A common misunderstanding about wave-particle duality

‘Particles caught morphing into waves’ was how a recent preprint from researchers in France was widely reported. The timing could not have been better, for this year is the centenary of Louis de Broglie’s remarkable and bold thesis – presented at the Sorbonne in Paris, where some of the team responsible for the new work are based – proposing that matter can behave like waves. De Broglie’s idea was dismissed at first by many of his contemporaries, but was verified three years later when Clinton Davisson and Lester Germer at Bell Laboratories in New York, US, observed diffraction of electrons – an unambiguously wave-like phenomenon – from crystalline nickel. Such waviness became enthroned as a central concept in the newly emergent quantum mechanics under the now famous rubric of ‘wave-particle duality’.

Except… None of this is so simple. The meaning and the significance of wave-particle duality is widely misunderstood, as some of the reporting of the latest work shows. The common perception is that quantum particles really are shape-changers: sometimes little balls of matter, other times smeared-out waves. But physicists have generally been dismissive of that idea. The notion of wave-particle duality was coined by researchers centred around Danish physicist Niels Bohr in Copenhagen, who together devised the so-called Copenhagen interpretation of quantum mechanics that is widely regarded as the ‘orthodox’ view today. But in fact the Copenhagen interpretation was never either consistent or entirely coherent, and wave-particle duality was one of the points of contention among its adherents.

For Bohr’s young colleague Werner Heisenberg, ‘light and matter are single entities and the apparent duality arises in the limitations of our language.’ Richard Feynman agreed: the electron, he said, ‘is like neither’ a wave nor a particle. Even Bohr himself, for whom wave-particle duality validated his concept of ‘complementarity’ – loosely, the necessity of accepting contradictory truths in quantum mechanics – did not say that quantum entities are sometimes waves and sometimes particles. Both, he said, are classical concepts, which are indispensable for interpreting quantum experiments but which say nothing about the ‘reality’ of the quantum world. Some consider that Bohr denied that there is any meaningful ‘quantum reality’ – how things are – at all. (It’s contentious, largely because Bohr’s statements are themselves so vague and inconsistent.)

There is no reason to say that quantum entities are ever really waves

At any rate, historian of science Mara Beller says that wave-particle duality is ‘neither unambiguous nor necessary in theoretical research.’ She’s right: there is no reason to say that quantum entities are ever really waves. Rather, the probabilities of where we will observe them in an experiment can be conveniently determined by the calculus of the Schrödinger equation, proposed in 1926 in response to de Broglie, which is formally analogous to a kind of wave equation. But a wave of what? Not of a physical thing – a density or field – but of a probability. The distribution of these probabilities, when observed over many repeated experiments (or a single experiment with many identical particles), echoes the amplitude distribution of classical waves, showing for example the interference effects of the famous double-slit experiment.

Which brings us to the latest findings, reported by Joris Verstraten and his coworkers.¹ The experiments are rather beautiful. The researchers trap ultracold lithium atoms in an optical lattice: interfering laser beams that create a two-dimensional eggbox array of potential wells, each of which can hold an atom. They image individual atoms by detecting fluorescence from excited atomic states. Confined in a well, an atom’s wavefunction is tightly confined: it looks like a discrete particle.

When the optical lattice is turned off, the atoms are free to wander – and the Schrödinger equation predicts that their wavefunctions spread in all directions. This doesn’t mean that the atoms themselves are smeared out like waves; rather, what spreads is the probability distribution of them being found subsequently in a given location. That is just what the researchers see: they image the atoms’ later positions, and find that the histograms of these positions over many repeated experiments on the same system reveal a distribution that evolves in time just as the Schrödinger equation predicts.

So the atoms themselves are only ever observed in a given experimental run as particles – just as quantum mechanics says they should be. The wavelike behaviour – which is to say, the smeared-out probability distribution – is reconstructed from many particle-like observations. It is in some ways analogous to reconstructing the classical probability distribution of a microscopic particle moving diffusively. We’re not directly seeing ‘matter waves’ as such.

The work thus offers a reminder of what Bohr – for all his inconsistencies – was implying. When we talk about ‘how things are’ in quantum mechanics, we are probably going to end up using classical concepts to describe something they do not fit. Wave-particle duality is not a property of the quantum world, but a flawed classical analogy for it.