A great deal of my work is just playing with equations and seeing what they give.

A mirror macho is not a big tough guy who spends the day looking at his face in the mirror.

It’s a macho—make that MACHO—made of matter from the mirror world, a hypothetical wonderland invented by physicists who didn’t have enough subatomic particles to play with.

Those physicists will tell you that every type of particle in nature has a “mirror partner.” If you looked into a mirror made of mirror matter, though, you might as well be a vampire, because you would see no reflection. In fact, you couldn’t even see the mirror. Mirror matter is utterly invisible; it does not interact with light. Mirror matter can be detected only by its gravity.

If mirror matter is real, there’s a lot more matter in the universe than astronomers can see. But guess what: astronomers already know that there is a lot more matter in the universe than they can see. They’ve been looking for it for years. Some of that “dark matter” lurks throughout the outer regions (or “halos”) of galaxies in the form of massive compact objects the size of small stars. Those massive compact halo objects are what scientists call MACHOs.

Astronomers have actually detected a handful of these MACHOs but aren’t really sure exactly what they are. Most MACHOs seem to be roughly half the mass of the sun, which would be the right size for burnt-out stars known as white dwarfs. But there’s no way the galaxy could have made enough white dwarfs to account for very much of the halo matter. Brown dwarfs are too small to be the MACHOs. Red dwarfs have also been ruled out. So MACHOs are a mystery. But some scientists think that solving it is as simple as looking in a mirror.

It is, of course, a mathematical mirror. Certain formulas suggest that every type of subatomic particle known to science is something like one of a pair of gloves—either left- or right-handed. The opposite glove should be out there, somewhere. Of course, there is no compelling reason for believing this possibility other than that the math suggests that it might be true. But scientists have learned through experience to respect what mathematics tells them, and no one taught that lesson more dramatically than Paul Adrien Maurice Dirac.

For Dirac, numbers always spoke louder than words. He was no macho man, but rather one of the twentieth century’s shiest and quietest physicists. He was unquestionably brilliant but handicapped by a harsh childhood, leaving him without a normal repertoire of human interaction skills. He remarked once that he had been brought up

“without any social contact.” His father, a stern high-school French teacher, insisted that while at home Paul speak only in French. Paul lacked confidence in his French and resolved this inner conflict by rarely speaking at all. “Since I found I couldn’t express myself in French, it was better for me to stay silent than to talk in English,” he recalled.¹

Terseness marked Dirac’s style for the rest of his life. A colleague once remarked that Dirac was suspected of knowing only three phrases: “Yes, no, and I don’t know.” When he did speak, his comments were always pointed. George Gamow recalled that after a lecture in Canada, Dirac asked for questions.

“I do not understand how you derived this formula,” a professor in the audience said. “This is a statement and not a question,” Dirac responded. “Next question, please.”²

Born in 1902 in Bristol, England, Dirac earned a degree in electrical engineering at the university there but couldn’t find a good job. He’d shown by then that he was a whiz at math, though, so Bristol offered him funding to spend two extra years as a math student. Afterwards Dirac went to Cambridge, where he mixed math with theoretical physics, and he found himself smack in the middle of the biggest scientific revolution since Newton. As the first phase of that revolution ended, Dirac produced what many regard as the greatest example of prediscovery in the history of physics: antimatter.

Dirac’s prediscovery grew from his efforts to understand the meaning of the math behind quantum mechanics, a field of study that didn’t even exist when he entered Cambridge in 1923. In those days physicists struggled with trying to understand the “old quantum theory,” the mathematical predecessor of quantum mechanics. The centerpiece of the old version was Niels Bohr’s quantum theory of the atom, published in 1913. But Dirac heard about it for the first time only after entering Cambridge a decade later.

In his 1913 papers, Bohr used the then-novel quantum ideas to explain the structure of the simplest atom in nature, hydrogen. Like

other atoms, hydrogen emits specific colors of light when heated up or otherwise energized. Various colors identify atoms like the flags of different nations. By recording the colors coming from a gas, you can deduce precisely what atoms it contains. (In this way, scientists were able to discover the element helium in the sun, many years before it was found on Earth, and can tell you what chemicals have been cooked up in distant stars.)

Scientists had long known about the colors and presumed that they had something to do with the way atoms were put together. But nobody knew how. A big clue emerged in 1911, though, when Ernest Rutherford, a New Zealander working then in England at Manchester, figured out that atoms consisted mostly of empty space.

Rutherford had instructed his assistants to fire alpha particles (subatomic bullets emitted by some radioactive atoms) at a thin gold foil surrounded by phosphorescent detectors. As expected, most of the alpha particles sailed through the foil—it was too thin to stop a fast-charging subatomic particle. But a few of the alpha particles were diverted far from their path, and some bounced almost straight back. Rutherford eventually deduced that the foil must contain some tiny, dense bits of matter, kind of like cherry pits, that unlucky alpha particles smashed into. With some simple calculations Rutherford showed that a very small, very dense nucleus resided in every atom’s core, carrying a positive electrical charge. Negatively charged electrons, lightweights compared to the nucleus, should be speeding about an atom’s outer edges, perhaps like planets orbiting the sun. An atom of hydrogen, for example, possessed a nucleus consisting of a single particle—a proton—with a single electron for its “planet.”

