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.
Is Nature Elegant?
“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.
Particle Mass
photon 0
gluon 0
neutrino less than 10–8 but not zero
electron 1
up-quark 8
down-quark 16
strange-quark 293
muon 207
tau lepton 3447
charmed-quark 2900
bottom-quark 9200
W-boson 157,000
Z-boson 178,000
top-quark 344,000
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 10500 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.
CHAPTER FIVE
Thunderbolt from Heaven
“I’m astounded by people who want to ‘know’ the universe when it’s hard enough to find your way around Chinatown.”
— WOODY ALLEN
Alexander Friedmann’s Universe
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!
Hubble’s technique for measuring the motion of a galaxy was a familiar one. The light from a galaxy was sent through a spectroscope that breaks it up into its component wavelengths. Isaac Newton, way back in the seventeenth century, did exactly that when he sent white sunlight through a triangular prism. The prism, a simple spectroscope, broke the sunlight into all the colors of the rainbow. Newton concluded, rightly, that sunlight is a composite of red, orange, yellow, green, blue, and violet light. Today, we know that each color of the spectrum corresponds to a wave of a particular (wave)length.
If one looks very carefully at the spectrum of starlight, some extremely narrow dark spectral lines can be seen superimposed on the rainbow of colors.
These mysterious lines of missing light are called absorption lines. They indicate that something along the line of sight has absorbed certain discrete wavelengths (colors) without disturbing the rest of the spectrum. What causes this curious phenomenon? The quantum mechanical behavior of electrons.
According to Bohr’s original quantum theory of the atom, electrons in atoms move in quantized orbits. Newtonian mechanics would allow the electron to orbit at any distance from the nucleus. But quantum mechanics constrains them to move like motor vehicles that are required, by law, to stay in definite lanes. Being between lanes violates the traffic laws: being between quantized orbits violates the laws of quantum mechanics. Each orbit has its own energy, and for an electron to jump from one orbit to another, the energy of the electron has to change. If an electron jumps from an outer to an inner orbit, it must radiate a photon to carry off the excess energy. Conversely, an inner electron can jump to a more distant orbit only if it gains some energy, possibly by absorbing a photon.
Normally an electron moves in the innermost available orbit that is not blocked by other electrons (remember that the Pauli exclusion principle prevents any two electrons from occupying the same quantum state). But if the atom is struck by another object, an electron can absorb some energy and make a quantum jump to a new orbit, one farther from the nucleus. The atom is temporarily excited, but eventually the electron will emit a photon and drop back to its original orbit. The light radiated in this way has definite wavelengths that are characteristic of the type of atom. Each individual chemical element has its own signature, a set of spectral lines that corresponds to these quantum jumps.
If a photon of the right color falls on an unexcited atom, the reverse process can happen: the photon can be absorbed while the electron jumps to a more energetic orbit. This has an interesting effect on starlight passing through hydrogen gas in the atmosphere surrounding a star. The hydrogen will deplete the starlight of precisely those colors that characterize the hydrogen spectrum. If helium or carbon or any other element is present, it will also leave its distinguishing mark on the starlight. Studying the spectra of starlight is the way we know about the chemical makeup of stars. But our interest right now is not the chemical composition but rather the velocity of the star. The point is that the exact details of the absorption spectrum, as seen from earth, depend on the relative velocity between us and the star. The key is the Doppler effect.
If you have heard the siren of a police car as it speeds past, then you’ve experienced the Doppler effect. The high-pitched whine, “eeee,” of the approach gives way to the lower sound, “ooo,” as the siren recedes. During the approach the sound waves coming toward you are bunched up, and conversely, while the car moves off, they are stretched out. Because wavelength and frequency are closely related, you hear “eeeeooooo.” You could amuse yourself by trying to estimate how fast the police car is moving by the magnitude of the frequency shift.
But the Doppler effect is not just an amusement for pedestrians. For astronomers it is nothing less than the key to the structure and history of the universe. The Doppler effect happens to all kinds of waves: sound waves, vibrational waves in crystals, even water waves. Try wiggling your finger in the water while hanging off the side of a slowly moving boat.1 The ripples spreading out along the direction of motion are bunched up. The ones going in the reverse direction are stretched.
Luckily for astronomers light emitted by a moving object does the same thing. A rocket-propelled lemon moving away from you might have the color of an orange or even a tomato if it were going fast enough.2 While it’s moving toward you, you might mistake it for a lime or even a giant blueberry. This is because light from sources moving away from the observer is redshifted and light from approaching sources is blueshifted. This applies just as well to the light from galaxies as from lemons. Moreover, the amount of shift is a measure of the velocity of the galaxy, relative to the earth.
Hubble used this phenomenon to determine the velocity of a large number of galaxies. He took very accurate spectra of the light coming fro
m each galaxy and compared the spectral lines with similar spectra taken in the laboratory. If the universe were static as Einstein originally thought, the galactic and laboratory spectra would have been identical. What Hubble found surprised him and everyone else. The light from every distant galaxy was distinctly on the red side. No doubt about it, Hubble knew that they were all moving away from us. Some galaxies were moving slowly, and some were racing away, but except for a few very nearby galaxies, they were all outward bound. This must have puzzled Hubble. It meant that in the future the galaxies would spread out to ever-farther distances. Even more bizarre, it meant that in the past the galaxies were closer to us, at some point maybe even on top of us!
Hubble was also able to make a rough determination of the distances to the various galaxies, and he found a pattern: the more distant the galaxy, the faster its recessional velocity. The closer galaxies were hardly moving, but the most distant ones were speeding away with tremendous velocities. On a piece of graph paper, Hubble made two axes: on the horizontal axis he plotted the distance to each galaxy; on the vertical axis, its velocity. Each galaxy was plotted as a single point on the graph. What he found was extraordinary; most of the points fell on or near a straight line.
This meant that the recessional velocity not only increased with distance but was directly proportional to the distance. One galaxy, twice as far as another, appeared to recede twice as fast. This was a new, totally unexpected, regularity in the universe: a new cosmological law, Hubble’s Law. Galaxies are receding away from us with velocity proportional to their distance. An even more precise formulation is: galaxies are receding away from us with velocity equal to the product of their distance and a numerical parameter called the Hubble constant.3
Well, actually it wasn’t completely unexpected. Alexander Friedmann was a Russian mathematician who had studied Einstein’s theory of the universe, and in 1922 he published a paper claiming that Einstein might have been wrong in his 1917 paper. He argued that if the universe were not static, if it were changing as time evolved, then the cosmological constant would be superfluous. The Friedmann universe was, like Einstein’s, a closed-and-bounded 3-sphere. But unlike Einstein’s, Friedmann’s universe grew with time. If Einstein’s universe was like a static balloon, Friedmann’s was like the surface of an expanding balloon. Get yourself a balloon and mark its surface with dots to represent the galaxies. Sprinkle them more or less uniformly. Then slowly blow it up. As the balloon expands, the dots get farther apart, every dot receding from every other dot. No dot is special, but each sees all the others moving away. This was the essence of Friedmann’s mathematical universe.