What the hell is quantum mechanics?

In 1965, the American physicist Richard Feynman shared the Nobel prize in physics for his work on “quantum electrodynamics”, a field in which the theory of quantum mechanics is used to understand how light and matter interact. Yet in the same year, Feynman said that “I think I can safely say that nobody understands quantum mechanics”.

Quantum mechanics is the theory that describes the behaviour of matter and light at the smallest scale, and has a reputation for deep complexity. But it’s not the maths that’s the problem. Feynman could do that just fine. The trouble was, that was all he could do. What he couldn’t understand was what the maths means: what it tells us about the nature of the world.

It seems there is still no agreement about that. Quantum mechanics itself is 100 years old this year, and to mark the centenary, the science journal Nature conducted a survey to probe what physicists today believe about the theory. The conclusion? “Physicists disagree wildly on what quantum mechanics says about reality.”

But even if there is still no consensus, we can do better now than Feynman’s admission of bafflement – of defeat, some might say. We don’t have all the answers to what quantum mechanics means, but we do have better questions, and a clearer sense of what matters most in this perplexing theory.

Quantum theory itself began earlier than 1925. It was launched in 1900 when the German physicist Max Planck found he could explain how warm bodies radiate heat by assuming that the energy of their vibrating atoms could only change in steps, like the rungs of a ladder, rather than smoothly and continuously. Planck called these discrete little packets of energy quanta.

Planck was just using quanta as a mathematical trick in his equations, not positing them as a feature of nature itself. But five years later, Albert Einstein suggested that this is indeed what they are. He said that we should regard light itself as little packets of energy, each having an amount of energy proportional to the frequency of the light waves.

Then in 1912 the Danish physicist Niels Bohr showed that Einstein’s idea could be used to explain why atoms emit and absorb light only at particular frequencies. Bohr said that these frequencies correspond to the energy change of electrons in the atoms as they hop between different quantum energy states.

But this early quantum theory was a makeshift, contradictory mix of old classical physics and new quantum ideas. What scientists wanted was a clear and consistent mathematical theory for calculating quantum properties: a genuine quantum mechanics.

Bohr gathered together a team of young physicists at his institute in Copenhagen to try to come up with such a theory. One of them was Werner Heisenberg.

In the summer of 1925, Heisenberg took a trip to the little island of Heligoland, off the German coast in the North Sea. Heisenberg was suffering from terrible hay fever at that time, and the sparsely vegetated island was reputed to offer respite from that condition. While he was there, Heisenberg made the breakthrough that allowed him and his colleagues Max Born and Pascual Jordan to work out a complete theory of quantum mechanics.

I went to Heligoland this June to take part in a centenary conference that brought together the leading experts in quantum mechanics. There we watched Nobel laureates flatly contradict one another about the best way to understand the theory. Here is what those arguments are about.

Normally the interpretation of a scientific theory is pretty obvious. Newtonian mechanics – the old classical mechanics that works for everyday objects – tells us about how things like tennis balls and spaceships move: what paths they take as forces act on them. We don’t have to ask, “What do you mean by object?” “What do you mean by path?”

That’s not so for quantum mechanics. To predict what a quantum object will do, in place of Newton’s equations of motion scientists generally use the equation devised by Erwin Schrödinger in late 1925 to describe the idea that quantum particles might act as waves.

Unlike Newton’s equations of motion, the Schrödinger equation doesn’t give us a trajectory for the quantum particle. Instead it uses something called a wavefunction. The wavefunction can be used to figure out where we might find a quantum object like an electron, say. Typically a particle’s wavefunction is spread out in space, rather like an ocean wave.

It’s often said that this means the particle too is smeared out over space. But that’s not right. The wavefunction tells us the chance that we might find the particle at each point in space if we look.

This is what is so odd about quantum mechanics. Compared to other scientific theories it seems to point in the wrong direction, not down towards the thing we’re studying, but up towards our experience of it. It says nothing – perhaps we should say, nothing obvious – about what the quantum system is “like”. In other words, the wavefunction is not a description of the quantum object. It is a prescription for what to expect when we make measurements on that object.

