The Cosmic Landscape (42 page)

But Dirac’s theory did have one serious problem. In the real world the energy associated with every particle is a positive quantity. At first Dirac’s theory seemed inconsistent—it had electrons, which carried negative energy! Particles with negative energy are a very bad sign. Remember that in an atom, electrons of higher energy eventually “drop down” to orbits of lower energy by emitting photons. The electrons seek out the lowest-energy orbit that isn’t blocked by the Pauli exclusion principle. But what if an infinite number of negative energy orbits were available to the electrons? Wouldn’t all the electrons in the world start cascading to increasingly negative energy, giving off enormous amounts of energy in the form of photons? Indeed, they would. This potentially damning feature of Dirac’s idea threatened to undermine his whole theory—unless something could prevent the electrons from occupying the negative energy states. Again Pauli saves the day. Pauli’s exclusion principle would rescue Dirac from disaster. Just suppose that what we normally call vacuum is really a state full of negative-energy electrons, one in every negative-energy orbit. What would the world be like? Well, you could still put electrons into the usual positive-energy orbits, but now when an electron gets to the lowest positive-energy orbit, it is blocked from going any farther. For all intents and purposes, the negative-energy orbits might as well not exist, since an electron is effectively blocked from falling into these orbits by the presence of the so-called Dirac Sea of negative-energy electrons. Dirac declared the problem solved, and so it was.

This idea soon led to something new and totally unexpected. In an ordinary atom an electron can absorb the energy of nearby photons and be “kicked up” into a more energetic configuration.
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Dirac now showed his real brilliance. He reasoned that the same thing could happen to the negative-energy electrons that fill the vacuum; photons could kick negative-energy electrons up to positive-energy states. What would be left over would be one electron with positive energy and a missing negative-energy electron—a hole in the Dirac Sea. Being a missing electron, the hole would seem to have the opposite electric charge from the electron and would look just like a particle of positive charge. This, then, was Dirac’s prediction: particles should exist identical to electrons, except with the opposite electric charge. These positrons, which Feynman would later interpret as electrons going backward in time, Dirac pictured as holes in the vacuum. Moreover, they should be created together with ordinary electrons, when photons collide with enough energy.

Dirac’s prediction of antimatter was one of the great moments in the history of physics. It not only led to the subsequent experimental discovery of positrons, but it heralded the new subject of quantum field theory. It was the forerunner of Feynman’s discovery of Feynman diagrams and later led to the discovery of the Standard Model. But let’s not get ahead of the story.

Dirac wasn’t thinking about any experiment when he discovered his remarkable equation for the relativistic quantum mechanics of electrons. He was thinking about how the nonrelativistic Schrödinger equation could be made mathematically consistent with Einstein’s Special Theory of Relativity. Once he had the Dirac equation, the way lay open to the whole of Quantum Electrodynamics. Theorists studying QED would certainly have found the inconsistencies that were papered over by renormalization theory.
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There was no obstruction to the discovery of modern quantum field theory. And physicists would have puzzled endlessly over the enormous vacuum energy and why it didn’t gravitate. We might question whether theorists would have been willing to carry on without experimental confirmation of their ideas. We might question whether young people would want to pursue such a purely theoretical enterprise. But I don’t think we can question the possibility of physics progressing up to this point. Moreover, the thirty-five-year history of String Theory suggests that as long as someone will pay them, theoretical physicists will continue to push the mathematical frontiers until the end of time.

What about the nucleus, the positively charged “sun” at the center of the tiny atomic solar system? How might the proton and neutron have been deduced? The proton would not have been too difficult. Dalton in 1808 had made the first step. The mass of any atom is an integer multiple of a certain numerical value. That certainly suggests a discrete collection of basic constituents in the nucleus. Moreover, because the electric charge of a nucleus is generally smaller than the atomic number, the constituents cannot all have the same charge. The simplest possibility by far would have to be a single type of positively charged particle and a single neutral particle with practically identical masses. Smart theorists would have figured this out in no time.

Or would they? One thing might have led them astray, for how long I don’t know. There was a possibility even simpler than the neutron—a possibility that required no new particle. The nucleus might be understood as a number of protons stuck together with a smaller number of electrons. For example, a carbon nucleus with six protons and six neutrons might have been mistaken for six electrons stuck to twelve protons. In fact the mass of a neutron is close to the combined mass of a proton and an electron. Of course a new type of force would have to be introduced: the ordinary electrostatic force between electron and proton would not have been nearly strong enough to tightly bind the extra electrons to the protons—and with a new force, a new messenger particle. Perhaps in the end they would have decided the neutron was not such a bad idea.

Meanwhile, Einstein had developed his theory of gravity, and curious physicists were exploring its equations. Here again, we don’t need to guess. Karl Schwarzschild, even before Einstein had completed his theory, worked out the solution of Einstein’s equations that we now call the Schwarzschild black hole. Einstein himself derived the existence of gravitational waves that eventually led to the graviton idea. That most certainly required no experiment or observation. The consequences of the General Theory of Relativity were worked out without appeal to any empirical proof that the theory was correct. Even the modern theory of black holes, which we will encounter in the tenth chapter of this book, only involved the Schwarzschild solution combined with primitive ideas of quantum field theory.

