# 4

The antielectron as a hypothetical elementary particle first appeared in Dirac’s paper in 1931, which also contained the first proposal of the antiproton. Yet the paper—Gamow once called it the last important paper in theoretical physics—was about something else. It introduced yet another hypothetical particle, no less strange than the antielectron. The particle is called a magnetic monopole and its fate in the history of modern physics is entirely different from that of the antielectron. To this day, the magnetic monopole—or just the monopole—remains merely an idea.

Consider a bar magnet consisting of a north pole at one end and a south pole at the other. If you cut it into two parts, you will not end up with two isolated poles but with just two smaller magnets, or “dipoles,” each with a north and a south pole. You may go on forever without isolating a magnetic pole. It is an empirical fact that while positive and negative electrical charges exist in nature, there are no corresponding magnetic charges or poles. The absence of magnetic monopoles is encoded in the fundamental Maxwell equations, which otherwise exhibit a nice symmetry between electricity and magnetism.

The Maxwell equations forbid monopoles, but only because the lack of monopoles in nature is built into the equations. One can easily modify the equations to accommodate monopoles, should such a particle be found.

In the absence of empirical evidence, the possible existence of monopoles attracted little attention in classical physics. In a few cases, physicists believed to have discovered phenomena that revealed the existence of the magnetic poles, but it quickly turned out that the claims were unfounded. When quantum mechanics arrived, it became even more difficult to believe in these hypothetical entities. The reason is that the quantum theory of the electromagnetic field relies on quantities that effectively rule out monopoles. In a nutshell, magnetic monopoles are inconsistent with quantum electrodynamics. Given this situation, it is understandable that monopoles were simply not an issue in the new physics—until 1931.

Why would Dirac reconsider something, which all quantum physicists knew did not and could not exist? The answer is that he did not, but he came to the idea in the same roundabout way that characterized some of his other discoveries. The monopole was yet another example of serendipity, as Dirac later explained: “It often happens in scientific research that when one is looking for one thing, one is led to discover something that one wasn’t expecting. This is what happened to me with the monopole concept. I was not searching for anything like monopoles at the time.” The “thing” he was looking for in 1931 was, as he stated at the beginning of the paper, “the reason for the existence of a smallest electric charge.”

Free electrical charges always appear as multiples of the smallest charge, called the elementary charge and denoted *e*. Whatever charge *Q* is, it always can be written as *Q* = *ne*, where *n* is a whole number. For example, for an electron *n* = − 1 and for a calcium ion *n* = + 2. The quantization of charge had been experimentally established in the 1910s and was doubted by no one. But *why* is charge quantized and *why* is the smallest charge *e* rather than something else? These were the questions that Dirac ambitiously addressed. If he could derive *e* from a fundamental theory, he would also have derived the strength of the electromagnetic force as given by the so-called fine-structure constant usually assigned the symbol α. This constant, as famous as it is enigmatic, is also the quantity determining the details of the hydrogen spectrum, as Dirac had explained it in his electron theory of 1928. It is a dimensionless number with the approximate value 1/137 or about 0.0073. Again, why this value? Dirac wanted to find out, and physicists today still want to know. The value of α is known with great precision, but, as Richard Feynman put it, “It’s one of the *greatest* damn mysteries of physics: a *magic number* that comes to us with no understanding by man.”

Dirac was forced to admit that he could not solve the problem he had initially addressed. His efforts were not wasted, though, for while pondering the problem he reached the surprising conclusion that magnetic monopoles were *not* ruled out by either electrodynamics or quantum mechanics.

In a lengthy introduction to his 1931 paper, Dirac reflected on the relationship between physics and mathematics, a subject he would return to on later occasions. In a general sense, he suggested that the inductive method starting with experimental data was unlikely to lead to progress in modern theoretical physics. Relativity theory relied on abstract mathematical ideas such as non-Euclidean geometry and quantum mechanics on no less abstract mathematics, like non-commuting algebra. Dirac advocated a deductive method based on mathematics, namely, “to employ all the resources of pure mathematics in attempts to perfect and generalise the mathematical formalism that forms the existing basis of theoretical physics, and *after* each success in this direction, to try to interpret the new mathematical features in terms of physical entities.” This was the method underlying Dirac’s own theory of holes—“a small step according to this general scheme of advance”—and now he used the same method to reconsider the magnetic monopole problem.

