As with the zero-point energy, scientists learned to ignore the infinite mass and charge of the electron. They don’t go all the way to zero distance from the electron when they calculate the electron’s true mass and charge; they stop short of zero at an arbitrary distance. Once a scientist chooses a suitably close distance, all the calculations using the “true” mass and charge agree with one another. This is a process called renormalization. “It is what I would call a dippy process,” wrote physicist Richard Feynman, even though Feynman won his Nobel Prize for perfecting the art of renormalization.
Just as zero punches a hole in the smooth sheet of general relativity, zero smooths and spreads out the sharp point charge of the electron, covering it in a fog. However, since quantum mechanics deals with zero-dimensional particle-points such as the electron, technically all particle-particle interactions in quantum theory deal with infinities: they are singularities. When two particles merge, for instance, they meet at a point: a zero-dimensional singularity. This singularity makes no sense in quantum mechanics or in general relativity. Zero is the wrench in the works of both great theories. So physicists simply got rid of it.
It is not obvious how to get rid of zero, as zero appears and reappears throughout time and space. Black holes are zero-dimensional, as are particles such as the electron. Electrons and black holes are real things; physicists can’t simply will them away. But scientists can give black holes and electrons an extra dimension.
This is the reason for string theory, which was created in the 1970s when physicists began to see the advantages of treating every particle as a vibrating string rather than as a dot. If electrons (and black holes) are treated as one-dimensional, like a loop of string, instead of as zero-dimensional, like a point, the infinities in general relativity and quantum mechanics miraculously disappear. For instance, the renormalization trouble—the infinite mass and charge of the electron—vanishes. A zero-dimensional electron has an infinite mass and charge because it is a singularity; as you get closer and closer to it, your measurements zoom off to infinity. However, if the electron is a loop of string, the particle is no longer a singularity. This means that the mass and charge don’t go off to infinity, because you are no longer passing an infinite cloud of particles as you approach the electron. Furthermore, as two particles merge, no longerdo they meet at a point-like singularity; they form a nice, smooth, continuous surface in space-time (Figures 54,55).
Figure 54: Point particles create a singularity…
Figure 55:…string particles don’t.
In string theory different particles are really the same type of string, just wiggling in different ways. Everything in the universe is made up of these strings, which are about 10-33 centimeters across; comparing the size of a string to the size of a neutron is like comparing the size of a neutron to the size of our solar system. From the perspective of beings as large as we are, the loops look like points because they are so tiny. Distances (and times) smaller than the size of the loops no longer matter; they don’t make any physical sense. In string theory, zero has been banished from the universe; there is no such thing as zero distance or zero time. This solves all the infinity problems of quantum mechanics.
Banishing zero also solves the infinity problems in general relativity. If you imagine a black hole as a string, no longer do objects fall through a rip in the fabric of space-time. Instead, a particle loop approaching a black-hole loop stretches out and touches the black hole. The two loops tremble, tear, and form one loop: a slightly more massive black hole. (Some theorists believe that the act of merging a particle to a black hole creates bizarre particles such as tachyons: particles with imaginary mass that travel backward in time and move faster than light. Such particles might be admissible in certain versions of string theory.)
Removing zero from the universe might seem like a drastic step, but strings are much more tractable than dots; by eliminating zero, string theory smooths out the discontinuous, particle-like nature of quantum mechanics and mends the gashes torn in general relativity by black holes. With these problems patched over, the two theories are no longer incompatible. Physicists began to think that string theory would unify quantum mechanics with relativity; they believed that it would lead to the theory of quantum gravity—the Theory of Everything that explains every phenomenon in the universe. However, string theory had some problems. For one thing, it required 10 dimensions to work.
For most people, four dimensions are one too many. It is easy to see three of them: left-right, front-back, and up-down represent the three directions we can move in. The fourth arrived when Einstein showed that time was similar to these three dimensions; we are constantly moving through time like a car that’s speeding down a highway. The theory of relativity shows that just as we can change how quickly we rush down a highway, we can change the rate at which we move through time—the faster we go through space, the quicker we move through time. To understand Einstein’s universe, we have to accept the idea that time is the fourth dimension.
Four is reasonable—but 10? We can measure four dimensions, but what happened to the other six dimensions? According to string theory, they are rolled up like little balls, too tiny to see. When you pick up a piece of paper, it seems two-dimensional. It has length and breadth, but it doesn’t seem to have any depth at all. Nevertheless, if you take a magnifying glass and gaze at the edge of the piece of paper, you begin to see that it has a wee bit of depth. You need a tool to help you see it, but that third dimension is there, too tiny to see under normal conditions. The same is true with those extra six dimensions. In everyday life they are way too tiny to see; they are too small to detect even with the most powerful equipment that we could possibly manufacture in the near future.
