by Michio Kaku
Let’s say I have an equation containing many subatomic particles and then I shuffle or rearrange them among one another. If the equation remains the same after interchanging these particles, I would then say that the equation has a symmetry.
THE POWER OF SYMMETRY
Symmetry is not just a matter of aesthetics. It is a powerful way to eliminate imperfections and anomalies in your equations. If you rotate the snowflake, you can rapidly spot any defects by comparing the rotated version with the original. If they are not the same, then you have a problem that needs correcting.
In the same way, when constructing a quantum equation, we often find that a theory is infested with tiny anomalies and divergences. But if the equation has a symmetry, then these defects are eliminated. In the same way, supersymmetry takes care of the infinities and imperfections often found in a quantum theory.
As a bonus, it turns out that supersymmetry is the largest symmetry ever found in physics. Supersymmetry can take all known subatomic particles and mix them together or rearrange them while preserving the original equation. In fact, supersymmetry is so powerful that it can take Einstein’s theory, including the graviton and the subatomic particles of the Standard Model, and rotate them or interchange them. This gives us a pleasing and natural way to unify Einstein’s theory of gravity and subatomic particles.
String theory is like a gigantic cosmic snowflake, except that each prong of the snowflake represents the entire set of Einstein’s equations and the Standard Model of subatomic particles. So each prong of the snowflake represents all the particles of the universe. As we rotate the snowflake, all the particles of the universe are interchanged. Some physicists have noted that even if Einstein had never been born, and billions of dollars were never spent on smashing atoms to create the Standard Model, then all of twentieth-century physics might have been discovered if you simply possessed string theory.
Most important, supersymmetry cancels the quantum corrections of particles with those of sparticles, leaving us with a finite theory of gravity. That is the miracle of string theory. This also explains the answer to the question most often heard about string theory: Why does it exist in ten dimensions? Why not thirteen, or twenty?
This is because the number of particles in string theory can vary with the dimensionality of space-time. In higher dimensions, we have more particles, since there are more ways in which particles can vibrate. When we try to cancel the quantum corrections from the particles against the corrections from the sparticles, we find that this cancellation can happen only in ten dimensions.
Usually, mathematicians create new, imaginative structures that physicists later incorporate into their theories. For example, the theory of curved surfaces was worked out by mathematicians in the nineteenth century and was later incorporated into Einstein’s theory of gravity in 1915. But this time, the reverse happened. String theory has opened up so many new branches of mathematics that the mathematicians were startled. Young, aspiring mathematicians, who usually scorn applications of their discipline, have to learn string theory if they want to be on the cutting edge.
Although Einstein’s theory allows for the possibility of wormholes and faster-than-light travel, you need string theory to calculate how stable these wormholes are in the presence of quantum corrections.
In summary, these quantum corrections are infinite, so removing these infinities is one of the fundamental problems in physics. String theory eliminates these quantum corrections, because it has two types of quantum corrections that precisely cancel each other. This precise cancellation between particles and sparticles is due to supersymmetry.
However, as elegant and powerful as string theory is, it is not enough; it must ultimately face the final challenge, which is experiment.
CRITICISMS OF STRING THEORY
Although this picture is compelling and persuasive, there are valid criticisms one can make of the theory. First, since the energy at which string theory (or any theory of everything for that matter) unifies all of physics is the Planck energy, no machine on Earth is powerful enough to rigorously test it. A direct test would involve creating a baby universe in the laboratory, which is obviously out of the question given current technology.
Second, like any physical theory, it has more than one solution. For example, Maxwell’s equations, which govern light, have an infinite number of solutions. This is not a problem because, at the very beginning of any experiment, we specify what we are studying, whether it’s a light bulb, laser, or a TV. Then later, given these initial conditions, we solve the equations of Maxwell. But if we have a theory of the universe, then what are its initial conditions? Physicists believe that a “theory of everything” should dictate its own initial state, that is, they would prefer that the initial conditions of the Big Bang somehow emerge from the theory itself. String theory, however, does not tell you which of its many solutions is the correct one for our universe. And, without initial conditions, string theory contains an infinite number of parallel universes, called the multiverse, each one as valid as the next. So we have an embarrassment of riches, with string theory predicting not only our own familiar universe but perhaps an infinite number of other equally valid alien universes as well.
Third, perhaps the most startling prediction of string theory is that the universe is not four-dimensional at all but exists in ten dimensions. In all of physics, nowhere have we seen a prediction this bizarre, a theory of space-time that selects out its own dimensionality. This was so strange that many physicists at first dismissed it as science fiction. (When string theory was first proposed, the fact that it could only exist in ten dimensions was a source of ridicule. Nobel laureate Richard Feynman, for example, would tease John Schwarz, one of the founders of string theory, by asking him, “So John, how many dimensions are we in today?”)
LIVING IN HYPERSPACE
We know that any object in our universe can be described by three numbers: length, width, and height. If we add time, then four numbers can describe any event in the universe. For example, if I want to meet someone in New York City, I might say that we should meet at Forty-Second Street and Fifth Avenue, on the tenth floor, at noon. But to a mathematician the need for only three or four coordinates might seem arbitrary, since there is nothing special about three or four dimensions. Why should the most fundamental feature of the physical universe be described by such ordinary numbers?