Dirac’s approach was complex, relying on a careful analysis of the mathematical structure of the wave function ψ appearing in quantum mechanics. He essentially demonstrated that without changing the basic structure it was possible to “perfect and generalise” the wave function in such a way that monopoles were possible objects, that is, consistent with quantum mechanics. A few pages of dense calculations were enough to prove that quantum mechanics under certain conditions could be brought to accommodate monopoles. The strength *G *of the magnetic poles turned out to be quantized in the same sense as the strength *Q* of electrical charges. As there exists a smallest electrical charge *e*, so there must exist a smallest magnetic charge *g*, the two being inversely proportional (*eg* = constant). To Dirac’s dismay, he was unable to calculate either *e* or *g* separately from pure theory, which he found to be “rather disappointing.”

Nevertheless, Dirac demonstrated that the hitherto inexplicable quantization of electricity would be explained *if *monopoles existed. From the *e*–*g* relationship he had derived between electricity and magnetism, it followed that a north pole and a south pole would form a strongly bound system, kept together much more strongly than a positive and negative elementary charge. It would, therefore, take a very large energy to break up an elementary dipole made up of monopoles. More precisely, two elementary poles of opposite sign will attract one another with a force nearly 5,000 times greater than that between two elementary charges at the same distance. This consequence of his theory was featured a year later in the *Faust* parody at Bohr’s Copenhagen Institute:

Two monopoles worshiped each other,

And all of their sentiments clicked.

Still, neither could get to his brother,

Dirac was so fearfully strict!

It is one thing to prove theoretically that an object is allowed according to fundamental physics, but quite another to claim that the object actually exists in either nature or laboratory. Dirac believed that his antielectrons and monopoles really existed. Referring to the consistency with quantum mechanics, he concluded, “Under these circumstances one would be surprised if Nature had not made use of it.” But if magnetic monopoles existed out there, why had they not been observed? One reason, Dirac suggested, might have been the strong coupling between two opposite poles.

“Lonely magnetic poles may change ideas of the universe,” *Science News Letter* reported on April 16, 1932, adding that scientists could use the new particles in “postulating how the universe is put together.” However, no revolution in our world picture occurred, and interest in Dirac’s theory soon waned. Although well known to the physics community, Dirac’s theory attracted relatively little attention and even less acceptance. Pauli found the theory to be satisfactory from a logical and mathematical point of view, yet he was skeptical about the actual existence of monopoles. In a 1949 letter, he sarcastically referred to Dirac as “Monopoleon.”

The main reason for the lukewarm response was that the monopole was not very useful. It was allowed according to theory, but not required to solve any of the problems with which the physicists struggled at the time. In short, it appeared to be superfluous. And then, of course, it was unsupported by experimental evidence. All in all, there were good reasons why the monopole did not cause excitement among the physicists. When the Nobel Committee evaluated Dirac as a candidate, it expressed a view probably shared by many physicists. The 1931 monopole paper, the Committee opined, was “strongly speculative but of pretty much interest to those who are not afraid of speculation.”

The only physicist of repute who was sympathetic to and seriously interested in Dirac’s theory was his colleague and sometime rival Pascual Jordan, who greatly admired Dirac’s approach to physics. In a 1938 paper, he carefully investigated the new theory, suggesting that magnetic poles might be more than just mathematical constructs. In 1931, the accepted number of elementary particles was just two (electron and proton), but since then the number had increased considerably. Not only had the neutron, and the positron been discovered, the neutrino and the muon (then called a “mesotron”) had also won acceptance, and physicists expected to find even more particles. In this situation, Jordan pointed out, “one would now rather be inclined to regard the Dirac pole as a possibility worthy of serious investigation.”