While Rutherford’s nucleus model offered a clue, it also posed a problem. An electron in orbit, with an electrical charge, should spit out light of some sort all the time. After all, light is just a form of electromagnetic radiation, and a charged particle changing direction should emit such radiation in the process, as James Clerk Maxwell had demonstrated in the nineteenth century. In fact, a simple calcula-

tion suggested that an electron would emit its energy so rapidly that it would spiral into the hydrogen nucleus in a fraction of a second, making hydrogen atoms rather too short-lived to be good for anything. Clearly hydrogen (and most other atoms) lived a lot longer than that. Somehow atoms remained in a stable, or “stationary,” state, emitting radiation only when provoked. Bohr, a Dane who had gone to Manchester for postdoctoral study with Rutherford, tackled this problem in 1913.

Among the theoretical physicists of the twentieth century, Bohr ranked second only to Einstein in intellectual power and influence. But unlike most theorists, who guide themselves through nature by interpreting maps written in mathematics, Bohr sought a deeper physical understanding. He wanted to know what was really going on—a difficult task when dealing in the invisible realm of the atom’s interior. While working with Rutherford, Bohr began to form his mental picture of the atomic blueprint for hydrogen. But at first he did not see how the pattern of colors that hydrogen emitted could help him.

“One thought that this is marvelous, but it is not possible to make progress there,” Bohr said years later, recalling his early efforts. “Just as if you have the wing of a butterfly, then certainly it is very regular with the colors and so on, but nobody thought that one could get the basis of biology from the coloring of the wing of a butterfly.”³

But then Bohr was told of a formula for the frequencies of light in the hydrogen spectrum, devised in 1885 by a Swiss mathematician named Johann Jakob Balmer. Balmer had no idea why his formula worked; he had merely discovered certain numerical tricks by which the frequency of some individual lines in the spectrum could be related to the frequencies of other lines. Balmer’s simple formula provided Bohr with a Eureka Moment.

“As soon as I saw Balmer’s formula,” Bohr remembered, “the whole thing was immediately clear to me.”⁴ Specifically, it became clear to Bohr that he could explain the hydrogen atom by borrowing

the still-young quantum theory, delivered to the world in 1900 by the German physicist Max Planck. Planck, studying the colors of light emitted from a hot cavity (sort of like an oven) concluded that energy gets absorbed or emitted in chunks, which he called quanta. Bohr showed how Planck’s idea could explain the pattern of colors coming from hydrogen. An electron could swallow a quantum of light (or other form of electromagnetic radiation) and jump into a higher, more energetic orbit. At some later time the electron could fall back into the closer, lower-energy orbit, emitting a definite color of light in the process.

Hydrogen’s colors depended on the size of the gaps between different possible orbits. An electron falling from a high orbit to one much lower would give off higher-energy radiation—ultraviolet light or maybe even an X ray. A jump between closer-spaced orbits would emit lower-energy light. Of course, the key to this picture was that only certain orbits are allowed—the electron could not hang out anywhere in between its permitted flight zones. Different atoms permitted different orbits, which was why each atom gave off its own set of colors.

When introduced to Bohr’s quantum atom in Cambridge, Dirac was instantly entranced. “I remember what a surprise it was to me when I first learned about the Bohr theory,” Dirac recalled in a 1975 lecture. “I still remember very well how strongly I was impressed. . . . It is really the most unexpected, the most surprising thing that such a radical departure from the laws of Newton should be successful.”⁵

Bohr’s model succeeded spectacularly in explaining the colors coming from hydrogen. But it didn’t work so well for helium—or for any other atom, either. Somehow the simplicity of the hydrogen atom, with only one electron, made it possible to compute the correct energy levels for the electron orbits using Bohr’s theory. All other atoms contained more than one electron, and Bohr’s theory broke down under the additional load.

“That was the situation,” Dirac recalled, “when I first started research on atomic theory.”

The year was now 1925, and Werner Heisenberg, one of Bohr’s protégés, suffered an attack of hay fever and ventured therefore to a remote island in the North Sea so he could breathe while he worked. Without the distractions of city sounds or airborne allergens, Heisenberg produced some strange looking math that seemed to solve the problem of multiple electrons. He decided to forget about the electron orbits—which couldn’t really be observed anyway—and focus on quantities that could be measured, such as the color (or frequency) differences between “orbits.” He worked out a way to describe frequencies using an array of numbers, called a matrix (although he didn’t know it was called a matrix at the time⁶). With help from his professor at the University of Göttingen, Max Born, and the mathematician Pascual Jordan, Heisenberg’s breakthrough led to the first formulation of the mathematical framework nowadays known as quantum mechanics.