Could theorists have guessed the full structure of the Standard Model? Protons and neutrons, perhaps, but quarks, neutrinos, muons, and all the rest? I don’t see any way that these things could have been guessed. But the basic underlying theoretical foundation—Yang Mills theory? Here I think I am on very firm ground. The experiment has been done, and the data are in. In 1953, with no other motivation than generalizing Kaluza’s theory of an extra dimension, one of history’s greatest theoretical physicists did invent the mathematical theory that today is called non-abelian gauge theory. Remember that Kaluza had added an extra dimension to the three dimensions of space and, in so doing, gave a unified description of gravity and electrodynamics. What Pauli did was to add one more dimension for a total of 5+1. The two extra dimensions he rolled up into a tiny 2-sphere. And what did he find? He found that the extra two dimensions gave rise to a new kind of theory, similar to electrodynamics but with a new twist. Instead of a single photon, the list of particles now had three photonlike particles. And, curiously, each photon carried charge; it could emit either of the other two. This was the first construction of a non-abelian, or Yang Mills, gauge theory.
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Today we recognize non-abelian gauge theory as the basis for the entire Standard Model. Gluons, photons, Z-particles, and W-particles are simple generalizations of Pauli’s three photonlike particles.

As I said, there was little or no chance that theorists would have been able to deduce the Standard Model with its quarks, neutrinos, muons, and Higgs bosons. And even if they had, it most likely would have been one of dozens of ideas. But I do think there is a possibility they could have found the basic theoretical ingredients.

Could they possibly have discovered String Theory? The discovery of String Theory is a good example of how the searching, probing minds of theorists often work. Again with absolutely no experimental basis, string theorists constructed a monumental mathematical edifice. The historical development of String Theory was somewhat accidental. But it easily could have arisen through other kinds of accidents. Stringlike objects play an important role in non-abelian gauge theories. Another plausible possibility is that it might have been developed through hydrodynamics, the theory of fluid flow. Think of the swirling vortex that forms when you let water drain from the sink. The actual center of the vortex forms a long, one-dimensional core that in many ways behaves like a string. Such vortices can form in air: tornadoes are an example. Smoke rings provide a more interesting example, vortex loops that resemble closed strings. Might fluid dynamics experts attempting to construct an idealized theory of vortices have invented String Theory? We will never know, but it doesn’t seem out of the question. Would physicists trying to explore the quantum theory of gravity have seized on it when the fluid people found closed strings that behaved like gravitons? I think they would have.

On the other hand, a skeptic could reasonably argue that for every good idea there would have been a hundred irrelevant, wrongheaded directions pursued. With no experiments to guide and discipline theorists, they would have gone off in every imaginable direction, with intellectual chaos ensuing. How would the good ideas ever be distinguished from the bad? Having every possible idea is just as bad as having no ideas.

The skeptics have a good point; they may be right. But it is also possible that good ideas have a kind of Darwinian survival value that bad ideas don’t. Good ideas tend to produce more good ideas—bad ones tend to lead nowhere. And mathematical consistency is a very unforgiving criterion. Perhaps it would have provided some of the discipline that would otherwise have come from experiment.

In a century without experiment, would physics have progressed the way I have suggested? Who knows? I don’t say it would have—only that it could have. In trying to gauge the limits of human ingenuity, I am certain that we are much more likely to underestimate where the limits lie than to overestimate.

In looking back I realize that in 1995 I was guilty of a very serious lack of imagination in speaking only of the ingenuity of theorists. In trying to console myself and the other physicists at the banquet about the poor prospects for future experimental data, I badly underestimated the ingenuity, imagination, and creativity of experimental physicists. Since that time they have gone on to create the revolutionary explosion of cosmological data that I described in chapter 5. In the last chapter of this book, I will discuss some other exciting experiments that will take place in the near future, but for now let’s return to String Theory and how it produces a huge Landscape of possibilities.

W
e come now to the heart of the matter. The unreasonable apparent design of the universe and the appeal to some form of Anthropic Principle is old stuff. What is really new, the earthquake that has caused enormous consternation and controversy among theoretical physicists and the reason that I wrote this book, is the recognition that the Landscape of String Theory has a stupendous number of diverse valleys. Earlier theories like QED (the theory of photons and electrons) and QCD (the theory of quarks and gluons) that had prevailed throughout the twentieth century had very boring Landscapes. The Standard Model, as complicated as it is, has only a single vacuum. No choices ever have to be made, or ever can be made, about which vacuum we actually live in.

The reason for the paucity of vacuums in older theories is not hard to understand. It was not that quantum field theories with rich Landscapes are mathematically impossible. By adding to the Standard Model a few hundred unobserved fields similar to the Higgs field, a huge Landscape can be generated. The reason that the vacuum of the Standard Model is unique is not any remarkable mathematical elegance of the kind that I explained in chapter 4. It has much more to do with the fact that it was constructed for the particular purpose of describing some limited facts about our own world. They were built piecemeal, from experimental data, with the particular goal of describing (not explaining) our own vacuum. These theories admirably do the job that they were designed to do but no more. With this limited goal in mind, theorists had no reason to add loads of additional structure just to make a Landscape. In fact most physicists (with the exception of farsighted visionaries like Andrei Linde and Alex Vilenkin) throughout the twentieth century would have considered a diverse Landscape to be a blemish rather than an advantage.

Until recently string theorists were blinded by this old paradigm of a theory with a single vacuum. Despite the fact that at least a million different Calabi Yau manifolds could be utilized for compactifying (rolling up and hiding) the extra dimensions implied by String Theory, the leaders of the field continued to hope that some mathematical principle would be discovered that would eliminate all but a single possibility. But with all the effort that was spent on searching for such a vacuum selection principle, nothing ever turned up. They say that “hope springs eternal.” But by now most string theorists have realized that, although the theory may be correct, their aspirations were incorrect. The theory itself is demanding to be seen as a theory of diversity, not uniqueness.

What is it about String Theory that makes its Landscape so rich and diverse? The answer involves the enormous complexity of the tiny, rolled-up geometries that hide the extra six or seven dimensions of space. But before we get to this complexity, I want to explain a simpler and more familiar example of similar complexity. In fact this example was the original inspiration for the term
Landscape.