One might expect that Dirac himself promoted the magnetic monopole, his brainchild, but this was not the case at all. He apparently lost interest in his theory, to which he only returned 17 years later. In a 1948 paper, Dirac revised and greatly improved the theoretical foundation of monopole physics, now basing it closely on the more advanced framework of quantum electrodynamics. The paper was mathematically impressive and theoretically innovative, the kind that was hardly understandable to the average physicist. But it did not provide much new physical insight. Nor did it succeed in explaining the quantization of electricity and magnetism from first principles, which had been Dirac’s original motivation. He did, however, calculate how a monopole would interact with matter—for example, when it passed a photographic plate. Ordinary charged particles leave an ionization track that broadens as the particles slow down, but, Dirac argued, a monopole would behave quite differently. If caught in a plate, its track would remain roughly constant. In this way, Dirac indicated a method of potential use for future monopole hunters.

At the time of Dirac’s 1948 paper, there had been only a few searches for magnetic poles, none of which was even remotely successful. It took another two decades until experimentalists got seriously interested and devised methods to catch the elusive particle, if it existed at all. With improvements in high-energy technology and the proliferation of new elementary particles, the magnetic monopole was no longer considered to be beyond experimental discovery. It was an exotic particle, but scarcely more exotic than other hypothetical particles in the zoo of high-energy physics. The monopole was now raised to the status of a “well-known missing particle,” a respectable object to hunt by the fast-growing community of high-energy experimentalists.

In 1975, a team of American physicists announced that they had discovered in balloon-born experiments a cosmic-rays particle with the properties that Dirac had predicted. The announcement attracted much media interest, including a suggestion in the *New York Times* that the discovery would most likely lead to “new medical therapies in the fight against diseases such as cancer, and new sources of energy.” Alas, the much-publicized claim turned out to be unfounded and after some controversy, it was retracted.

History repeated itself seven years later when Blas Cabrera, an experienced physicist at Stanford University, detected a signal with the telltale characteristics of a Dirac monopole. It was measured on February 14, 1982, and is therefore known in physicists’ lore as the Valentine’s day event. A year later, Cabrera received a Valentine card from a group of Harvard physicists headed by Sheldon Glashow, a particle theorist and Nobel laureate of 1979. It said:

Roses are red, violets are blue.

The time has come for monopole two.

No monopole number two ever passed through Cabrera’s or someone else’s detector. A single event was not enough to change the status of the monopole from being a well-known missing particle to one really existing.

It is ironic that monopole physics only began to flourish after the death of its originator. During the last couple of decades, hundreds of papers have been written on the subject, some of them theoretical and others experimental. Many still refer to Dirac’s old papers, which until the present have received a total of nearly 5,000 citations in scientific journals. However, the monopoles, which have attracted the most interest in modern physics, are not quite the same as Dirac’s.

In the mid-1970s, it was shown that early versions of the so-called grand unified theory predicted a new kind of monopole that complied with Dirac’s quantization rule *eg* = constant. But the GUMs (Grand Unified Monopoles) are exceedingly massive, and rather than being point-like in the way that the Dirac monopoles were, they are endowed with a complex inner structure. Much of the present interest in GUMs and monopoles, in general, is cosmologically motivated. The reason is that according to some models, these magnetic particles were produced in copious amounts at the birth of the universe. Based on grand unified theory, it was estimated that the number of primordial monopoles was enormous, even if annihilation with anti-monopoles was taken into account (strangely, Dirac never mentioned the anti-monopole). But then, what happened to all these particles? Why has a monopole never been seen?

While trying to answer this question in 1979, Alan Guth, a 31-year-old particle physicist at Cornell University, came up with the idea of the inflating universe. This hypothesis suggested that in an exceedingly brief span of time after the Big Bang, the universe expanded at a phenomenal rate. According to Guth, the monopoles did not disappear, but because of the extreme dilution following the inflation, they became so rare that it is unlikely that we should ever be able to meet one. The inflation theory, in one of its many versions, is today widely accepted, even if still considered controversial by some cosmologists.

So, does the particle first proposed by Dirac more than 80 years ago exist or not? We don’t know. Dirac himself eventually lost faith in the particle he had so boldly invented. His last comment on the subject was in a letter from 1981: “I am inclined now to believe that monopoles do not exist.”