What do these six extra dimensions mean? Nothing, really. They don’t measure anything that we are accustomed to, like length, breadth, width, or time. They are simply mathematical constructs that make the mathematical operations in string theory work in the manner that they have to. Like imaginary numbers, we can’t see them or feel them or smell them, even though they are necessary for doing calculations. Though it is a strange concept physically, it is the predictive power of the equations that interests scientists, rather than their comprehensibility—and an extra six dimensions do not constitute an insurmountable problem, mathematically. Spotting them might. (Ten seems small nowadays. In the past few years physicists realized that the many competing varieties of string theory are actually, in a sense, the same thing. Scientists realize now that these theories are dual to each other just as Poncelet realized that lines and points were dual to each other. Scientists now believe that there is a monster theory that underlies all of these competing theories: the so-called M-theory, which lives in 11 dimensions, not 10.)
Strings (or their more general counterparts, branes, a term for multidimensional membranes) are so tiny that no instrument can hope to spot them—at least until our civilization becomes much more advanced. Particle physicists look at the subatomic realm with particle accelerators: they use magnetic fields or other means to get tiny particles moving very fast; when these particles collide with one another, they spit off fragments. Particle accelerators are the microscopes of the subatomic world, and the more energy you put into those particles—the more powerful the microscope—the smaller the objects you can see.
The Superconducting Super Collider, a multibillion dollar project that was contemplated until the early 1990s, was going to be the most powerful particle accelerator ever built. It was to have more than 10,000 magnets arranged in a loop 54 miles around, about the size of the beltway highway that circles Washington, D.C. This is still not nearly powerful enough to see strings or curled-up dimensions—viewing strings would require a particle accelerator about 6,000,000,000,000,000 miles around. Even traveling at the speed of light, a particle would take 1,000 years to make the circuit.
No instrument currently imaginable will give scientists the power to observe strings directly; nobody can th
ink of an experiment that will give physicists evidence about whether black holes and particles are, indeed, strings. This is the chief objection to string theory. Because science is based upon observation and experiment, some critics argue that string theory is not science but philosophy. (A recent set of theories proposes that some of these rolled-up dimensions might be 10-19 centimeters or even larger, which would put them within the realm of experimentation. But at the moment, these theories are considered rogues—interesting ideas, but very long shots at best.)
Newton’s laws of motion and gravitation gave physicists an explanation for the way planets and objects move through the universe. Whenever a new comet was discovered, it gave additional support to Newton’s calculations. There were a few problems. Mercury’s orbit, for instance, wobbled in a way that disagreed with what Newton predicted, but on the whole, Newton’s theories were tested again and again, and they usually passed.
Einstein’s theories corrected Newton’s errors; they explained Mercury’s wobble, for instance. These theories also made testable predictions about the way gravity works. Eddington observed the bending of starlight during a solar eclipse, confirming one of those predictions.
String theory, on the other hand, ties together a number of existing theories in a very pretty way, and makes a number of predictions about the way black holes and particles behave, but none of those predictions are testable or observable. While string theory might be mathematically consistent, and even beautiful, it is not yet science.*
For the foreseeable future, banishing zero from the universe with string theory is a philosophical idea rather than a scientific one. String theory might well be correct, but we may never have the means to find out. Zero has not yet been banished; indeed, zero seems to be what created the cosmos.
The Zeroth Hour: The Big Bang
Hubble’s observations suggested that there was a time, called the big bang, when the universe was infinitesimally small and infinitely dense. Under such conditions all the laws of science, and therefore all ability to predict the future, would break down.
—STEPHEN HAWKING, A BRIEF HISTORY OF TIME
The universe was born in zero.
Out of the void, out of nothing at all, came a cataclysmic explosion that created all the matter and energy that the entire universe is made of. This event—the big bang—was a horrible idea to many scientists and philosophers. It took a long time before astrophysicists came to agree that our universe was finite—that it did, in fact, have a beginning.
The prejudice against a finite universe is ancient. Aristotle rejected the creation of the universe out of the void because he believed that the void could never exist. But this caused a paradox. If the universe could not spring forth from the void, then something had to be floating about before the birth of the universe; there had to be a universe before the universe was born. To Aristotle, the only possible way out of this quandary was to assume that the universe was eternal. It had always existed in the past, and would always exist.
Western civilization eventually had to make a choice between Aristotle and the Bible, which says that the finite universe sprang forth from the void and prophesies its ultimate destruction. Though the Semitic biblical cosmos toppled the Aristotelian one, the idea of an eternal, unchanging universe was not expunged completely, enduring even to the twentieth century. It led Einstein to what he called the greatest mistake of his career.
To Einstein, the general theory of relativity had a crucial flaw. It foretold the end of the universe. According to the equations of general relativity, the universe was unstable. There were only two choices, and both were equally unpleasant.
One possibility was that the universe would collapse under its own gravity. As the universe gets smaller and smaller, it heats up more and more. It burns brightly with radiation, destroying all life and eventually destroying the atoms that make up matter. It would be death by fire. Eventually, the universe would crunch itself into a zero-dimensional point—like a black hole—and would disappear forever.
