Inside the Knotty World of ‘Anyon’s, A New Kind of Quantum Particle
Frank Wilczek writes in Quanta:
Prior to the emergence of quantum mechanics, fundamental physics was marked by a peculiar dualism. On the one hand, we had electric and magnetic fields, governed by Maxwell’s equations. The fields filled all of space and were continuous. On the other hand, we had atoms, governed by Newtonian mechanics. The atoms were spatially limited — indeed, quite small — discrete objects. At the heart of this dualism was the contrast of light and substance, a theme that has fascinated not only scientists but artists and mystics for many centuries.
One of the glories of quantum theory is that it has replaced that dualistic view of matter with a unified one. We learned to make fields from photons, and atoms from electrons (together with other elementary particles). Both photons and electrons are described using the same mathematical structure. They are particles, in the sense that they come in discrete units with definite, reproducible properties. But the new quantum-mechanical sort of “particle” cannot be associated with a definite location in space. Instead, the possible results of measuring its position are given by a probability distribution. And that distribution is given as the square of a space-filling field, its so-called wave function.
Conceptually, quantum particles differ so significantly from their classical ancestors that a different name seems in order. Just as the quantum “qubit” was named by analogy to the classical “bit” of information, I will use the term “quarticle” (pronounced kwort-icle) for a quantum particle. This emphasis on the particle aspect (as opposed to “wavicle”) is appropriate, because in practice quantum physicists usually analyze quantum behavior by visualizing the behavior of particles, and then refining — and, if necessary, correcting — their picture until it works for quarticles.
The quantum unification of light and substance, while satisfying, is limited in scope. For when we go beyond single quarticles to consider the behavior of collections of identical quarticles, a new dualism appears. Indeed, the world of quantum particles divides into two great, mutually exclusive kingdoms. There is the kingdom of bosons, named after Satyendra Bose, and the kingdom of fermions, named after Enrico Fermi. Every species of quarticle is either a boson or fermion.
Interactions among bosons are very different from those of fermions. We call this effect “quantum statistics.” For purposes of orientation, a simple introduction may be in order.
Bosons are conformists. They like to behave in the same way. (More technically: Identical bosons have enhanced probability to occupy the same quantum state.) Photons belong to the kingdom of bosons. A laser beam is the epitome of boson-ness. It consists of many photons of the same wavelength (that is, color) moving in the same direction, the result of “stimulated emission” of photons in an imitative cascade.
Fermions, by contrast, are individualists. They absolutely refuse to occupy the same quantum state, a fact known as the Pauli exclusion principle. Electrons belong to the kingdom of fermions, and this is a key reason why the periodic table exists. Electrons, being negatively charged, are strongly attracted to positively charged atomic nuclei, but they prevent one another from surrounding the nucleus in a simple, efficient way. Instead they build up complex configurations that can support interesting chemistry.
Supersymmetry is a theoretical speculation that — if true — would reconcile the two kingdoms. According to supersymmetry, every elementary quarticle has a mate in the opposite kingdom, its superpartner. The superpartner of a boson is a fermion, and vice versa. Superpartners share the same electric charge and several other properties, but differ in mass and spin.
Supersymmetry is an attractive, logical extension of known physics, and it can be implemented with elegant mathematics. Many physicists, including me, feel that it deserves to be true.
But the last word, naturally, goes to nature. While there is compelling circumstantial evidence for supersymmetry, as yet there is no direct proof. For that, we need to find some superpartners. Searching for superpartners of known particles is a major preoccupation of experimentalists working at the Large Hadron Collider. Sadly, the results so far are negative. Yet there is still considerable potential for discovery, as the machine comes to operate at higher energy and more collisions get analyzed.
Clearly, quantum statistics lies at the foundation of our understanding of nature. Also, as we’ve seen, it raises a profound question about the unity of matter. Addressing that question suggests new possibilities for discovery.
Such an important concept deserves a worthy grounding. What is quantum statistics, at bottom?
The modern answer to that question is deep, beautiful and surprisingly recent. It emerged in the late 1970s, . . .
Good ending. Fascinating column. I get the feeling that the universe is as it is because that is the way it must be if it consists of exploiting every possible quantum niche, as it were. Everything must happen the way it does because all of quantum reality’s possibilities are being utilized (at the quantum level) and that ripples up into our visible world of everyday life—that is, maybe there is indeed no free will, but our lives are spent in filling out our actual possibilities, given everything (including who we are).