When Dirac received an advance copy of Heisenberg’s first paper, in September 1925, he studied it for a few weeks, and then was struck during a Sunday walk with a mathematical insight, enabling him to reconstruct Heisenberg’s findings a little more elegantly. Soon, in 1926, the Austrian physicist Erwin Schrödinger offered yet another approach, known as wave mechanics, describing the electron orbits as closed waves encircling a nucleus. After a short period of consternation, it became clear to everybody that all these approaches ended up being mathematically equal. Dirac, Schrödinger and Heisenberg, Born and Jordan are generally regarded as the originators of quantum mechanics.

With the breakthroughs of 1925 and 1926, the job was still not done, however. Dirac realized, more so than the other players in the

quantum game, that Einstein’s special relativity theory had to be inserted into the action. Schrödinger had at first attempted to derive a form of his wave equation that incorporated relativity. But when he calculated the results, he found answers that did not agree very well with the best experimental measurements of the day. So he published the nonrelativistic version instead. As it turned out, the experiments had been inaccurate. Schrödinger blew it.

“Schrödinger lacked courage to publish an equation that gave results in disagreement with observation,” Dirac commented later.⁷ But as it turned out, Dirac was soon to exhibit a certain lack of courage as well.

“There was a real difficulty in making the quantum mechanics agree with relativity,” Dirac recalled half a century later. “That difficulty bothered me very much at the time, but it did not seem to bother other physicists, for some reason which I am not very clear about.”⁸

Dirac was, however, not the only physicist to pursue a relativistic description of the electron. Oskar Klein, working at Bohr’s physics institute in Copenhagen, had already produced an equation describing the electron that incorporated the math of Einstein’s relativity. Dirac was not satisfied with Klein’s version, though. “I was worrying over this point for some months,” Dirac reported.⁹ Ultimately, he found a new equation—more in tune with the basic principles of quantum mechanics than Klein’s. Much to Dirac’s amazement, the equation held within it the notion of electron spin, the property at the root of magnetism. Electron spin itself had just been discovered.

On the other hand, the new equation posed a somewhat thorny problem. It permitted electrons to possess negative energy.

Now, negative energy is one of those amazing concepts that make quantum physics so interesting. At first glance, it’s absurd, but on

closer examination, it’s deeply intriguing. How can an electron have negative energy? You would think it either has no energy or some energy, and that less than no energy is nonsense. But think a little more. It is possible to have less than no money, for instance, if you spend too much on credit. You could earn a lot of money yet still not have any, as all your earnings went straight to your creditors. There is certainly something real about being in debt.

And in a not too dissimilar way, there is something real about negative energy.

For Dirac, it was simply a matter of listening to what the math had to say. In this case, the math was speaking in the language of square roots. So if you’ve seen the movie Stand and Deliver, you know basically all you need to know to understand Dirac’s prediction of the existence of antimatter.

In algebra, negative numbers come into play all the time, just as they do sometimes in bank statements. If you subtract a big number from a smaller number, the result is a negative number. If you want to multiply negative numbers, it gets a little more complicated. In Stand and Deliver (1987), math teacher Jaime Escalante, played by Edward James Olmos, drills a basic fact of algebra into his students’ heads by forcing them to repeat, over and over, that “a negative times a negative equals a positive.” So, for instance, a negative 2 times a negative 2 equals a positive 4.

It’s a good thing to know for passing algebra tests, and it also turns out to be important in physics, as Dirac emphasized, especially when dealing with square roots. The square root of a number is simply some other number that, when multiplied by itself, yields the original number: 2 times 2 is 4, so 2 is the square root of 4. But if you have an equation with a square root in it, you must not forget that there are usually two solutions—negative and positive. Sure, 2 is the square root of 4. But so is negative 2, because negative 2 times negative 2 is also equal to 4. A negative times a negative equals a positive.

Now in Dirac’s math, the equation giving the energy of an elec-

tron had a square root in it. (It’s a consequence of applying Einstein’s special theory of relativity, which includes the square of the speed of light in the energy formula.)¹⁰ Dirac saw no escape: electrons could possess either negative or positive energy.

Did that matter? Well, in the old world of Newtonian physics, it wouldn’t have. You could show (or at least Dirac could show) that a particle starting out in life with negative energy could never attain a state of positive energy. And a particle starting out life with positive energy could never slow down so much that it had negative energy—could never go into energy debt, so to speak. So the possibility of negative energy could be safely ignored.

But in the new era of quantum mechanics and Einstein’s relativity, the situation changed significantly. Under the quantum rules, electrons could make quantum jumps; a positive energy electron might jump to a negative state, or vice versa. At least, Dirac reasoned, that possibility should not be ignored, even though all other physicists of the day were in fact ignoring it.

So when Dirac published his paper containing his electron equation (known evermore as the Dirac equation) in 1928, he pointed out the problem with negative energies, suggesting that maybe they had something to do with particles carrying an electric charge opposite the electron’s. He was on the verge of anticipating the existence of antimatter, but hesitated.

