A Brilliant Darkness

To put it simply, the Majorana neutrino is what happens when Dirac’s antiworld meets a shy and left-handed particle. But hiding behind Ettore’s 1937 paper on the neutrino there’s a complex human drama. By comparison, the scoops that haunted Fermi and Salam feel like prepubescent self-aggrandizement. Ettore’s scientific tragedy, in contrast, had nothing to do with vanity. There’s strong evidence that Ettore had finished his neutrino paper as early as 1932 and kept it in the drawer. He did this because the neutrino paper was nothing but a minor appendix to another paper he published in 1932, which he regarded as his real masterpiece. “Relativistic Theory of Elementary Particles with Arbitrary Spin,” reads its title. I must prepare you for what follows. Seventy-five years on, I sometimes have the impression that physics is all wrong—and that the contents of that paper hold the key to our errors.

It’s amazing that Ettore’s 1932 masterpiece reached the public at all, given his history of abandoning his work. That he bothered to publish it suggests he knew his theory was so crazy it might even be true. But he published only in Italian; when he was in Leipzig he mentioned in a letter that he was working on an extension with a view to publishing in German, but he never finished it, or if he did, it was lost (much of his work went missing in strange circumstances). His masterpiece had to wait for a revival in the 1960s. It’s a gem that was quickly forgotten and even today no one knows quite what to make of it. My personal view is that it set up a fork on the road of twentieth-century physics, and we didn’t take Ettore’s path. We may yet live to regret it.

Ettore didn’t like Dirac’s theory. A sea of infinite particles with negative energies being defined as the vacuum? Nah, it sounded bogus. His original motivation in writing his masterpiece was to do away with Dirac’s negative-energy sea and the prediction of antimatter. Ettore examined the root of the problem with a clinical eye, deconstructing Dirac’s elegant mathematics and homing in on the source of the negative energies, and he decided to do something entirely orthogonal. It’s hard to explain without mathematics, but it’s beautiful, even more so than what Dirac had done. Mathematical beauty isn’t easily explained. As Fernando Pessoa stated in a poem: “Newton’s binomial is as beautiful as the Venus of Milo; it’s just that very few people notice it.”

Essentially, he allowed himself to be guided singly by the principle of relativity—that there are no preferred observers in the universe—and didn’t require his equation to describe an electron from the start but to describe anything with spin and consistent with relativity. Only at the end did he require the electron to be an aspect of this “anything.” More mathematically he considered infinite dimensional representations of the Lorentz group. In fact, what Ettore did is a more obvious way to unify relativity and quantum mechanics than Dirac’s theory. I find it a bit surprising that Dirac in 1927 didn’t follow Ettore’s path.

Dirac had been shocked to find two types of particles emerging from his equation: matter and antimatter. Ettore found instead an infinite tower of particles, all described by the same equation, unified into a single quantum-mechanical wave. At low energies they seemingly split into distinct particles (including the electron), unfolding a particle rainbow, each “color” with a different spin and mass. But as with Dirac’s electron and positron, at a deeper level they were in fact the same object showing different faces. The crucial fact that the various particles in Ettore’s tower had different masses (unlike the electron and positron) allowed him to ignore all but one (and to “decouple” the rest, to use the modern terminology). He didn’t need to appeal to a Dirac sea because there were no negative energies or antiparticles in his theory.

Ettore was very proud of his accomplishment. His construction was even more graceful than Dirac’s; by Dirac’s own aesthetical token, it should therefore have been correct. In Leipzig, Ettore continued to polish his masterpiece while he worked on strong nuclear forces with Heisenberg. He referred to it in his official reports sent to Italy and in letters to his father and to his friend Gentile. It’s obvious he valued it more than anything else he’d done. Not many understood it, but he didn’t care. He knew Dirac’s theory was tripe, both theoretically and experimentally. Just to mention one problem, where was Dirac’s so-called antielectron or positron, anyway?

