Identity physics

Of all features of the quantum realm, the forms that particles take are surely among the most bizarre. There are only two possibilities: identical objects that can mash together (bosons), and identical objects that cannot (fermions). Bosons obey a mathematics called Bose–Einstein statistics, while fermions follow Fermi–Dirac statistics. These two possibilities were found independently in 1924–1925 with Satyendra Nath Bose and Albert Einstein discovering the properties of bosons, and Wolfgang Pauli’s exclusion principle articulating the basic behaviour of fermions.

In 1926 Paul Dirac synthesized these possibilities in a mathematical framework. Crudely, if you exchange two identical objects and the “phase factor” of the wave function is the same, or “symmetric”, the objects can occupy the same quantum state and physical position and are bosons. (A group of bosons falling into the lowest possible energy state creates a Bose–Einstein condensate.) If the phase factor is negative, or “antisymmetric”, the objects cannot occupy the same position and are fermions.

The mathematics of the quantum world restricts objects to these two possibilities, which means that bosons and fermions play vastly different roles in the quantum realm. Bosons serve as force-carrying particles – photons, for example, are particles corresponding to electromagnetic forces. As for fermions, Pauli’s exclusion principle and the uncertainty principle regulate the atom’s energy levels, which determine the chemical properties of elements and the structure of matter.

Bosons and fermions are familiar to physicists. But writing in the journal Philosophy of Science in 1944 – the year before Pauli won the Nobel prize – the physicist and philosopher of science Henry Margenau said it was “strange” that there was “so little discussion of the exclusion principle in the philosophical literature”. He could have added that there was scant presence of it – or of Bose–Einstein condensation – in popular culture either.

Popular culture often exploits quantum weirdness, finding such terms as quantum leap, complementarity, superposition and parallel worlds packed with creative force. US President Barack Obama has even invoked Heisenberg’s uncertainty principle to explain his occasional reluctance to confront advisers directly about their opinions, while his recent opponent – former governor Mitt Romney – was satirically labelled a “quantum politician” for the way he articulated randomly fluctuating views, held superposed positions and asserted complementary statements on subjects depending on the context.

Yet the Pauli principle and Bose–Einstein condensation are all but absent from popular culture. Identity is the quantum shoe that hasn’t dropped.

But why not?

Tag-ability

Classical mechanics depends on the distinguishability of even primal bits of matter. In other words, you could, if you wanted, put tags on things and follow them around. Sure, atoms and molecules of the same type were thought to be identical, but each one was in principle “tag-able”. Those scientists, such as James Clerk Maxwell, who stopped to ponder the marvel of a universe full of identical yet distinguishable objects, had no explanation. Some cosmic factory had produced perfect duplicates of atoms, and all Maxwell could figure was that God was somehow responsible.

But one hint that something might be amiss came with a puzzle uncovered in the late 19th century by the American scientist Josiah Willard Gibbs. He imagined two adjacent boxes containing equal amounts of a gas at the same temperature. What happens, he asked, if a partition between the two boxes were removed? The molecules mix, of course. Indeed, if you label each molecule by a different number – even numbers, say, for molecules from the first box and odd numbers for molecules from the second – the evens and odds start together and eventually mix uniformly.

As an irreversible process, this should – according to classical physics – increase entropy. But because the entropy actually stays the same, the molecules must therefore be indistinguishable. In other words, they are different from all macroscopic objects. But until the appearance of the quantum – which early on was recognized to imply indistinguishability – nobody knew what to make of this puzzle.

The critical point

Both versions of quantum identity are bizarre. On the macroscopic level, fermion identity is like fraternal but non-identical twins being able to co-inhabit a space. Boson identity is like that old vaudeville gag of a crowd of people emerging from a small space like a phone booth – except that an infinite number of people could do so.

Given our cultural obsession with cloning and identity, why has popular culture, which celebrates the bizarre, not noticed quantum identity? Why isn’t it on T-shirts or coffee mugs, or mentioned in TV shows that appeal to geeks?

It is true that the exclusion principle seems almost commonsensical – a quantum extension of the classical reality that no two things can be in the same place at the same time; it may seem, that is, simply like saying that you cannot do on the microscopic scale what you cannot do on the macroscopic scale. Yet this misses the weirdness that what cannot be in the same place at the same time is something identical.

There must be more to it. Non-scientists often apply scientific language to experiences for which ordinary words are inadequate. So does the absence of quantum identity in popular culture signify our satisfaction with our present language of identity? Or have our imaginations shrivelled? More positively, what kinds of experiences do we humans have that might cry out for metaphors involving quantum identity?

Here, then, is a challenge for readers. Can you devise a situation drawn from the everyday world in which the phrases “quantum identity”, “Pauli exclusion”, Bose–Einstein behaviour”, or some variant of those phrases, would be poetic, enlightening or simply meaningful? I will write about responses in a future column.