The other possibility is, if anything, more grim. The universe would expand forever. Galaxies would become ever more distant from one another, and the star stuff that drives all the energetic reactions in the universe would become more rarefied. Stars would burn out as they exhausted their fuel, and galaxies would become darker and darker—and then cold and silent. The cold, dead matter of the stars would decay away, leaving nothing but a smear of radiation that spreads equally throughout the universe. The cosmos would be a cold soup of dimming light. It would be death by ice.
To Einstein, these ideas were abhorrent. Like Aristotle, he implicitly assumed that the universe was static, constant, and eternal. The only way out was to “correct” his equations of general relativity to stave off the impending destruction. He did this by adding a cosmological constant, an as yet undetected force that counteracts the force of gravity. The cosmological constant’s push would balance out gravity’s pull; instead of collapsing, the universe could stay in a steady balance, neither collapsing nor expanding. Postulating the existence of such a mysterious force was a desperate act. “I have…again perpetrated something about gravitation theory which somewhat exposes me to the danger of being confined in a madhouse,” wrote Einstein, but he was so worried about the impending destruction of the universe that he was forced to take such a dramatic step.
Einstein wasn’t bundled off to an asylum. Einstein had proposed stranger things and had been entirely right. However, this time he was not so lucky. The stars themselves destroyed Einstein’s vision of a static, eternal cosmos.
In 1900 the Milky Way was the known universe. Astronomers had little idea that anything lay beyond our own dusty little disk of stars. Though astronomers had spotted some glowing, swirly clouds, there was little reason to believe that they were anything but glowing gas inside our galaxy. In the 1920s that all changed, thanks to an American astronomer named Edwin Hubble.
A special type of star, called a Cepheid variable, had a property that allowed Hubble to measure the distance to faraway objects. Cepheid stars pulsate, getting brighter and dimmer in a very predictable way; the way they pulsate is closely related to how much light they put out. They are standard candles, objects of known brightness, and became a key tool for Hubble. They were like the headlights of a train.
If you watch a train coming at you, you will see that its headlight gets brighter and brighter as it approaches. If you know how much light the headlight puts out—if the headlight is a standard candle—you can tell how bright the headlight will appear at any given distance. The closer it gets, the brighter it seems. The same logic works in reverse; if you know how much light a train’s headlight emits, you can measure its apparent brightness and calculate the train’s distance from you.
Hubble did the exact same thing with Cepheid stars. Most stars he saw were tens or hundreds or thousands of light-years away. But when he found a Cepheid blinking in one of these swirly clouds—the Andromeda nebula, as it was then called—he measured the light and calculated that the nebula was a million light-years away, far beyond the outer reaches of our galaxy. Andromeda was not a cloud of glowing gas; it was a cloud of stars so distant that they looked like a smear rather than individual points of light. Other swirly galaxies were even more distant. Today, astronomers suspect that the universe is about 15 billion light-years across and peppered everywhere with clusters of galaxies.
This was an astounding discovery; the universe was millions of times bigger than previously suspected. As amazing as this observation was, it was not what Hubble is best remembered for. Hubble’s second discovery was what shattered Einstein’s eternal universe.
Hubble measured the distance to galaxy after galaxy with his Cepheid stars, but soon began to notice an alarming pattern: all the galaxies were fleeing with high speed, shooting away from the Milky Way at speeds of hundreds of miles a second or more. The galaxies were so distant that even these great velocities were not directly measurable.
&nbs
p; The only way to clock the speed of a galaxy is by using the Doppler effect—the same principle used in state troopers’ radar guns. You might have noticed that when a train zooms by, the pitch of its horn changes. As the train approaches, its horn is high-pitched, but as it passes you, all of a sudden its pitch drops dramatically. This happens because the motion of the train crushes the sound waves in front of it (making a higher-frequency, higher-pitch tone) and stretches out the waves behind it (making a lower-frequency, lower-pitch tone) (Figure 56). This is the Doppler effect, and it works with light, too. If a star is moving toward Earth, the light is crushed and has a higher frequency than normal; it is shifted toward the blue end of the spectrum, blueshifted. If a star is moving away, the opposite happens; the light is stretched out and redshifted.
Police can tell how fast a car is going by testing how light—in the form of radio waves—reflected off the speeding vehicle gets shifted. In the same way, by looking at how a star’s light spectrum gets shifted, astronomers can deduce how fast the star is moving—toward us or away.
Hubble combined the distance data with Doppler speed data, and found something shocking. Not only were galaxies speeding away from us in all directions, the farther away the galaxies were, the faster they were going away.
Figure 56: The Doppler effect
How could this be? Imagine a polka-dotted balloon; the polka dots are like galaxies, while the balloon itself is the fabric of space-time. As the balloon inflates, the dots get farther and farther apart from one another. From any one dot’s perspective, the other dots are all rushing away, and the more distant dots are rushing faster than the close dots (Figure 57). The universe seemed to be expanding, like a balloon. (The balloon analogy has one flaw. Unlike the polka dots, which also get bigger as the balloon expands, the galaxies are staying about the same size, held together by their own gravity.)
Zero Page 17