So mathematicians have no problem with string theory. But to visualize these higher dimensions, physicists often use analogies. When I was a child, I used to spend many hours gazing at the Japanese Tea Garden in San Francisco. Watching the fish swim in the shallow pond, I asked myself a question that only a child would ask: “What would it be like to be a fish?” What a strange world they would see, I thought. They would think the universe was only two-dimensional. They could only swim in this limited space by moving sideways, but never up or down. Any fish who dared mention a third dimension beyond the pond would be considered a crackpot. I then imagined there was a fish living in the pond who would scoff anytime someone mentioned hyperspace, since the universe was just what you could touch and feel, nothing more. Then I imagined grabbing that fish and lifting him into the world of “up.” What would he see? He would see beings moving without fins. A new law of physics. Beings breathing without water. A new law of biology. Then I imagined putting the scientist fish back into the pond and he would have to explain to the other fish the incredible creatures that live in the world of “up.”
Similarly, perhaps we are the fish. If string theory is proven correct, it means that there are unseen dimensions beyond our familiar four-dimensional world. But where are these higher dimensions? One possibility is that six of the ten original dimensions have “curled up” so they cannot be seen anymore. Think of taking a sheet of paper and rolling it up into a tight tube. The original sheet was two-dimensional, but the rolling-up process has created a one-dimensional tube. From a distance, you only see the one-dimensional tube, but in reali
ty it is still two-dimensional.
In the same way, string theory says that the universe was originally ten-dimensional, but for some reason six of these dimensions curled up, leaving us with the illusion that our world has only four. Although this feature of string theory seems fantastic, efforts are under way to actually measure these higher dimensions.
But how do higher dimensions help string theory unify relativity and quantum mechanics? If you try to unify the gravitational, nuclear, and electromagnetic forces into a single theory, you find that there is not enough “room” in four dimensions to do this. They are like pieces of a jigsaw puzzle that don’t fit together. But once you start to add more and more dimensions, you find enough room to assemble these lower theories, like matching jigsaw pieces together to make the whole.
For example, think of a two-dimensional world of Flatlanders, who, like cookie men, can only move left or right, but never “up.” Imagine that there was once a beautiful three-dimensional crystal that exploded, showering fragments onto Flatland. Over the years, the Flatlanders have reassembled this crystal into two large fragments. But as hard as they try, they are unable to fit these last two fragments together. Then one day, a Flatlander makes the outrageous proposal that if they move one fragment “up,” into the unseen third dimension, then the two fragments would fit together and form a beautiful three-dimensional crystal. So the key to re-creating the crystal was moving the fragments through the third dimension. By analogy, these two fragments are relativity theory and the quantum theory, the crystal is string theory, and the explosion was the Big Bang.
Even though string theory fits the data neatly, we still need to test it. Although as discussed a direct test is not possible, most physics is done indirectly. For example, we know that the sun is made mainly of hydrogen and helium, yet no one has ever visited the sun. We know the sun’s composition because we analyze it indirectly, looking at sunlight through a prism, which breaks it up into bands of colors. By studying these bands within the rainbow, we can identify the fingerprint of hydrogen and helium. (In fact, helium was not found on Earth first. In 1868, scientists discovered evidence of a strange new element when analyzing sunlight during an eclipse, which was christened “helium,” meaning “metal from the sun.” It wasn’t until 1895 that direct evidence of helium was discovered on the Earth, when scientists realized it was a gas and not a metal.)
DARK MATTER AND STRINGS
In the same way, string theory might be proven via a variety of indirect tests. Since each vibration of the string corresponds to a particle, we can in our particle accelerators search for entirely new particles that represent higher “octaves” of the string. The hope is that by smashing protons together at trillions of volts, you briefly create a new particle among the debris that is predicted by string theory. This, in turn, may help explain one of the great unsolved problems in astronomy.
In the 1960s, when astronomers examined the rotation of the Milky Way galaxy, they found something strange. It was rotating so fast that, by Newton’s laws, it should fly apart, yet the galaxy has been stable for about ten billion years. In fact, the galaxy rotated about ten times faster than it should according to traditional Newtonian mechanics.
This posed a tremendous problem. Either Newton’s equations were wrong (which was almost unthinkable) or there was an invisible halo of unknown matter surrounding the galaxies, increasing their mass sufficiently for gravity to hold them together. This meant that perhaps the pictures we see of gorgeous galaxies with their beautiful spiral arms are incomplete, that they are actually surrounded by a gigantic invisible halo that is ten times more massive than the visible galaxy. Since photographs of galaxies only show the beautiful swirling mass of stars, whatever is holding the mass together must not interact with light—it must be invisible.
