Chapter 9

The idea that someone or something controls all events goes a long way back. Democritus, for instance, said two and a half millennia ago that any apparent randomness in the world is just down to a lack of information. Faced with quantum theory, Einstein felt the same: ‘Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal, but hardly brings us closer to the secret of the Old One. I am at all events convinced that He does not play dice.’

Einstein’s problem starts with the Schrödinger equation, the one I have scratched onto the wall of Jerome’s cell. This describes how the properties of a particle — an electron, say — will evolve over time. Let’s consider the position of our electron. The quantum description of that position — given by the Schrödinger equation — cites an ‘amplitude’, formed from psi, which is composed of two components: a set of real positive or negative numbers, and a set of Jerome’s imaginary numbers. The particular numbers — real and imaginary — that are relevant to a real world experimental situation depend on the kind of measurement being considered.

All you can do with this amplitude is to specify a position and work out the probability that a single measurement on the electron will give that particular position as the result. When you actually perform the measurement, you might not get that result. But if you do the measurement many times, resetting the system each time, the distribution of results will match the probability-based predictions of the Schrödinger equation. That’s why, ultimately, our world becomes deterministic — the predictable pattern is the net result of many, many unpredictable individual events and processes.

Here is Einstein’s dilemma. Probability and statistics has produced a useful theory that matches experimental observations. But the theory does not explain anything. It can be used to predict what will be observed in experiments, but says nothing about why electrons, photons, and atoms behave as they do. Electrons jump between energy levels, producing radiation at wavelengths and intensities that the theory predicts. But why do they jump when they do?

An analogy might be the ancient saying, ‘Red sky at night, shepherd’s delight.’ Humans have known for millennia that an orange-scarlet tint to the evening sky is a herald of sunny weather when morning comes. It is useful and mostly accurate. But it doesn’t have anything to say about why the two phenomena are linked. The fact is that a red evening sky does not cause a sunny morning. When the saying was invented they were two facets of some mysterious meteorological phenomenon.

Not that it has remained mysterious: we know now that the red evening sky is the result of a region of high atmospheric pressure moving in from the west. This pressure traps dust in the atmosphere and the dust scatters blue light away from our line of vision, leaving only a red glow. Because of the way the Earth turns, dragging the atmosphere with it, that high pressure ridge moves in from the west overnight to be overhead in the morning, and high pressure generally means good weather.

In stark contrast, we have failed to find any mechanism behind quantum events. Einstein thought there must surely be some way to predict when an electron will make its jump and send out a flicker of light. Until we have that in our hands, he reasoned, we cannot call quantum theory ‘the real thing’. At the moment of writing that passage to Max Born, in December 1926, Einstein felt quantum mechanics was incomplete.

Now, almost a century later, it is still incomplete by Einstein’s standards. Our fundamental belief now is that quantum mechanics operates at random. The Old One does play dice, if you will, which means probability is the only way to quantify what will happen in our experiments. Jerome wrote that his book On Subtlety — published in 1550, when he was forty-nine years old — aimed to be his ‘complete account of the universe in a single volume’. But it turns out that his Book on Games of Chance, written three decades earlier, might have been a more succinct account of the operating principles of the universe.

No one worked harder than Einstein to think through the issue of fundamental randomness. He worried at it for years, formulating thought experiments and seeking acceptable, sensible solutions to the conundrums it threw up. In the end, he went all the way back to the Schrödinger equation and worked with Schrödinger to try to make sense of it all.

Together, Einstein and Schrödinger alighted on two thought experiments that have become the touchstones for quantum strangeness. They are known as ‘Schrödinger’s cat’, and ‘EPR’ (where the P and the R refer to Boris Podolsky and Nathan Rosen, the colleagues who helped Einstein formulate his ideas).

Schrödinger’s cat goes back to the equation that bears his name. Apply it to a radioactive source, such as a lump of radium, and it gives a probability that an atom within the radium will decay, emitting a burst of radiation, within a certain time. According to the Copenhagen interpretation, until that decay is measured the atom is in a superposition of decayed and not-decayed. In 1935, Schrödinger published a paper containing a novel thought experiment that Einstein considered the ‘prettiest way’ to show the incompleteness of quantum theory. In it, the radium is placed next to a radiation detector that causes a hammer to fall when it detects a burst of radiation. If the hammer falls, it smashes a vial of cyanide. Next to the vial is a live cat. Should the vial of cyanide be smashed, the cat will inhale the toxic gas and die. All of this is held within a closed box so that no one can tell whether the cat is dead or alive.

Now, instead of a superposition of different photon trajectories, as in the double slit experiment, we have a superposition of live and dead cat. The radium atom’s decayed-and-not-decayed state — a reasonable scenario within the normal parameters of quantum theory — has been strung out into an absurdity. Clearly, Schrödinger said (and Einstein agreed), this shows that something is missing from quantum theory.

If it was missing then, it still is now. We could have endless discussions about the question of measurement. Does the cat seeing the hammer fall count as a measurement? If Schrödinger opens the box with his eyes closed, is that a measurement? The simple truth is that no one has resolved this paradox. We simply live with it.

