unified field theory. The quest for unification, once derided by physicists as being hopelessly beyond reach, is perhaps now tantalizingly within our grasp. It dominates the agenda of almost every meeting of theoretical physicists.

  After two thousand years of investigation into the properties of matter, ever since Democritus and fellow Greeks asked what the universe was made of, physics has produced two competing theories that are totally incompatible. The first is the quantum theory, which is incomparable in terms of describing the world of atoms and subatomic particles. The second is Einstein’s general relativity, which has given us breathtaking theories of black holes and the expanding universe. The ultimate paradox is that these two theories are total opposites. They are based on different assumptions, different mathematics, and different physical pictures. The quantum theory is based on discre
te packets of energy, called “quanta,” and the dance of subatomic particles. The relativity theory, however, is based on smooth surfaces.

  Physicists today have formulated the most advanced version of quantum physics, embodied in something called the “Standard Model,” which can explain subatomic experimental data. It is, in some sense, the most successful theory in nature, able to describe the properties of three (the electromagnetic and the weak and strong nuclear forces) of the four fundamental forces. As successful as the Standard Model is, there are glaring two problems with it. First, it is supremely ugly, perhaps one of the ugliest theories ever proposed in science. The theory simply ties together the weak, strong, and electromagnetic forces by hand. It’s like using Scotch tape to connect a whale, aardvark, and a giraffe together, and claiming that this is the supreme achievement of nature, the end product of millions of years of evolution. Up close, the Standard Model consists of a bewildering, motley collection of subatomic particles with strange names that do not make much sense, like quarks, Higgs bosons, Yang-Mills particles, W-bosons, gluons, and neutrinos. Worse, the Standard Model does not mention gravity at all. In fact, if one tries to graft gravity onto the Standard Model by hand, one finds that the theory blows up. It yields nonsense. All attempts for almost fifty years to graft the quantum theory and relativity together have proved fruitless. Given all its aesthetic defects, we conclude that the only thing going for the theory is that it is undeniably correct within its experimental domain. Clearly, what is needed is to go beyond the Standard Model, to re-examine the unification approach of Einstein.

  After fifty years, the leading candidate for a theory of everything, one that can unify both the quantum theory and general relativity, is something called “superstring theory.” In fact, it is the only game in town because all rival theories have been ruled out. As physicist Steven Weinberg said, “String theory has provided our first plausible candidate for a final theory.” Weinberg believes that the maps that guided the ancient mariners all pointed to the existence of a fabled North Pole, though it would take centuries before Robert Peary actually set foot on it in 1909. Similarly, all the discoveries made in particle physics point to the existence of the “North Pole” of the universe, that is, a unified field theory. Superstring theory can absorb all the good features of the quantum theory and relativity in a surprisingly simple way. Superstring theory is based on the idea that subatomic particles can be viewed as notes on a vibrating string. Although Einstein compared matter to wood because of all its tangled properties and seemingly chaotic nature, superstring theory reduces matter to music. (Einstein, who was an excellent violinist, probably would have liked this.)