by Lee Smolin
But if this is true, it works both ways: We will not be able to solve the other big problems unless we also find a sensible replacement for quantum mechanics.
The idea that physics should be unified has probably motivated more work in physics than any other problem. But there are different ways that physics can be unified, and we should be careful to distinguish them. So far we have been discussing unification through a single law. It is hard to see how anyone could disagree that this is a necessary goal.
But there are other ways to unify the world. Einstein, who certainly thought as much about this as anyone, emphasized that we must distinguish two kinds of theories. There are theories of principle and constructive theories. A theory of principle is one that sets up the framework that makes a description of nature possible. By definition, a theory of principle must be universal: It must apply to everything because it sets out the basic language we use to talk about nature. There cannot be two different theories of principle, applying to different domains. Because the world is a unity, everything interacts ultimately with everything else, and there can be only one language used to describe those interactions. Quantum theory and general relativity are both theories of principle. As such, logic requires their unification.
The other kind of theories, constructive theories, describe some particular phenomenon in terms of specific models or equations.1 The theory of the electromagnetic field and the theory of the electron are constructive theories. Such a theory cannot stand alone; it must be set within the context of a theory of principle. But as long as the theory of principle allows, there can be phenomena that obey different laws. For example, the electromagnetic field obeys laws different from those governing the postulated cosmological dark matter (thought to vastly outnumber the amount of ordinary atomic matter in our universe). One thing we know about the dark matter is that, whatever it is, it is dark. This means it gives off no light, so it likely doesn’t interact with the electromagnetic field. Thus two different theories can coexist side by side.
The point is that the laws of electromagnetism do not dictate what else exists in the world. There can be quarks or not, neutrinos or not, dark matter or not. Similarly, the laws that describe the two forces—strong and weak—that act within the atomic nucleus do not necessarily require that there be an electromagnetic force. We can easily imagine a world with electromagnetism but no strong nuclear force, or the reverse. As far as we know, either possibility would be consistent.
But it is still possible to ask whether all the forces we observe in nature might be manifestations of a single, fundamental force. There seems, as far as I can tell, no logical argument that this should be true, but it is still something that might be true.
The desire to unify the various forces has led to several significant advances in the history of physics. James Clerk Maxwell, in 1867, unified electricity and magnetism into one theory, and a century later, physicists realized that the electromagnetic field and the field that propagates the weak nuclear force (the force responsible for radioactive decay) could be unified. This became the electroweak theory, whose predictions have been repeatedly confirmed in experiments over the last thirty years.
There are two fundamental forces in nature (that we know of) that remain outside the unification of the electromagnetic and weak fields. These are gravity and the strong nuclear force, the force responsible for binding the particles called quarks together to form the protons and neutrons making up the atomic nucleus. Can all four fundamental forces be unified?
This is our third great problem.
Problem 3: Determine whether or not the various particles and forces can be unified in a theory that explains them all as manifestations of a single, fundamental entity.
Let us call this problem the unification of the particles and forces, to distinguish it from the unification of laws, the unification we discussed earlier.
At first, this problem appears easy. The first proposal for how to unify gravity with electricity and magnetism was made in 1914, and many more have been offered since. They all work, as long as you forget one thing, which is that nature is quantum mechanical. If you leave quantum physics out of the picture, unified theories are easy to invent. But if you include quantum theory, the problem gets much, much harder. Since gravity is one of the four fundamental forces of nature, we must solve the problem of quantum gravity (that is, problem no. 1: how to reconcile general relativity and quantum theory) along with the problem of unification.
Over the last century, our physical description of the world has simplified quite a bit. As far as particles are concerned, there appear to be only two kinds, quarks and leptons. Quarks are the constituents of protons and neutrons and many particles we have discovered similar to them. The class of leptons encompasses all particles not made of quarks, including electrons and neutrinos. Altogether, the known world is explained by six kinds of quarks and six kinds of leptons, which interact with each other through the four forces (or interactions, as they are also known): gravity, electromagnetism, and the strong and weak nuclear forces.
Twelve particles and four forces are all we need to explain everything in the known world. We also understand very well the basic physics of these particles and forces. This understanding is expressed in terms of a theory that accounts for all of these particles and all of the forces except for gravity. It’s called the standard model of elementary-particle physics—or the standard model, for short. This theory does not have the problem of infinities mentioned earlier. Anything we want to compute in this theory we can, and it results in a finite number. In the more than thirty years since it was formulated, many predictions made by this theory have been checked experimentally. In each and every case, the theory has been confirmed.
The standard model was formulated in the early 1970s. Except for the discovery that neutrinos have mass, it has not required adjustment since. So why wasn’t physics over by 1975? What remained to be done?