At the time, science knew of only two basic particles in nature: protons and electrons. Everybody believed that the atomic nucleus contained both protons and electrons (but always more protons than electrons, so the nucleus would retain a positive charge). It seemed like a very neat way to make the world—two kinds of particles, co-operating to make atoms that could do all the wonderful things that

nature does. So Dirac began to suspect that maybe his electron theory could also explain protons—if you thought of physicists (and all other people) as being something like fish in water.

Presumably (although I’m not sure fish would agree), a fish has no sense of living in an ocean of H₂O. At least a fish would give no more thought to the water around it than people ordinarily do to the atmosphere. In a similar way, Dirac reasoned, scientists would never notice a uniform sea of particles if it engulfed all of us all the time. And that’s just what he thought was going on with the negative-energy electrons.

All particles of matter are ultimately couch potatoes—as lazy as they can be. In physics terms, that means seeking the lowest possible state of energy. Like the rock on top of a mountain that would like to roll downhill, electrons in an atom are always trying to fall to the lowest energy orbit whenever a spot is available.

But why only if an open spot is available? Why don’t all electrons fall all the way to the nucleus, as low an energy as they could get? Because they aren’t allowed to, prohibited by a declaration from the Austrian physicist Wolfgang Pauli. No two electrons could occupy the same energy state, Pauli had determined in the midst of the quantum mechanics revolution. His “exclusion principle” served a valuable guidance role in the efforts to understand the electron.

Applying Pauli’s principle to the problem, Dirac realized that the vacuum of space could be filled up with negative-energy electrons. All the electrons in the universe would have sought negative energy levels to get as low an energy berth as they could find. Sooner or later, all the negative energy states would have been filled up, and Pauli’s principle would have allowed none to enter after that. So the leftover electrons, forced to maintain positive energy, are the ones that scientists observe and that play important roles in daily life. The negative ones make up a smooth undetectable ocean in which people go about daily life unaware.

But even a fish occasionally notices something fishy about its ocean world, as when air bubbles gurgle by. To a fish, a bubble might seem like a small particle traveling through “space.” In other words, the absence of water looks not like nothing, but like something. And so, Dirac reasoned, maybe every once in a while some jolt of energy kicked a negative-energy electron out of its ocean. We would then see a hole in the ocean that would look to us much like a bubble to a fish—a definite particle moving through space.

“Let us assume . . . that all the states of negative energy are occupied except perhaps a few of small velocity,” Dirac wrote in a 1930 paper spelling out these ideas. “We shall have an infinite number of electrons in negative-energy states . . . but if their distribution is exactly uniform we should expect them to be completely unobservable. Only the small departures from exact uniformity, brought about by some of the negative-energy states being unoccupied, can we hope to observe.”¹¹

But what, precisely, would scientists observe? A particle of course, but what kind? Here Dirac was on the verge of prediscovering a new kind of matter, namely “antiparticles.” But, a bit like Schrödinger, Dirac lacked courage. The bubble-particle, he knew, would appear to carry a positive charge, since a gap in a sea of undetected negative charge would be positive by comparison. Dirac, along with every other physicist, knew of only one particle in nature that carried a positive charge—the proton. So he suggested that the holes were protons. But protons were known to weigh nearly 2,000 times as much as an electron. Dirac could not explain how a hole the size of an electron could have a mass 2,000 times greater.

“When I first thought of this idea, it occurred to me that the mass would have to be the same as that of the electron because of the symmetry,” Dirac remembered. “But I did not dare to put forward that idea, because it seemed to me that if this new kind of particle (having the same mass as the electron and an opposite charge) existed, it would certainly have been discovered by the experimenters.”¹²

In other words, Dirac chickened out.

“That, of course, was really quite wrong of me,” he admitted later. “It was just lack of boldness. I should have said in the first place that the ‘hole’ would have to have the same mass as the original electrons.”

Soon the mathematician Hermann Weyl noted this discrepancy and argued that purely on mathematical grounds the mass of the hole would have to be the same as the mass of an electron. And then J. Robert Oppenheimer, later to become the father of the atomic bomb, ripped the proton idea to shreds in a 1930 paper published in The Physical Review.

“There are several grave difficulties which arise when one tries to maintain the suggestion that the protons are gaps of negative energy,” Oppenheimer wrote.¹³ For one thing, there are lots of protons around. If they are really “holes” in an electron sea, positive-energy electrons would constantly be falling into them and thereby disappearing (and the proton would disappear as well). In fact, Oppenheimer calculated, an ordinary electron should encounter a proton and disappear in about one ten-billionth of a second. Whereas in fact, electrons and protons happily coexist for much longer times than that. Therefore, Oppenheimer concluded, there are no holes. All the negative electron locations remain filled.

“Oppenheimer just said that there was some reason, which we do not understand, why the holes are never observed,” Dirac recalled. In other words, Oppenheimer also chickened out.