The second thought experiment — EPR — has been resolved, but not in a way that makes the quantum world an easier place to understand. Einstein’s EPR paper was published in 1935, the same year as the Schrödinger’s cat paradox. Its title was ‘Can quantum-mechanical description of physical reality be considered complete?’ The answer that it suggested, using a simple setup, is a resounding ‘no’.

EPR is, essentially, this: imagine two quantum particles, A and B, that briefly interact, then move away from each other. The way the mathematics of the Schrödinger equation work out — including a significant contribution from the imaginary numbers — means that an interaction between two particles leaves them as somewhat altered entities They are now one system and the properties of one cannot be separated from the properties of the other.

According to the Schrödinger equation, the interaction creates a new quantum state, one that Schrödinger called ‘entangled’. Entanglement, he said, is the ‘defining trait’ of quantum theory, setting it apart from any other field of physics. Once the particles are entangled, they have no individual existence. Though they might become physically separated, the information needed to describe their various properties fully — and thus to make predictions about the outcomes of measurements on either one — is shared between them.

As Einstein and Schrödinger noted, this had very odd repercussions. Perform a measurement on one, turning its inherent, random potential into a defined property, and you have also affected the outcome of a subsequent measurement on the other. The mathematics of the link between them — the entanglement — means their properties on measurement will be ‘correlated’. That might not seem strange at first glance, but delve into the implications and you’ll soon see why Einstein called it ‘spooky’.

Imagine those two measurements were carried out within a split second of each other, with the particles extremely widely separated in space. So widely, in fact, that there is no way that a signal travelling from one to the other, limited as it would be by the speed of light, can allow one measurement to influence the outcome of the second.

Now let’s focus on the details of the measurement. EPR uses the fact that position and momentum share what is known as ‘an uncertainty relation’. We’ll get into the details of this oddity later; for now, let’s simply use the fact that, if we measure the position of particle A precisely, there is a concomitant fuzziness to its momentum. If we measure A’s momentum, the position becomes uncertain. Now apply that to entangled particles and the Schrödinger equation tells you that the choice of measurement — position or momentum — on particle A will immediately affect the outcome of a measurement onThe two are ‘correlated’, in other words. Instantaneously, B somehow knows which property — its position or momentum — must be precisely defined. That is true regardless of whether A is on Earth and B is on the surface of Mars. A signal travelling at the speed of light — the maximum speed of the universe — would take thirteen minutes to pass between A and B, so there is no way for B to ‘know’ how it should behave. That’s why Einstein dismissed this whole thing as impossible ‘spooky action at a distance’.

In their paper, Einstein, Podolsky, and Rosen made it clear how they felt. ‘No reasonable definition of reality could be expected to permit this,’ they said. They argued that there must be something missing from the Schrödinger equation — that quantum theory was, as yet, incomplete, with some missing information they called ‘hidden variables’ waiting to be included.

They were wrong, as it turns out.

In 1964, an Irishman called John Bell formalised Einstein’s objections and laid out an explicit test for the existence of the hidden variables. He started with pairs of entangled particles — two photons, say, that have interacted at some point in the past. These photons now have shared properties — that is, a full description of photon A involves some of the characteristics of photon B, and vice versa.

According to standard quantum theory, a measurement on photon A produces a random result, something like a coin flip. But according to the Schrödinger equation, the entanglement means a measurement on photon A will instantaneously affect what you’ll get as the result of a measurement on photon B — even if they are millions of light years apart. So the result of measurement B is not quite random when compared against the value yielded by a measurement on A. Is that because there are as yet undiscovered properties — hidden variables — in A and B that correlate the outcomes of the measurements? Or is there really something in quantum theory that spookily defies our cherished notions of space and time?

Bell thought up a way to tell if the results are determined by hidden variables or by random processes. His setup is complex and subtle, but you can imagine it as a hypothetical team sport, based on choosing a type of measurement to perform and guessing the outcome.

The teams play in two different kinds of universe. Team Einstein makes the choice of measurements in a common sense universe, where there are hidden variables that carry information. These variables are constrained by the laws of physics, meaning their influence cannot travel faster than the speed of light. Here, any apparent magical correlation between the outcome of a pair of distant measurements is an illusion created by the hidden variables.

Team Bohr, meanwhile, is working in a universe where the result of a measurement really is utterly random, but correlations exist between the two particles’ properties that will be manifest once one particle’s properties become definite.

The setup of the game runs something like this (I’m only going to be able to convey a rough impression — the real world version is fiendishly complicated). Each team is composed of two players, one of whom is on Earth and the other on Mars. It takes thirteen minutes for a signal limited by the speed of light to travel between them. Each of the players has one of an entangled pair of photons. Playing the game involves making measurements: first on the Earth-bound photon, then on the one on Mars. To avoid accusations of cheating, the second measurement must happen within thirteen minutes of the first, so that there can have been no communication between the two players, who we’ll call Alice and Bob.

