Everybody knows by now that quantum mechanics is an extraordinarily successful scientific theory, on which much of our modern, tech-obsessed lifestyles depend. It is also completely mad. Although the theory quite obviously

*works*, we’re left to puzzle over what we think it’s telling us, with all its ghosts and phantoms; its cats that are at once both alive and dead; its collapsing wavefunctions; and its seemingly “spooky” goings-on. It leaves us with a rather desperate desire to lie down quietly in a darkened room.

This business has been going on for more than 90 years, and shows no signs of letting up. The debate about the interpretation of quantum mechanics began in 1927, as Albert Einstein and Niels Bohr faced off about the nature of quantum reality. And it continues today, as witnessed by a succession of recent popular books on the subject, including Philip Ball’s

*Beyond Weird*, Adam Becker’s

*What is Real?*, and Anil Ananthaswamy’s

*Through Two Doors at Once*, soon to be arriving on bookshelves. We can also look forward to Lee Smolin’s

*Beyond the Quantum*, to be published next year, and my own

*A Game of Theories*in 2020 (though I’m pretty confident that this title will not survive to publication).

What is it about this question of interpretation that has proved so stubbornly intractable, yet provokes such seemingly endless fascination?

As the name implies, quantum mechanics is the extension of the science of mechanics to the quantum domain of molecules, atoms, and sub-atomic particles. Mechanics is simply concerned with stuff that moves, governed by a very handy set of physical laws and mathematical equations of motion. In the 200 years after Newton, physicists worked to establish these laws and equations, employing concepts that are entirely familiar, such as mass, velocity, momentum and acceleration. These concepts sit right “on the surface” of the equations, and scientists don’t typically trouble themselves much about what they mean. It’s obvious.

But as physicists sought to extend this mechanics to describe the inner workings of atoms, in which the things that move are electrons orbiting atomic nuclei, they found that the old laws and equations no longer applied. The quantum nature of matter and radiation means that a particle like an electron can behave as though it is distributed through space, like a wave. In 1926, Erwin Schrödinger developed a theory to describe such combined wave-particle behaviour, in which the electron’s motion is described by a quantum

*wavefunction*.

We’re all familiar with the shape of a sine wave, rising smoothly and continuously from zero to a peak, falling gracefully back down through zero to a trough, before turning up again and returning to zero. This is a simple wavefunction, and its interpretation in classical wave theory is straightforward. But the wavefunction of quantum mechanics is quite different. For one thing, an electron wavefunction must somehow carry the mass of its associated electron. Schrödinger scrambled to find a new interpretation for it, arguing that although the wavefunction in quantum mechanics had become much more abstract, it must surely still represent a physically real thing.

“As physicists sought to describe the inner workings of atoms, they found that the old laws no longer applied”Max Born disagreed, however. He argued that the wavefunction isn’t a physically real thing. It simply summarises what we

*know*about a quantum system, and the square of the wavefunction then represents the

*probability*of finding the associated electron. Why the square of the wavefunction? As for a sine wave, the electron wavefunction oscillates between positive and negative amplitudes, but the square of the wavefunction is always a positive quantity, and there can be no such thing as a negative probability.

In this case, “finding” an electron is equivalent to making a measurement on it to see where it is, and Born’s probabilistic interpretation extends to all other kinds of measurements. For example, if the wavefunction describes two possible outcomes in a measurement (up and down, say), then all we can hope to do is predict the probability of getting one or the other. So, how does the quantum system get from two different measurement possibilities to just one outcome? There’s actually nothing in the quantum equations of motion to account for this, so the instantaneous jump from up and down to a single outcome (down, say), has to be postulated. The wavefunction is assumed to “collapse” as part of the measurement process.

Einstein didn’t like this at all, famously declaring that “God does not play dice.” Schrödinger sought to expose the absurdity of this description of the measurement process by pointing out that, even if we accept the “collapse” postulate, the theory has no prescription for where in the chain of events this is supposed to occur. Why not then extend the chain all the way up to a cat, locked in a box. Is the cat both alive (up)

*and*dead (down) until we lift the lid, and look?

In his great debate with Einstein, Bohr argued that the wavefunction shouldn’t be taken literally. It isn’t real. Bohr tended to focus on the limitations posed by making measurements on quantum systems with classical apparatus. But in his more modern version, called the

*relational interpretation*, Italian theorist Carlo Rovelli argues that such limitations are irrelevant.

What happens is that we make use of what we know about a quantum system based on previous experiments and experience and we code this in the wavefunction—say a combination of up and down. We perform a measurement and we get a single outcome—down. Make no mistake, this is a physical measurement, but in seeking to represent this all we’ve done is use the theory to manipulate information, as a way of connecting past events to predictions of the future. If the wavefunction is just coded information then it isn’t physically real and there’s no need to postulate a collapse. All that changes with the measurement is our knowledge, and: “this change is unproblematic,” writes Rovelli, “for the same reason for which my information about China changes discontinuously any time I read an article about China in the newspaper.”

