Matter vs. Force: Why There Are Exactly Two Types of Particles
Fermions must keep to themselves, while bosons can play together in the same place.
Irene Pérez for Quanta Magazine
Introduction
Beneath the richness of our world lies a pristine simplicity. Everything is made of a set of just 17 fundamental particles, and those particles, though they may differ by mass or charge, come in just two basic types. Each is either a “boson” or a “fermion.”
The physicist Paul Dirac coined both terms in a speech in 1945, naming the two particle kingdoms after physicists who helped elucidate their properties: Satyendra Nath Bose and Enrico Fermi.
In 1924, Bose was working at the University of Dhaka, in what is known today as Bangladesh. Earlier, around 1900, Max Planck had proposed a law for how much light of each color a hot object emits. (Planck’s insight that this light comes in discrete packets, or “quanta,” set physicists on the path to quantum mechanics.) Bose found a stronger mathematical derivation of Planck’s law. He wrote to Albert Einstein, asking for help in submitting the result to a German journal, then collaborated with Einstein to flesh out the idea.
Bose and Einstein’s math described a situation where multiple particles can be perfectly alike: not just have the same charge, mass and energy but even exist in the same place at the same time. Photons, the particles of light, behave this way. A laser, for instance, consists of many photons synchronized at the same wavelength, together in a single beam. We now call such particles bosons.
The same math would turn out to work for more than just photons. Anything we experience as a force is a collective effort of uncountably many bosons. Photons combine to exert the electromagnetic force, while other bosons give rise to the forces that bind the nucleus together and cause radioactive decay. Physicists expect the hypothetical “gravitons” that produce gravity to be bosons as well. And beyond the fundamental forces, certain composite particles — for example, helium atoms — also behave like bosons.
But Bose and Einstein’s math didn’t work for the electron.
Mark Belan/Quanta Magazine
When physicists tried to analyze electrons in metal, they found strange contradictions. For example, there appeared to be an inconsistency between the way electrons carried electric currents and the way they held heat. Working independently in 1926, Fermi and Dirac both figured out what was going wrong: Electrons are not bosons. Unlike photons, identical electrons cannot pile up in the same place. Instead, each electron must differ from its comrades in at least one way: a different location, energy or orientation. We now call such particles fermions. (Another physicist, Pascual Jordan, hit on the same idea a year earlier but didn’t publish in time to share the credit.)
Fermions make the complexity of matter possible. No two electrons can occupy the same place in an atom, so the more electrons an atom has, the more they spread out into distinct layers, giving rise to the different chemical properties of hydrogen, helium, gold, silver and all the other elements of the periodic table.
Beyond electrons, the quarks that make up protons and neutrons in atomic nuclei are also fermions. So are neutrinos. And fermions need not be fundamental particles; in materials, there are groups of electrons that collectively obey the same exclusionary math, like the configurations known as Majorana fermions that might someday power quantum computers.
Satyendra Nath Bose (left) was a little-known physicist at the University of Dhaka when he devised a theory describing collectivist particles that are now named for him — bosons. Enrico Fermi (right) later developed a theory of particles that always maintain their independence, now called fermions.
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The difference between how fermions and bosons behave in groups goes hand in hand with a second distinction between them: their spin, a measure of how they change when rotated. Bosons have whole-number amounts of spin. (Photons have one unit, for instance, and gravitons would have two.) That means that when you turn a boson in a full circle, you’ll find the same particle you started with, with the same mathematical characteristics. Fermions, meanwhile, have half-integer amounts of spin — for example, ½ for electrons. This means that after making one full rotation, an electron does not stay the same. Its mathematical representation acquires a minus sign, and you must turn it around a second time to get it back to the way it was.
These two defining characteristics initially seemed unrelated. But in 1939, Markus Fierz proved that both are consequences of the mathematical structure of quantum theory, a connection now known as the spin-statistics theorem. (His adviser, Wolfgang Pauli, published a spruced-up version of the proof the following year.)
The proof is quite abstract, even for physicists, and it is famously hard to explain intuitively. But the upshot is that if you try to write down equations for a spin-½ particle that follows Bose and Einstein’s math, or a spin-1 particle that obeys Fermi-Dirac statistics, these theorized particles will violate sacred physical principles like causality.
The number of particle kingdoms depends on the number of dimensions. The spin-statistics theorem proves that bosons and fermions are the only two possibilities in our three-dimensional world (unless you rethink what makes two particles identical). This has to do with the fact that in 3D, a particle can turn in a spiral, passing under its old path. Spirals aren’t possible on a 2D surface, where there isn’t a notion of “under.” As a result, new types of particles called anyons can exist in 2D, with behavior falling somewhere between that of bosons and fermions. And in one dimension, the distinction breaks down altogether. In such a world on a wire, bosons and fermions are like two different equations with the same solution: the two kingdoms are secretly one.