By this time, though, Dirac was ready to accept the consequences of his own mathematical actions, and he wrote a paper explicitly predicting that the holes would be seen as new particles, positively charged, with precisely the mass of the electron. “A hole, if there were one, would be a new kind of particle, unknown to experimental physics, having the same mass and opposite charge of the electron,” Dirac wrote in his new paper, which appeared in May of 1931.¹⁴

So even though he reached this conclusion rather timidly, Dirac nevertheless foresaw the discovery of an entirely new type of basic

particle of matter. “I think Dirac’s prediction of antiparticles is the most dramatic prediction in the history of science,” the physicist Gordon Kane told me. “Nobody ever predicted new things like that before.”¹⁵

Of course, Dirac had not really answered Oppenheimer’s question: Why had nobody seen these “antielectrons”? Years later, though, Dirac offered an explanation: “The reason why the holes were not observed was simply that the experimental people had not looked for them in the right place, or if they had looked, they had not recognized what they saw.”¹⁶ Experimenters, Dirac proclaimed, “were prejudiced against new particles.”¹⁷

In fact, the experimenters had seen the antielectrons, without realizing it. It was common in those days to use cloud chambers to study the particles known as cosmic rays that assaulted the Earth from outer space. Particles passing through such a chamber leave visible tracks as vapor condenses along the route that the particle takes. Add a magnet, and the path of any electrically charged particle will bend, depending on the particle’s mass and amount of charge. Pictures of the chamber can then be studied to analyze the paths and identify the particles that made them.

Using this technique, Patrick M. S. Blackett, at Cambridge, actually detected some strange cosmic ray particle tracks that turned out to be Dirac’s antielectrons. Dirac even told Blackett that’s what they were. But Blackett remained unconvinced and failed to publish his data. Blackett chickened out, too.

A young American in California, on the other hand, followed the particle tracks where they led.

Carl Anderson, born in 1905 in New York City, headed west as a very young man (he was 7) and grew up in Los Angeles and then

went to college at Caltech in Pasadena (despite the warnings of teachers who told him if he managed to get accepted, he’d probably just flunk out). By 1930, he had earned his Caltech Ph.D.

Anderson wanted to stay on at Caltech as a postdoc, but the school’s president, the famous Robert Millikan, advised otherwise. Having all your degrees from the same school is a good reason to go somewhere else for a while, Millikan said, and he recommended that Anderson apply for a National Research Council fellowship to continue his studies elsewhere. So Anderson made plans to go to the University of Chicago and soon convinced himself that it was much the better opportunity.

His enthusiasm for Chicago at a peak, Anderson was then summoned to Millikan’s office. Millikan had changed his mind. Famous for measuring the electrical charge on the electron, Millikan now wanted to gather good data on the energy of electrons in cosmic rays. He needed a postdoc with Anderson’s expertise. Anderson, now eager to head east, protested. “I used all the arguments that he had previously made as to why I should not stay on at Caltech,” he recalled.¹⁸ But Millikan offered a strong counterargument—Anderson had not yet been granted the National Research Council fellowship, and Millikan was on the fellowship selection committee. Anderson’s chances of getting the fellowship would be a lot better if he stayed another year at Caltech, Millikan mentioned.

So, in a sort of reverse serendipity, Anderson stayed and studied the electrons in cosmic rays. Some of those electrons behaved oddly. Their negative charge should have caused them all to follow a similar curved path in the cloud chamber’s magnetic field. But the photographs showed some particles curving in the opposite direction. “Something new and mysterious must be occurring,” Anderson concluded.

Maybe the particles curving the opposite way were protons— positively charged and therefore expected to curve in paths opposite

to electrons. But further analysis showed that many of the particles were much too light to be protons. Perhaps, Anderson believed, they were electrons traveling upward rather than downward. That would explain the opposite curve. But Millikan didn’t like that explanation, insisting that cosmic ray particles came down from above, not up from below.

So Anderson modified the experiment, putting a thin lead plate in the middle of the chamber to slow the particles down and thereby show whether they were traveling upwards or downwards. (Slower particles have less momentum and therefore resist the pull of the magnetic field less and curve more sharply. A particle track coming in from above the plate would curve more sharply below it.) When he inspected the new photographs, Anderson was doubly surprised. For one of the pictures showed a particle traveling upward—and turning in the direction opposite that of ordinary electrons. Yet its mass was obviously very close to the mass of an electron. It was, Anderson realized, an electron with a positive charge. He called it a “positive electron,” a term he later shortened to positron, and published the report of its discovery in Science on September 9, 1932. It was, in fact, the discovery of Dirac’s antielectron.

Curiously, though, Anderson did not seem very impressed by Dirac’s anticipation of this discovery. In the account of the positron discovery in his autobiography, Anderson doesn’t mention Dirac at all. In a lecture presented for Anderson at a 1980 conference (he was unable to attend himself), he explicitly discounts Dirac’s contribution.

“It has often been stated in the literature that the discovery of the positron was a consequence of its theoretical prediction by Paul A. M. Dirac, but this is not true,” Anderson declared. “The discovery of the positron was wholly accidental. Despite the fact that Dirac’s relativistic theory of the electron was an excellent theory of the positron, and despite the fact that the existence of this theory was

well known to nearly all physicists, including me, it played no part whatsoever in the discovery of the positron.”¹⁹

Frankly, I find this attitude rather strange—if Anderson knew about the antiparticle theory, how could he not have been influenced by it? In any case, the fact remains that Dirac anticipated Anderson’s discovery. By exploring the implications of squiggles on paper, Dirac had deduced the existence of something that nature had been concealing from the inquiring eyes of the observers.