It’s worth noting that neither Bohr nor Rovelli deny the existence of an objective reality—the moon continues to exist when nobody looks at it or thinks about it. They also accept the reality of “invisible” entities such as electrons. What they reject is a realistic interpretation of the quantum

*representation*. As far as Bohr was concerned (and as far as Rovelli is concerned today), the theoretical structure of quantum mechanics was already complete in 1927 and there’s nothing more to add.

Such an anti-realist interpretation forces us to resist the temptation to ask:

*but how does nature actually do that?*Like emergency services personnel at the scene of a tragic accident, Bohr and Rovelli advise us to move along, as there’s nothing to see here. And there lies the rub: for what is the purpose of a scientific theory if not to aid our understanding of the physical world? We

*want*to rubberneck at reality.

Einstein preferred to interpret the wavefunction more literally and realistically. He was not content to accept a representation to be used simply as an instrument to code knowledge, perform calculations, and so make predictions, and this was the basis for his great debate with Bohr.

“Is the cat both aliveThe choice we face is a philosophical one, which is why the question of interpretation remains so darn stubborn. There is absolutely nothing scientifically wrong with an anti-realist interpretation in which there is no mystery and the theory is complete. But if instead we choose to pull on the loose thread we are inevitably obliged to take the representation at face value, and interpret its concepts more realistically. Surprise, surprise. The fabric unravels to give us all those things about the quantum world that we find utterly baffling and, just as Einstein himself concluded, we’re obliged to accept that the theory can’t be complete.anddead until we lift the lid, and look?”

Taking different philosophical positions leads to different interpretations or even modifications of the quantum representation and its concepts, in what I call (with acknowledgements to George RR Martin)

*a game of theories*. I like to think that playing this game involves navigating the “ship of science” on the perilous “sea of representation.” (Yes, I’ve obviously read too many fantasy novels.)

We sail the ship back and forth between two shores. These are the deceptively welcoming, soft, sandy beaches of metaphysical reality and the broken, rocky and often inhospitable shores of empirical reality. The former are shaped by our abstract imaginings, free-wheeling creativity, and personal values and prejudices. These summarise how we think reality ought to be.

To make a scientific representation we sail the ship to the rocky shores of empirical reality. This is where we discover how nature actually appears, as revealed in the rather brutal, hard facts of observational and experimental data. This is where, according to Thomas Huxley, we might witness the “great tragedy of science—the slaying of a beautiful hypothesis by an ugly fact.” We can then go back and forth as often as we need in order to strengthen the relationships between our metaphysical prejudices, the empirical facts, and the representation that connects them.

Within this sea there are two grave dangers. The rock shoal of Scylla lies close to the shores of empirical reality. It is an anti-realist and rather empty instrumentalism, perfectly empirically adequate but devoid of any real physical insight and understanding. Charybdis lies close to the beaches of metaphysical reality, a whirlpool of wild, unconstrained metaphysical nonsense about the nature of reality.

The challenge to theorists is to discover safe passage across the sea, and in the last 90 years, this is roughly where we’ve got to:

**Bohr was right**: quantum mechanics is complete and there are no problems. Rovelli agrees. Though unpalatable to many with different metaphysical prejudices, there’s absolutely nothing wrong with this conclusion. This is the view from Scylla.

**Bohr was (mostly) right**: quantum mechanics is complete but, to make better sense, the conventional representation needs to be interpreted in a different way. Several approaches have been, and are being, actively explored.

**Einstein was right (I)**: quantum mechanics can be completed by including so-called hidden variables, which sit “beneath” the wavefunction and govern the physics. Certain classes of hidden variables have now been ruled out through experimental tests based on relationships devised by John Bell and Anthony Leggett. Other types of hidden variable theory (including the so-called “pilot wave” interpretation) are hard if not impossible to distinguish from conventional quantum mechanics. The choice then becomes a matter of taste.

**Einstein was right (II)**: quantum mechanics can be completed by introducing a physical mechanism to account for the collapse of the wavefunction. Such mechanisms include a kind of quantum friction called decoherence (which only resolves some of the problems), the involvement of gravity (curved spacetime), or some kind of spontaneous collapse. In other interpretations, the collapse is triggered when the wavefunction encounters a conscious mind, thus conflating two of the most troublesome problems of modern science—quantum mechanics and consciousness—which has never seemed to me to be a very productive way to go.

**Einstein was right (III)**, but in a way that I think would have appalled him. In a quantum measurement,

*all*the possibilities are realised at once, but each in different universes. This is the “many worlds” interpretation, the ultimate consequence of assuming the wavefunction is real. Some argue that it meets Bohr’s requirements, too, in that nothing further needs to be added to the theory. I profoundly disagree: an entire multiverse is not nothing. This is the view from Charybdis.

The debate continues. After a 30-year personal journey in search of the meaning of quantum mechanics, I can happily attest to the fact I still don’t understand it. But I think I now understand why. And, having long favoured Einstein’s philosophical position, I now confess to some doubts.

Like the great philosopher Han Solo, I’ve got a very bad feeling about this.

**Jim Baggott is a freelance science writer and author. His next book,**

*Quantum Space: Loop Quantum Gravity and the Search for the Structure of Space, Time, and the Universe*, will be published by Oxford University Press in November