But it’s even more peculiar than this, because the wavefunction doesn’t tell us where the particle is likely to be at any instant, which we can then verify by making measurements. Rather, the wavefunction tells us nothing about where the particle is until we make a measurement. Strictly speaking, we shouldn’t really talk about the particle at all except in terms of the measurements we make of it.

Suggested Reading

2026: the year of the American basketcase

Philip Ball

In other words, in quantum mechanics it looks as though measurements or observations don’t reveal reality but in a sense produce it. One way of speaking about that is to say that before the measurement, a wavefunction is typically a broad, spread-out thing. But when we make a measurement and find the particle to be in a particular place, then the wavefunction switches suddenly to being a sharp spike at one place.

This is generally called collapse of the wavefunction. We have to be careful about what it means. What it doesn’t mean is that the particle itself goes from being smeared out to being sharply defined when we made a measurement on it. All we can say is that, before the measurement, there were different probabilities that a measurement would reveal it in different places, whereas after the measurement we can say for sure that it is here. Our knowledge has changed. This account of quantum mechanics is known as the Copenhagen interpretation, which remains (judging from the Nature poll) the most popular interpretation among physicists today.

Other physicists prefer the Many Worlds interpretation, in which there is no collapse of the wavefunction, but rather, a splitting of the entire universe into parallel, mutually inaccessible worlds whenever a definite classical outcome of a quantum event is manifested. But many physicists find this rather extravagant. The challenge, as yet unmet, is to find an experimental way to distinguish between such alternative interpretations.

The idea that some quantum property was not just unknown in practice but unknowable in principle before we look at it was unpalatable for Schrödinger and Einstein. It seemed to them to contravene common sense. In 1935 Schrödinger sought to illustrate the illogicality of this supposition with his famous thought experiment in which a quantum event could, depending on how it came out, either kill a cat or not. Schrödinger argued that Bohr and his fellow Copenhagenists were saying that, unless we actually made a measurement on the cat – unless we looked at it – it could be simultaneously both alive and dead, which seemed nonsensical.

But the Copenhagen interpretation doesn’t say the cat is both alive and dead before you open the box to look. It says that when we open the box, we might find the cat either alive or dead. It is silent about the state of affairs before that.

Einstein’s response came in 1935, when he and two junior colleagues, Boris Podolsky and Nathan Rosen, came up with a different thought experiment which they argued proved that quantum mechanics as it then stood had to be an incomplete description of reality.

In the version of this “EPR” experiment usually considered today, two quantum particles are fired out from a source in opposite directions. They have some property with only two possible states when measured – let’s call them 0 and 1. The crucial point is that the way these particles are produced makes these properties correlated, so that if one is in state 1, the other must be in state 0. We can’t specify which is which at the outset, but we know for sure that they are correlated. So then if we measure one particle and find it is a 1, we know the other must be a 0. Schrödinger named this quantum correlation entanglement.

Crucially, according to the Copenhagen interpretation the states of these entangled particles aren’t determined until we actually observe one of them. If that’s so, the EPR experiment seemed to be saying that making a measurement on one particle instantly fixes the state of the other, as if some communication is passing between them. This is an example of what Einstein called “spooky action at a distance”.

But Einstein’s own theory of special relativity had shown that this kind of instantaneous communication is impossible. So he argued that quantum mechanics couldn’t be the whole story.

The problem was that it didn’t seem possible to distinguish experimentally between Bohr’s Copenhagen view and Einstein’s, because they both predicted the same measurement outcome. So the issue was largely swept under the rug – until 1964, when the Irish physicist John Bell reformulated the EPR experiment in a way that showed how it could be conducted for real. Those experiments were first done in the 1970s using lasers to produce entangled photons. They have been repeated many times since to rule out possible loopholes in Bell’s argument, and they have always shown that the prediction from quantum mechanics is right.

The EPR argument relied on the perfectly reasonable assumption of locality: that the properties of a particle are localised on that particle, and what happens here can’t affect what happens there without some way of transmitting the effects across the intervening space.

Perfectly reasonable – but as Feynman once said, at the quantum level nature isn’t reasonable. Once they are entangled, we can’t regard the two particles in the EPR experiment as separate entities, even though they are separated by space.