As Dirac soon realized, it makes no sense to say that only electrons have antimatter counterparts. The same mathematical reasoning applies to every other sort of particle as well. So there must be antiprotons, for example, and there are—although they weren’t actually observed until 1955. All the other particles discovered in later years have antiparticles, too (if you count the occasional odd case of certain particles, such as the photon, whose antiparticle is exactly the same as itself).²⁰

Antimatter’s existence provides nature with a nice example of symmetry. To physicists, symmetry is more than pretty wallpaper patterns or kaleidoscopic colors. It’s a deep mathematical expression of constancy in nature. Describing nature with laws, expressed by unchanging math, requires a faith in something that remains constant beneath all the obvious changes in the world. Physicists express that concept in terms of symmetry. Symmetry allows change without change. Convert every particle in nature to its antiparticle, for example, and everything seems to remain the same. All the original laws of physics continue to apply with equal accuracy. Well, almost.

It turns out that keeping everything constant requires more than just giving every particle of antimatter an opposite electrical charge. At first glance, all natural processes would appear to happen in the

same way in an antimatter world. But if you looked closely, you’d notice a subtle difference. Pictures of some processes would appear as though printed with the negative flipped upside down. To make them look like the original real world, you’d have to view them in a mirror.

In other words, when antimatter enters the picture, preserving the symmetries in the laws of physics requires switching left with right—converting the picture into its mirror image. In physicsspeak, that’s called reversing the parity. (Parity is a fancy word for mirror symmetry.)

You might expect—and until the mid-1950s, every physicist would have agreed with your suspicion—that the universe in a mirror would look just like the universe always looks. Left and right would be switched, but the laws of nature would all work in just the same way. A baseball player would have to start running toward third base, then to second, then first, but would arrive back at home plate to score a run in the ordinary way, and otherwise the rules of baseball would stay the same.

In nature, things almost work that way, but not quite. Flipping parity leaves almost everything the same, but only almost. Somehow, the universe seems to know left from right.

Before the 1950s, nobody suspected that nature knew the difference between left and right. “There can be no doubt,” Hermann Weyl once wrote, “that all natural laws are invariant with respect to an interchange of right and left.”²¹ It seemed pretty obvious that the laws of nature applied equally to Lefty Gomez and Bob Feller or Ted Williams and Joe DiMaggio. But in 1956, Chen Ning Yang and Tsung Dao Lee published an insightful paper in The Physical Review pointing out that the evidence for left-right symmetry was weak in cases where the nuclear force was also weak—specifically, in processes whereby subatomic particles disintegrated into other particles.

Soon careful experiments based on Yang and Lee’s suggestions proved that left-right symmetry was indeed violated in weak nuclear interactions, such as the form of radioactivity known as beta decay. In one of those experiments, atoms of a radioactive form of cobalt (known as cobalt-60) were lined up in a magnetic field, so the nucleus of every cobalt atom would be spinning in the same direction. (To keep the nuclei lined up like that, the apparatus must be maintained at extremely low temperatures, close to absolute zero.) When a cobalt-60 nucleus decays, it spits out an electron, or beta particle. To test for conservation of parity, it is necessary to record the direction in which the electrons emerge from the cobalt nuclei (that is, whether they fly off in the same direction as the nuclei are spinning, or in the opposite direction). That trick is accomplished by using two detectors, one positioned to record electrons going one direction, the second placed in the path of electrons going the other direction. Sure enough, when Chien-Shiung Wu and a team of collaborators conducted the experiment at Columbia University late in 1956, they found that one detector recorded more electrons than the other, demonstrating the inequality of left and right in the beta decay of cobalt-60.

Of course, maybe there was just something funny about cobalt-60, and parity violation was not a general feature of weak nuclear interactions. But shortly after the Wu experiment, Leon Lederman and colleagues at Columbia tried another approach, using the subatomic particle known as the muon. Muons are unstable, giving off electrons when they decay, in another example of the weak nuclear interactions at work. Lederman and his collaborators realized that in a beam of muons, the electrons produced by muon decay would emerge more in one direction than the other if parity symmetry is violated. It was a technically challenging experiment, but it succeeded. Early one morning in January 1957, Lederman called Lee on the phone and announced, “Parity is dead.”²²

It’s not overly dramatic to say that the physics world was shocked. “It was socko!” recalled Lederman.²³

Reflecting on the situation, Yang and Lee had pointed out in their paper that there was a way to restore left-right symmetry to nature. Sort of the way Dirac enforced charge symmetry by requiring every known particle to have an oppositely charged antimatter counterpart, Yang and Lee proposed that every right-handed particle might have a left-handed counterpart, and vice versa. In other words, in addition to the antimatter world, there might also exist a mirror world.

