The Cosmic Landscape (20 page)

Excitingly, all of String Theory’s consequences have unfolded in a mathematically consistent way. String Theory is a very complex mathematical theory with very many possibilities for failure. By failure I mean internal inconsistency. It is like a huge high-precision machine, with thousands of parts. Unless they all fit perfectly together in exactly the right way, the whole thing will come to a screeching halt. But they do fit together, sometimes as a consequence of mathematical miracles. String Theory is not only a physical theory about nature. It is also a very sophisticated mathematical structure that has provided a great deal of inspiration for pure mathematicians.

But is String Theory beautiful? Does String Theory live up to the standards of elegance and uniqueness that physicists demand? Are its equations few and simple? And, most important, are the Laws of Physics implied by String Theory unique?

Elegance requires that the number of defining equations be small. Five is better than ten, and one is better than five. On this score, one might facetiously say that String Theory is the ultimate epitome of elegance. With all the years that String Theory has been studied, no one has ever found even a single defining equation! The number at present count is zero. We know neither what the fundamental equations of the theory are nor even if it has any. Well then, what is the theory, if not a collection of defining equations? We really don’t know.

As for the second question—are the Laws of Physics defined by String Theory unique?—here we can be more definite. Although no one can identify the defining equations, the methodology of the theory is very rigorous. It could easily have failed any of a large number of mathematical consistency tests. It didn’t, but it was thought that the very tight mathematical constraints would lead to either a completely unique theory or, at most, a very small number of possibilities. There was a great sense of euphoria in the mid-1980s, when string theorists thought they were zeroing in on the final answer, a single, unique theory that would explain why the world is the way it is. It was also believed that the deep and often miraculous mathematical properties of the theory would guarantee that the cosmological constant was exactly zero.

The superintellectual, rarefied atmosphere of the Institute for Advanced Study, in Princeton—once the home of both Albert Einstein and J. Robert Oppenheimer—was the center of this excitement. And at the center of the center were some of the greatest mathematical physicists in the world. Edward Witten and the people around him seemed to be making rapid strides toward a unique answer. That was then.

Today we know that the success “just around the corner” was a mirage. As we learned more about the theory, three unfortunate things began to happen. Number one was that new possibilities kept turning up, new mathematically consistent versions of what was supposed to be a unique theory. During the 1990s the number of possibilities grew exponentially. String theorists watched with horror as a stupendous Landscape opened up with so many valleys that almost anything can be found somewhere in it.

The theory also exhibited a nasty tendency to produce Rube Goldberg machines. In searching the Landscape for the Standard Model, the constructions became unpleasantly complicated. More and more “moving parts” had to be introduced to account for all the requirements, and by now it seems that no realistic model would pass muster with the American Society of Engineers—not for elegance in any case.

Finally, adding insult to injury, the potential candidates for a vacuum like the one we live in all have a nonzero cosmological constant. The hope that some elegant mathematical magic of String Theory will guarantee a zero value for the cosmological constant is rapidly fading.

Judged by the ordinary criteria of uniqueness and elegance, String Theory has gone from being Beauty to being the Beast. And yet the more I think about this unfortunate history, the more reason I think there is to believe that String Theory is the answer.

“The great tragedy of science—the slaying of a beautiful hypothesis by an ugly fact.”

— THOMAS HENRY HUXLEY

String Theory has no lack of enemies who will tell you that it is a monstrous perversion. Among them are condensed-matter theorists who think the right theory is emergent. Condensed-matter physics is the study of the properties of ordinary matter in solid, liquid, or gaseous form. According to this school, space and time emerge from some unspecified microscopic objects in the same way that crystal lattices and superconductors emerge from the collective behavior of large numbers of atoms. In many cases emergent behavior hardly depends on the particular microscopic details. In the view of condensed-matter physicists, the world may emerge from such a wide variety of microscopic starting points that there is no point in trying to identify the microscopic details. Instead, it is argued, physicists should be trying to understand the rules and mechanisms of emergence itself. In other words, they should study condensed-matter physics.

The trouble with this view is that no ordinary condensed-matter system can ever behave anything like a universe regulated by quantum mechanics together with Einstein’s laws of gravity. Later, when we meet the
Holographic Principle,
in chapter 10, we will see that there are profound reasons for this. The idea that there are many microscopic starting points that can lead to a world with gravity may be true, but none is anything like the ordinary materials that condensed-matter physicists study.

Another source of criticism is from some (certainly not all) high-energy experimental physicists who are annoyed that the new phenomena implied by String Theory are too remote from experiment, as if that were the theorists’ fault. These physicists are troubled because they can’t see how their experiments can ever address the questions that string theorists are trying to answer. They suggest that theorists keep to problems that directly address the near-term future experimental agenda. This is an extremely myopic view. In the present age, high-energy physics experiments have become so large and complicated that they take decades to complete. Brilliant young theoretical physicists are like restless explorers. They want to go where their curiosity about the world takes them. And if it’s out into the great sea of the unknown, so be it.

Most really good experimental physicists don’t pay too much attention to what theorists think. They build the machines they can build and do the experiments they can do. Most really good theoretical physicists don’t pay much attention to what experimenters think. They build their theories based on their own instincts and go where intuition leads them. Everyone hopes that at some point the two paths will cross, but exactly when and how is anybody’s guess.