Astrophysicists dubbed this missing mass “dark matter.” Its existence forced them to revise their theories, which said that the universe is made mainly of atoms. We now have maps of dark matter throughout the universe. Although it is invisible, it bends starlight just as anything with mass should. Therefore, by analyzing the distortion of starlight surrounding galaxies, we can use computers to calculate the presence of dark matter and map its distribution across the universe. Sure enough, this map shows that most of the total mass of a galaxy exists in this form.
In addition to being invisible, dark matter has gravity, but you can’t hold it in your hand. Since it does not interact with atoms at all (because it is electrically neutral) it will pass through your hand, the floor, and through the crust of the Earth. It would oscillate between New York and Australia as if the Earth did not exist at all, except that it would be bound by Earth’s gravity. So although dark matter is invisible, it still interacts via gravity with other particles.
One theory is that dark matter is a higher vibration of the superstring. The leading candidate is the superpartner of the photon, which is called the “photino,” or “little photon.” It has all the right properties to be dark matter: it is invisible because it does not interact with light, and yet it has weight and is stable.
There are several ways to prove this conjecture. The first is to create dark matter directly with the Large Hadron Collider by smashing protons into each other. For a brief instant of time, a particle of dark matter would be formed inside the accelerator. If this is possible, it would have enormous repercussions for science. It would represent the first time in history that a new form of matter has been found that is not based on atoms. If the LHC is not powerful enough to produce dark matter, then perhaps the ILC can.
There also is another way to prove this conjecture. The Earth is moving in a wind of this invisible dark matter. The hope is that a dark matter particle may smash into a proton inside a particle detector, creating a shower of subatomic particles that might be photographed. At present, there are physicists around the world patiently waiting to find the signature of a collision between matter and dark matter in their detectors. There is a Nobel Prize waiting for the first physicist to do so.
If dark matter is found, either with particle accelerators or with ground-based sensors, we will be able to compare its properties with those predicted by string theory. In this way, we will have evidence to evaluate the validity of the theory.
Although finding dark matter would be a great step toward proving string theory, other proofs are possible. For example, Newton’s law of gravity governs the motion of large objects like stars and planets, but little is known about the force of gravity acting over small distances, like a few inches or feet. Since string theory postulates higher dimensions, this means that Newton’s famous inverse square law (that gravity diminishes in proportion with the square of the distance) should be violated at small distances because Newton’s law is predicated on three dimensions. (If space were four-dimensional, for instance, then gravity should diminish in proportion to the inverse cube of the distance. So far, tests of Newton’s law of gravity have not shown any evidence of a higher dimension, but physicists aren’t giving up.)
Another possible avenue is to send gravity wave detectors into space. The Laser Interferometer Gravitational-Wave Observatory (LIGO) based in Louisiana and Washington State was successful in picking up gravity waves from colliding black holes in 2016 and colliding neutron stars in 2017. A modified version of the space-based Laser Interferometer Space Antenna (LISA) may be able to detect gravity waves from the instant of the Big Bang. The hope is that one might be able to “run the videotape backward” and make conjectures about the nature of the pre–Big Bang era. This would allow a crude test of some of the predictions of string theory concerning the pre–Big Bang universe.
STRING THEORY AND WORMHOLES
Still other tests of string theory may involve finding other exotic particles predicted by the theory, such as micro black holes, which resemble subatomic particles.
We have seen how physics allows us to speculate about civilizations far into the future, making reasonable conjectures based on their
energy consumption. Civilizations can be expected to evolve from a Type I planetary civilization to a Type II stellar civilization and finally to a Type III galactic civilization. A galactic civilization, in turn, is likely to explore the galaxy via von Neumann probes or by laser porting their consciousness across the galaxy. The key point is that a Type III civilization may be able to access the Planck energy, the point where space-time becomes unstable and faster-than-light travel might be possible. But to calculate the physics of faster-than-light travel, we need a theory that goes beyond Einstein’s theory, which might well be string theory.
The hope is that using string theory, we will be able to calculate the quantum corrections necessary to analyze exotic phenomena such as time travel, interdimensional travel, wormholes, and what happened before the Big Bang. For example, assume that a Type III civilization is capable of manipulating black holes and thereby creating a gateway to a parallel universe through a wormhole. Without string theory, it is impossible to calculate what happens when you enter. Will it explode? Will gravitational radiation close it just as you enter it? Will you be able to pass through it and live to tell about it?
String theory should be capable of calculating how much gravitational radiation you would encounter when you pass through the wormhole and answer these questions.
Another hotly debated question among physicists is what happens if you enter a wormhole and go backward in time. If you then kill your grandfather before you are born, then you have a paradox. How can you exist at all if you just killed your ancestor? Einstein’s theory actually allows for time travel (if negative energy exists) but says nothing about how to resolve these paradoxes. String theory, because it is a finite theory in which everything can be calculated, should be able to resolve all these mind-twisting paradoxes. (My own strictly personal opinion is that the river of time forks into two rivers when you enter a time machine—in other words, the timeline splits. This means that you have killed someone else’s grandfather who looks just like your own grandfather but exists in another timeline in an alternate universe. So the multiverse resolves all time paradoxes.)