“If such asymmetry is indeed found, the question could still be raised whether there could not exist corresponding elementary particles exhibiting opposite asymmetry such that in the broader sense there will still be over-all right-left symmetry,” Yang and Lee wrote.²⁴

For instance, they speculated, “normal” protons might all be from the “right-handed” world. For all we knew, corresponding left-hand world protons might exist as well but merely were exceedingly rare in our corner of the universe. Perhaps both right-handed and left-handed protons might interact with the same electromagnetic field, Yang and Lee suggested. But as other physicists remarked later, maybe the mirror particles did not interact electromagnetically—in which case a universe of mirror-image matter would be invisible. So in a certain sense, the cosmos would have something in common with vampires. In principle, all the basic particles of ordinary matter could have invisible twins in the mirror world, governed by mirror forces, perhaps forming mirror stars, mirror planets, and mirror people.

While such ideas are an offshoot of Yang and Lee’s original suggestion, the math is much more sophisticated now. Strictly on the basis of those squiggles on paper, it now appears that nature does in fact allow a complete set of mirror particles. If the math is right, the only effect of mirror matter on ordinary matter would be via the force of gravity. People made of ordinary matter could neither see,

feel, nor smell mirror matter. A normal-matter object encountering mirror matter would pass right through it.²⁵

Mirror matter is truly one of the most fantastic not-yet-discovered ideas floating around the world of physics today. Yet it’s one that many physicists take seriously. Starting with Yang and Lee’s suspicion, several physicists have speculated about the existence of a mirror world. But like most prediscoveries, mirror matter will be a bigger deal if somebody actually finds it. Unfortunately, it’s not the sort of thing where you can say you’ll know it when you see it, because it can’t be seen. So the possibility exists that mirror matter’s presence has already been detected, but physicists just don’t believe it yet.

I recall some excitement about mirror matter in the 1980s, but I didn’t take it seriously until 1996, when Vic Teplitz told me about a paper he had written with Rabindra Mohapatra, a physicist at the University of Maryland. A year earlier, Mohapatra and a Russian physicist, Zurab Berezhiani of the Georgian Academy of Sciences in Tbilisi, Georgia, invoked mirror matter to explain one of the greatest mysteries in astronomy, having to do with how the sun shines.

Since the 1930s, physicists had understood that nuclear reactions deep in the sun produce the energy that makes it shine so brightly, supplying us with ample heat and light. Those nuclear reactions produce tiny particles called neutrinos (another example of prediscovery to be discussed in Chapter 4). Many neutrinos stream from the sun into space, some passing through the Earth. But scientists count too few neutrinos to account for the fact that the sun shines the way it is supposed to. Mohapatra and Berezhiani proposed that the solar neutrino mystery, and other neutrino oddities as well, could be explained by the existence of a “mirror” neutrino.

Teplitz explained to me that if mirror neutrinos existed, no doubt other mirror particles did also; in fact, the universe could be as full of mirror matter as it is of the matter we can see. Alas, he confessed, the

prospect of parallel mirror civilizations turned out to be quite unlikely. If mirror matter really consisted of identical counterparts to ordinary matter, the opening instants of the universe would have cooked up a different soup of subatomic particles and atoms. (Mirror matter would have affected the expansion rate of the universe, in turn modifying the cooking temperature.)

But perhaps, Teplitz said, a mirror universe might still exist—if the “mirror” is sufficiently distorted, sort of like in a carnival funhouse. Suppose that mirror particles are a little bit heavier than the ordinary particles that physicists are used to playing with. A mirror electron might be 10 to 100 times heavier than the garden variety that people use to send e-mail. Protons and neutrons might be more massive than their nonmirror cousins as well.²⁶

Such an overweight neutron would be unstable, decaying away even if trapped in an atomic nucleus. Thus this version of the mirror world could contain no atoms other than hydrogen, ruling out mirror people. But space could still contain interesting mirror-matter structures, perhaps helping to solve some of the deepest mysteries in the cosmos.

In their March 1996 paper, Teplitz and Mohapatra identified three possibilities: One, globs of mirror matter might have formed in the early universe and are now large and puffy; two, the puffy globs could have cooled rapidly into “cluster” globs containing large chunks of mirror matter; or three, puffy globs cooled slowly to form “black globs,” condensed regions of mirror matter mimicking massive black holes.

It is feasible, Teplitz and Mohapatra calculated, that a million mirror-matter globs originally occupied the Milky Way galaxy and that some of them (say 10,000 or so) escaped into intergalactic space. “Thus one might consider searches for . . . globs both inside the galaxy and outside,” they wrote.²⁷

But how to search for the invisible? One way would be finding distant stars traveling along paths that seem to be deflected by an invisible glob-sized mass. (Such deviations in the path of the planet Uranus were the clues used by astronomers to discover the planet Neptune.) A similar strategy has been used by astronomers to search for those MACHOs wandering about the outer edges of the Milky Way galaxy.²⁸ In their paper, Teplitz and Mohapatra implied that collisions of mirror-matter globs could disperse some bodies into space that might masquerade as MACHOs. But they didn’t pursue the idea at the time (although a paper by Berezhiani discussed the mirror MACHO possibility in a little more detail).