For all its usefulness, the standard model has a big problem: It has a long list of adjustable constants. When we state the laws of the theory, we must specify the values of these constants. As far as we know, any values will do, because the theory is mathematically consistent no matter which values we put in. These constants specify the properties of the particles. Some tell us the masses of the quarks and the leptons, while others tell us the strengths of the forces. We have no idea why these numbers have the values they do; we simply determine them by experiments and then plug in the numbers. If you think of the standard model as a calculator, then the constants will be dials that can be set to whatever positions you like each time the program is run.
There are about twenty such constants, and the fact that there are that many freely specifiable constants in what is supposed to be a fundamental theory is a tremendous embarrassment. Each one represents some basic fact of which we are ignorant: namely, the physical reason or mechanism responsible for setting the constant to its observed value.
This is our fourth big problem.
Problem 4: Explain how the values of the free constants in the standard model of particle physics are chosen in nature.
It is devoutly hoped that a true unified theory of the particles and forces will give a unique answer to this question.
In 1900, William Thomson (Lord Kelvin), an influential British physicist, famously proclaimed that physics was over, except for two small clouds on the horizon. These “clouds” turned out to be the clues that led us to quantum theory and relativity theory. Now, even as we celebrate the encompassing of all known phenomena in the standard model plus general relativity, we, too, are aware of two clouds. These are the dark matter and the dark energy.
Apart from the issue of its relationship with the quantum, we think we understand gravity very well. The predictions of general relativity have been found to be in agreement with observation to a very precise degree. The observations in question extend from falling bodies and light on Earth, to the detailed motion of the planets and thei
r moons, to the scales of galaxies and clusters of galaxies. Formerly exotic phenomena—such as gravitational lensing, an effect of the curvature of space by matter—are now so well understood that they are used to measure the distributions of mass in galactic clusters.
In many cases—those in which velocities are small compared with that of light, and masses are not too compact—Newton’s laws of gravity and motion provide an excellent approximation to the predictions of general relativity. Certainly they should help us predict how the motion of a particular star is influenced by the masses of stars and other matter in its galaxy. But they don’t. Newton’s law of gravity says that the acceleration of any object as it orbits another is proportional to the mass of the body it is orbiting. The heavier the star, the faster the orbital motion of the planet. That is, if two stars are each orbited by a planet, and the planets are the same distances from their stars, the planet orbiting the more massive star will move faster. Thus if you know the speed of a body in orbit around a star and its distance from the star, you can measure the mass of that star. The same holds for stars in orbit around the center of their galaxy; by measuring the orbital speeds of the stars, you can measure the distribution of mass in that galaxy.
Over the last decades, astronomers have done a very simple experiment in which they measure the distribution of mass in a galaxy in two different ways and compare the results. First, they measure the mass by observing the orbital speeds of the stars; second, they make a more direct measurement of the mass by counting all the stars, gas, and dust they can see in the galaxy. The idea is to compare the two measurements: Each should tell them both the total mass in the galaxy and how it is distributed. Given that we understand gravity well, and that all known forms of matter give off light, the two methods should agree.
They don’t. Astronomers have compared the two methods of measuring mass in more than a hundred galaxies. In almost all cases, the two measurements don’t agree, and not by just a small amount but by factors of up to 10. Moreover, the error always goes in one direction: There is always more mass needed to explain the observed motions of the stars than is seen by directly counting up all the stars, gas, and dust.
There are only two explanations for this. Either the second method fails because there is much more mass in a galaxy than is visible, or Newton’s laws fail to correctly predict the motions of stars in the gravitational field of their galaxy.
All the forms of matter we know about give off light, either directly as in starlight or reflected from planets or interstellar rocks, gas, and dust. So if there is matter we don’t see, it must be in some novel form that neither emits nor reflects light. And because the discrepancy is so large, the majority of the matter in galaxies must be in this new form.
Today most astronomers and physicists believe that this is the right answer to the puzzle. There is missing matter, which is actually there but which we don’t see. This mysterious missing matter is referred to as the dark matter. The dark-matter hypothesis is preferred mostly because the only other possibility—that we are wrong about Newton’s laws, and by extension general relativity—is too scary to contemplate.
Things have become even more mysterious. We have recently discovered that when we make observations at still larger scales, corresponding to billions of light-years, the equations of general relativity are not satisfied even when the dark matter is added in. The expansion of the universe, set in motion by the Big Bang some 13.7 billion years ago, appears to be accelerating, whereas, given the observed matter plus the calculated amount of dark matter, it should be doing the opposite—decelerating.