It was while Ettore was in Copenhagen, in March 1933, that news started to trickle in that the positron had been discovered by American physicist Carl Anderson. Examining cosmic rays in a cloud chamber subject to a magnetic field, Anderson had seen the telltale curling track of a particle with a mass and charge like the electron, but bending in the opposite direction, implying that it carried a charge with the opposite sign. At first Anderson couldn’t believe his eyes. Then he let out a sigh of relief. Of course his prank-loving friends had just reversed the polarity of his magnets. The idiots! But when he saw that no one had tampered with the magnets, it gradually dawned on him that he’d discovered something new. A bit shaken, Anderson eventually published a cautious note titled “The Apparent Existence of Easily Deflectable Positives.” Only much later did he make the connection with Dirac’s positron.⁴²

No one believed Anderson’s results. Pauli, who, like Ettore, hated Dirac’s theory, poured scorn all over Anderson. Even Dirac, who had a vested interest in these findings, was skeptical. Niels Bohr went as far as to suggest that Anderson’s anomalous tracks were caused by air currents in the cloud chamber. “Here everyone has taken it for a formidable equivoque,” Ettore reported sarcastically in a letter from Copenhagen. “The positive electrons are nothing but normal electrons [moving in the opposite direction]. This is also Rutherford’s opinion.”

All this cheerfulness on the matter dissipated after the Easter break. In England, Patrick Blackett and Giuseppe Occhialini independently confirmed Anderson’s discovery. Pauli was so incensed by this little twist of nature that he went on holiday to southern France, so he wouldn’t have to hear news of the confirmation of the positron. But the evidence in favor of the positron kept mounting, and even Heisenberg began working on Dirac’s theory. “Season’s news,” Ettore wrote in a letter, “credence is being given to Dirac’s theory of the positive electrons. Heisenberg is working on it seriously.” Ettore then makes fun of the prediction of creation and annihilation of pairs of matter and antimatter particles in Dirac’s theory, but the joke falls flat. Soon afterwards Occhialini and Blackett observed precisely these outlandish creations and annihilations. Dirac was right; and by the most linear extension, Ettore’s theory was dead.

Ettore lost heart. I don’t know why: He’d only proposed a theoretical idea that wasn’t upheld by nature. So what? That’s science. Better to have a good idea than a bad one or none at all, even if nature doesn’t choose our idea. But he took it very personally; some suggest that this was the trigger for his 1933 fall into depression.

I’m not sure how Dirac would have reacted if the positron had never been found and instead Ettore’s infinite tower had been discovered in cosmic rays. He probably would have fared better than Ettore: Even with all of Dirac’s emotional scars, Ettore’s mind was on much shakier ground. But seventy-five years later, the story is far from finished. Ettore’s 1932 paper is a box of surprises, quite apart from the fact that it led to an amazing prediction about the neutrino. As Dirac himself put it, “The opposite of a correct statement is a false statement; but the opposite of a profound truth may well be another profound truth.” Ettore’s and Dirac’s mathematical constructions are so beautiful that being opposites doesn’t preclude them from being complementary, and possibly both true.

The problem with Ettore’s paper is that it was too far ahead of its time. I have a sneaking suspicion that it may be the most lasting contribution he left us. Ettore’s theory is a gem in unification. And we badly need it.

Current particle physics is built upon the so-called standard model, which is a glorious mess. Twelve fundamental particles make up matter, another four carry forces and mediate interactions between things, one “auxiliary” particle is thrown in for good measure, and this still neglects gravity (see Figure 13.1). The electron and neutrino have been joined by two more families of similar but more massive particles, the muon and the tauon, plus their corresponding neutrinos, the whole lot called leptons. The proton and neutron are no longer fundamental, but are instead known to be made up of two types of “quark” (the up and down quarks.) As if this weren’t enough, four more quarks have been discovered (the charm, strange, top, and bottom quarks). Fermi’s weak force is known to be carried by the W and Z bosons, while light and electromagnetic interactions are transmitted by photons. Ettore and Heisenberg’s strong force is mediated by gluons. We need the Higgs particle to give mass to particles, if appropriate.