In December 1998, though, Teplitz heard a presentation in Paris by astrophysicist Katherine Freese of the University of Michigan. Her analysis basically ruled out all the ordinary MACHO possibilities. Teplitz then applied Sherlock Holmesian reasoning to the problem—if you eliminate everything else, whatever remains must be the answer, even if it’s something as crazy as mirror matter.

So he and Mohapatra began to calculate away. Assuming a mirror mass distortion factor of 15—in other words, mirror particles with masses 15 times that of their ordinary matter counterparts—the physicists investigated the formation of massive mirror-matter stars and their subsequent explosion, which would leave mirror black holes behind. (Ordinary black holes form when stars much more massive than the sun explode and then collapse under the force of their own gravity.) Because of the mirror mass distortion factor, a mirror black hole would not be heavier than the sun, but lighter, maybe half a sun’s mass or so—just the right mass for MACHOs, the calculations showed.²⁹

“This is for the theorist the same thrill that the biologist gets when the new chemical kills all the germs in the whole damn petri dish, and a lot in the next one over to boot,” Teplitz told me.

This result didn’t exactly prove anything, of course, but it made the possibility of mirror MACHOs more interesting.

More recently, others have proposed even more interesting mirror-matter possibilities. Robert Foot and Ray Volkas, of the University of Melbourne in Australia, have pursued a mirror-matter agenda that differs in key respects from that of Teplitz and Mohapatra. In the Australian version, the mirror particles possess precisely the same mass as their normal counterparts. This idea has the advantage of restoring the original mirror-matter motivation of overall mirror symmetry but assumes some way can be found to elude the problems posed by the element-cooking temperature considerations in the early universe.

In any event, Foot and Volkas don’t stop with mirror MACHOs. They see signs of mirror matter almost everywhere. Foot has gone so far as to suggest that mirror matter has unwittingly been detected already, in the form of mirror planets orbiting distant stars.

By the beginning of 2002, astronomers had spotted telltale signs of more than 70 planets around stars far from the sun. Nobody can see these planets, of course—they’re much too far away for even the Hubble telescope. But the light from a distant star is distorted by the presence of a planet. As it orbits, the planet tugs slightly on its star (because of gravity), pulling the star a little bit away and then a little bit toward Earth. The to and fro motion alternately changes the colors of light reaching Earth-based telescopes. If a planet really is the cause, the color change would follow a regular schedule corresponding to the planet’s orbit; from the regularities in the pattern, astronomers can deduce something about the size of the accompanying planet and its distance from its parent star.

In one paper, Foot argued that nobody could know for sure what those planets are made of. Perhaps even if you hopped into the Starship Enterprise and cruised to the vicinity of such a star, you’d see nothing in orbit at all—if the planet were made of mirror matter.

A similar possibility arose in October 2000, when astronomers reported 18 large planets wandering through space in the constellation Orion without any stars around. It was hard to explain—after all, astronomers believe that planets form in the debris surrounding a star following its birth. No star, no debris. And therefore, presumably, no planets.

“This new kind of isolated giant planet . . . offers a challenge to our understanding of the formation processes of planetary mass objects,” astronomer Maria Rosa Zapatero Osorio and collaborators reported in the journal Science.³⁰

One possible explanation was that the “planets” weren’t planets at all, but fizzled stars known as brown dwarfs. Brown dwarfs are much bigger than planets but not quite big enough to generate the internal pressure needed to burst into starhood. Zapatero Osorio, of the Instituto de Astrofísica de Canarias in Tenerife, Spain, and her colleagues estimated the Orion planets to be 5 to 15 times the mass of Jupiter, and the upper end of that range reaches the lower range for the masses of brown dwarfs. Since it was hard to deduce the mass of the Orion planets more precisely, it’s possible that they belonged in the brown dwarf category.

On the other hand, there’s another possibility. Maybe those orphan planets are orbiting stars, but the stars themselves are invisible— because they’re made of mirror matter.

Foot, Volkas, and another Melbourne physicist, Alexandre Ignatiev, produced a paper proposing that the Orion planets orbit mirror stars. “Because ordinary matter is known to clump into compact objects such as stars and planets, mirror matter will also form compact mirror stars and mirror planets,” the Melbourne researchers wrote.³¹

It’s perfectly possible, they suggested, that ordinary matter might coalesce into a planet around a mirror star. And that would explain why the Orion planets appear to be floating freely. If the Orion plan

ets really orbit mirror stars, the Australians said, it should be possible to detect shifts in the radiation emitted by the planets caused by the gravity of the mirror stars. If such signals are detected, the case for mirror matter as a spectacular example of prediscovery might grow just a bit stronger. Then again, somebody else might come along with a different explanation.

Still, the mirror-matter scenario offers an attractive feature that many physicists find compelling—it is built on the notion of symmetry. And symmetry, physicists agree, is super.