Again, there are two possible explanations. General relativity could simply be wrong. It has been verified precisely only within our solar system and nearby systems in our own galaxy. Perhaps when one gets to a scale comparable to the size of the whole universe, general relativity is simply no longer applicable.
Or there is a new form of matter—or energy (recall Einstein’s famous equation E = mc2, showing the equivalence of energy and mass)—that becomes relevant on these very large scales: That is, this new form of energy affects only the expansion of the universe. To do this, it cannot clump around galaxies or even clusters of galaxies. This strange new energy, which we have postulated to fit the data, is called the dark energy.
Most kinds of matter are under pressure, but the dark energy is under tension—that is, it pulls things together rather than pushes them apart. For this reason, tension is sometimes called negative pressure. In spite of the fact that the dark energy is under tension, it causes the universe to expand faster. If you are confused by this, I sympathize. One would think that a gas with negative pressure would act like a rubber band connecting the galaxies and slow the expansion down. But it turns out that when the negative pressure is negative enough, in general relativity it has the opposite effect. It causes the expansion of the universe to accelerate.
Recent measurements reveal a universe consisting mostly of the unknown. Fully 70 percent of the matter density appears to be in the form of dark energy. Twenty-six percent is dark matter. Only 4 percent is ordinary matter. So less than 1 part in 20 is made out of matter we have observed experimentally or described in the standard model of particle physics. Of the other 96 percent, apart from the properties just mentioned, we know absolutely nothing.
In the last ten years, cosmological measurements have gotten much more precise. This is partly a side effect of Moore’s law, which states that every eighteen months or so, the processing speeds of computer chips will double. All the new experiments use microchips in either satellites or ground-based telescopes, so as the chips have gotten better, so have the observations. Today we know a lot about the basic characteristics of the universe, such as the overall matter density and the rate of expansion. There is now a standard model of cosmology, just as there is a standard model of elementary-particle physics. Just like its counterpart, the standard model of cosmology has a list of freely specifiable constants—in this case, about fifteen. These denote, among other things, the density of different kinds of matter and energy and the expansion rate. No one knows anything about why these constants have the values they do. As in particle physics, the values of the constants are taken from observations but are not yet explained by any theory.
These cosmological mysteries make up the fifth great problem.
Problem 5: Explain dark matter and dark energy. Or, if they don’t exist, determine how and why gravity is modified on large scales. More generally, explain why the constants of the standard model of cosmology, including the dark energy, have the values they do.
These five problems represent the boundaries to present knowledge. They are what keep theoretical physicists up at night. Together they drive most current work on the frontiers of theoretical physics.
Any theory that claims to be a fundamental theory of nature must answer each one of them. One of the aims of this book is to evaluate just how well recent physical theories, such as string theory, have done in achieving this goal. But before we do that, we need to examine some earlier attempts at unification. We have a great deal to learn from the successes—and also from the failures.
2
The Beauty Myth
THE MOST CHERISHED goal in physics, as in bad romance novels, is unification. To bring together two things previously understood as different and recognize them as aspects of a single entity—when we can do it—is the biggest thrill in science.
The only sane response to a proposed unification is surprise. The sun is just another star—and the stars are just suns that happen to be very far away! Imagine the reaction of a late-sixteenth-century blacksmith or actor on hearing this wild idea of Giordano Bruno’s. What could be more absurd than to unify the sun with the stars? People had been taught that the sun was a great fire created by God to warm the earth, while the stars were pinholes in the celestial sphere that let in the light of heaven. Unification instantly turns your world upside down. What you used to believe becomes impossi
ble. If the stars are suns, the universe is vastly bigger than we thought! Heaven cannot be just overhead!
Even more important, a new proposal for unification brings with it previously unimagined hypotheses. If the stars are other suns, there must be planets around them, on which other people live! The implications often extend beyond science. If there are other planets with other people on them, then either Jesus came to all of them, in which case his coming to Man was not a unique event, or all those people lose the possibility of salvation! No wonder the Catholic Church burned Bruno alive.
Great unifications become the founding ideas on which whole new sciences are erected. Sometimes the consequences so threaten our worldview that surprise is quickly followed by disbelief. Before Darwin, each species was in its own eternal category. Each had been made, individually, by God. But evolution by natural selection means that all species have a common ancestor. They are unified into one great family. Biology before Darwin and biology afterward are hardly the same science.
Such powerful new insights lead quickly to new discoveries. If all living things have a common ancestor, they must be similarly made! Indeed, we are made of the same stuff, because all life turns out to be composed of cells. Plants, animals, fungi, and bacteria seem very different from one another, but they are all just groups of cells arranged in different ways. The chemical processes that construct and power these cells are the same, across the whole empire of life.