A hell of a zoo of building blocks for the world! (To think that the Greeks were happy with earth, air, water, and fire.) Anderson may have received the Nobel Prize for discovering the positron, but nowadays the view is that the finder of a new elementary particle ought to be punished by a $10,000 fine. And if you consider all the “free parameters” that have to be dialed to exactly the right values for the model to agree with the data, then between masses, interaction strengths, mixing angles, and so on, you have almost thirty independent numbers. All thrown into the theory by hand, as input, without a glimmer of justification.

So far, attempts to improve the overcomplicated state of particle physics have focused on unifying forces; i.e., turning the many particles mediating interactions into a single unifying force particle. For example, Fermi’s weak force, electricity, and magnetism now fall under the single umbrella of the “electroweak model,” discovered by Salam, Steve Weinberg, and Sheldon Glashow. Some voice hopes that the strong force (or even gravity) may join the “interactions” party. All very well, but this still leaves us with a ridiculous proliferation of fundamental particles that don’t carry forces: quarks, leptons and the Higgs: the forgotten side of unification. To my mind, this signifies one of two things. Either these particles are composites—little “molecules” composed of smaller and simpler constituents we haven’t yet discovered; or we should seriously revisit Ettore’s 1932 theory.

The underlying idea is easy to grasp: No one ever counts electrons and positrons in Dirac’s theory as two different types of particle. They’re just two different states of the same particle, much like spin up and spin down for a spin half particle. A single quantum wave describes the doublet: They’re different “entries” of the same object. By analogy Ettore’s construction throws us a lifeline in unifying the whole wild menagerie of particles we insist on calling fundamental. Perhaps they are really manifold expressions of the same fundamental object, just like the electron and the positron. The different states in Ettore’s infinite tower have different masses and spins, and these don’t match experiment. His symphony is unfinished. But an adaptation of Ettore’s 1932 idea just might provide the ultimate unification.

After his 1933 descent into depression, Ettore was quoted by Amaldi as saying, “Physics is on the wrong road, we’re all on the wrong road.” This quote has made its way into Italian comics, with references to atomic weapons and visions of Armageddon. But it could just as well be applied to the state of modern physics. We had a choice in 1932, and we took Dirac’s path, when in fact we never actually needed to choose one path exclusively (it’s possible to fold antiparticles into Ettore’s scheme). We got ourselves into a terrible muddle and are now appealing to string theory, supersymmetry, and other complex constructions containing infinite towers of particles that don’t fit the observed world any better than Ettore’s infinite dimensional wave function. Ettore, with a simpler approach, in a sense had already achieved as much as string theory—it’s ironic that what excites some people so much nowadays is no better than what for Ettore seemed an utter failure. But why not go back to where he left off and adapt his construction to clear up the chaos pervading our cherished “standard model”?

“In all probability Majorana knew exactly what had happened . . . and had guessed the destructive potential of the discovery. . . .” Ettore’s speech balloon: “Physics is on the wrong road . . . we are all on the wrong road . . .”

Late at night, I often have a lingering feeling that a variation on Ettore’s theory may provide the essential clue. It could unify in a single particle what then unfolds into the fundamental-particle avalanche we’re struggling with. But his 1932 masterpiece is not only unfinished: It has largely been forgotten. As for its appendix, left to gather dust in his drawer for almost five years, that certainly can’t be ignored. I know I advocated a Nobel Prize for Ettore based on the Majorana neutrino, but this work was insignificant in comparison to the majestic views he unveiled in 1932. The Majorana neutrino was a mere sidekick to a forgotten, ill-understood masterpiece: Majorana’s unfinished symphony.

It’s always tough to be disproved, but was this the only cause of Ettore’s sudden collapse in 1933? One certainly cannot discount the effects of the main undercurrent to all the waves in these stormy seas: the specter of the burnt baby—the leitmotif of his tragedy. It was a curse that had been continuously hacking at his soul for almost a decade, sapping precious stability and coherence, year after year wearing away the remainder of his certainties. The charred-baby blight changed Ettore’s worldview forever, and had a similar effect upon his brother Salvatore. Neither was ever the same again. And when its troubles finally relented, in the months just before his visit to Leipzig, it may well have been too late for Ettore to feel any relief. Permanent soul damage had been sustained.