Finally, there are proponents of other theories. That’s as it should be. Other avenues need to be explored, but as far as I can tell, none of these theories is very well developed. At present they have very little to say.

What I have never heard is criticism based on the unfortunate inelegance or the lack of uniqueness of String Theory.
⁵
Either of these tendencies might be thrown back at the string theorists as evidence that their own hopes for the theory are misguided. Perhaps part of the reason that the enemies of String Theory haven’t pounced is that string theorists have kept their Achilles heel under wraps until fairly recently. I suspect that now that it is becoming more public, partly through my own writings and lectures, the kibitzers on the sidelines will be grinning and loudly announcing, “Ha ha, we knew it all along. String Theory is dead.”

My own guess is that the inelegance and lack of uniqueness will eventually be seen as strengths of the theory. A good, honest look at the real world does not suggest a pattern of mathematical minimality. Below is a list of the masses of the elementary particles of the Standard Model, expressed in terms of the electron mass. The numbers are approximate.

There is very little pattern here other than the obvious increase as we go down the list.

The numbers don’t seem to have any simple connection to special mathematical quantities like π or the square root of two. The only reason any pattern exists at all is that I purposely listed the particles in order of increasing mass.

These dozen numbers are just the tip of an iceberg. We know with certainty that in the Standard Model at least twenty additional independent coupling constants governing a wide range of different forces belie claims of simplicity. Even that list is probably far from exhaustive. There is more to the world than just the Standard Model of particle physics. Gravitation and cosmology introduce many new constants, such as the mass of dark-matter particles.
⁶
The consensus among particle physicists, especially those who expect supersymmetry to be a feature of nature, is that well over one hundred separate constants of nature are in no known way related. Far from being the simple, elegant structure sometimes suggested by physicists, the current most fundamental description of nature seems like something Rube Goldberg himself might have designed. A Rube Goldberg theory, then, may be fitting.

While the Standard Model is a huge advance in describing elementary particles, it doesn’t explain itself. It is rather complicated, far from unique, and certainly incomplete. What, then, is special about our beloved Standard Model? Absolutely nothing—there are 10
⁵⁰⁰
others, just as consistent. Nothing, that is, except that it permits—maybe even encourages—the existence of life.

Cosmologists are not usually as infected by the elegance-uniqueness bug as string theorists—probably because they are more likely to take a good hard look at nature rather than at mathematics. What some of them see is a bunch of remarkable coincidences:

•  The universe is a fine-tuned thing. It grew big by expanding at an ideal rate. If the expansion had been too rapid, all of the material in the universe would have spread out and separated before it ever had a chance to condense into galaxies, stars, and planets. On the other hand, if the initial expansion had not had a sufficient initial thrust, the universe would have turned right around and collapsed in a big crunch much like a punctured balloon.
  
•  The early universe was not too lumpy and not too smooth. Like the baby bear’s porridge, it was just right. If the universe had started out much lumpier than it did, instead of the hydrogen and helium condensing into galaxies, it would have clumped into black holes. All matter would have fallen into these black holes and been crushed under the tremendously powerful forces deep in the black hole interiors. On the other hand, if the early universe had been too smooth, it wouldn’t have clumped at all. A world of galaxies, stars, and planets is not the generic product of the physical processes in the early universe; it is the rare and, for us, very fortunate, exception.
  
•  Gravity is strong enough to hold us down to the earth’s surface, yet not so strong that the extra pressure in the interior of stars would have caused them to burn out in a few million years instead of the billions of years needed for Darwinian evolution to create intelligent life.
  
•  The microscopic Laws of Physics just happen to allow the existence of nuclei and atoms that eventually assemble themselves into the large “Tinkertoy” molecules of life. Moreover, the laws are just right, so that the carbon, oxygen, and other necessary elements can be “cooked” in first-generation stars and dispersed in supernovae.
  

The basic setup looks almost too good to be true. Rather than following a pattern of mathematical simplicity or elegance, the laws of nature seem specially tailored to our own existence. As I have repeatedly said, physicists hate this idea. But as we will see, String Theory seems to be an ideal setup to explain why the world is this way.

Let us return now to hard science issues. In the next chapter I will explain the surprising—amazing may not be too strong a word—cosmological developments that have been pushing physics and cosmology toward a new paradigm. Most significantly I will explain what we have learned about the early prehistory of our universe—how it arrived at its present precarious condition—and the shocking facts concerning the 120th decimal place of the cosmological constant.

“I’m astounded by people who want to ‘know’ the universe when it’s hard enough to find your way around Chinatown.”

— WOODY ALLEN

Mention of the year 1929 brings shudders to anyone old enough to remember it: bank runs, Wall Street suicides, mortgage foreclosures, unemployment. It was the year that brought on the Great Depression. But it wasn’t all bad. On Wall Street the stock market did collapse like a popped balloon, but out in sunny California Edwin Hubble discovered the Big Bang, an explosion out of which the entire known universe was born. As previously noted, contrary to what Einstein had thought back in 1917, the universe changes and grows with time. According to Hubble’s observations, the distant galaxies are all rushing away from us, as if they had been shot out of a gigantic cannon, a cannon that could shoot in all directions, and from every location, simultaneously. Hubble not only discovered that the universe is changing: he discovered that it is growing like an expanding balloon!