Having seen the outcome of the first measurement, Alice then chooses to hold up her left or right hand. Bob, who doesn’t know anything about the outcome of Alice’s measurement, or which hand she has raised, then performs his measurement and chooses a hand to raise depending on the outcome. There are two ways the pair can score a point: either by raising the same hand when the two measurement results are different, or by raising different hands when the two measurement results are the same.

If you slave your way through all the possibilities, using Jerome’s mathematics of probability, you can work out that the best that Team Einstein can do in their common sense universe is score a point on seventy-five per cent of its plays. But Team Bohr, which is operating in a universe with entanglement, can score points on eighty-four per cent of its plays. Why? Because entanglement slightly alters the probabilities. The instantaneous, appear-from-nowhere correlations of entanglement skew the properties of the second photon in a way that makes it slightly more likely that Bob’s guess about which hand to raise will be correct. In other words, entanglement means that Team Bohr should always win.

To determine which kind of universe we live in, you just have to play the game. It’s possible to do this without going to Mars; you just have to situate your two experimenters far enough apart that the time elapsing between their measurements is less than that needed for communication between them at the speed of light.

The first people to do it properly were Stuart Freedman and John Francis Clauser. They played Bell’s game in 1972 and their results showed clearly that we live in Team Bohr’s universe. The players scored points eighty-four per cent of the time and there is no way they could do that if they were living in Team Einstein’s universe.

Freedman and Clauser’s experiment showed entanglement is real. The outcome of the second measurement was influenced by the choice made in the first measurement. The first photons’ properties materialised at random when measured. But the measurement choice for the first photon instantaneously affected what would happen when its entangled twin was measured: its properties were not quite as random.

In the years since that first experiment, we have got better and better at exploring the nature of quantum entanglement. A notable landmark came in 2008, when a Swiss physicist called Nicolas Gisin separated his photons by eighteen kilometres. One was in Jussy, a town east of Geneva. The other was in Satigny, a town to the west. The measurements allowed the players to score points eighty-four per cent of the time, and the time between measurements was so short that any influence would have had to travel at ten thousand times the speed of light. Entanglement, that phenomenon that is written into the Schrödinger equation and results from the phase and its imaginary numbers, is indubitably real.

No one knows how it works. The entangled particles are chained together by a connection that we don’t understand. They may be one particle that manifests in our world in two separate places. They may even be, by some hidden, contorted geometry of space, right next to each other.

We just don’t have any idea of how the measurements can be so well correlated.

ψ

‘Fate,’ Jerome says.

I shrug. ‘Maybe.’

As a trained physicist, you might think I shouldn’t believe in fate, but you would be wrong. I can believe that everything is controlled by an external influence, that all things are ordained, and there is no such thing as a choice. Why? Because Gerard ‘t Hooft can believe it. He has a Nobel Prize in Physics, is universally respected as one of the smartest physicists on the planet, and believes in something called superdeterminism, another selection among the interpretations of quantum theory.

Remember how Jerome once said that wisdom is to ‘say nothing ludicrous’ about the cause of an effect? I am going to have to ignore that advice. We’ll start from the premise that quantum mechanics is nothing more than a mathematical tool that gives you a way to calculate the outcomes of experiments. By the end, you will have lost all free will and will understand that you are nothing but a biological tool of the universe … Ready?

It begins at the beginning of the universe. There was a Big Bang moment and some of the energy of that moment condensed into matter, taking the form of particles that went on to create atoms. That means the fundamental particles — the electrons, quarks, neutrinos, and so on — all had a common origin. In that case, could their common origin have a lasting effect? What if certain aspects of their properties are, and always will be, correlated?

The consequence would be, essentially, that we are fooling ourselves when we think we are conducting experiments on uncorrelated, independent, entirely separated systems. That is what the superdeterminism interpretation of quantum mechanics says: all those conclusions we have drawn about spookiness or weird superpositions are a consequence of our blindness to the threads that connect everything in the universe.

Superdeterminism doesn’t permit randomness. There is always cause and effect. So when a radioactive atom decays, that doesn’t happen at random. There is a reason for it — and that reason is tied up in the hidden threads that we can’t access.

Similarly, if we prepare two identical atoms in the same state, put them in exactly the same environment, and watch what happens, we may well see two different end results. The Copenhagenists put this down to inherent randomness in the evolution of quantum systems. Superdeterminists say it’s because you were fooling yourself when you assumed you had prepared the atoms in the same state. You couldn’t have because you have no way of controlling the hidden threads. And the difference between the hidden threads controlling the properties of the two atoms is what gave you two different outcomes. There is no randomness, only ignorance.

Essentially, the superdeterminists’ view is that we are not in control of our experiments.

There is no way to separate the settings of a detector, say, from the state of the particles it is about to detect. So you can try all you like to control your test for eighty-four per cent correlations. You can set up and operate your double slit experiment, if you so desire. But who is to say that the atoms of the material that is emitting the photons are not linked to the apparatus used to detect the photons? Maybe a tweak to the emitter tweaks the detector in some hidden way, giving you the illusory result of an interference pattern at the detector — which makes you think that the photon went through both slits simultaneously, or that entanglement is real.

There is no superposition in the superdeterminists’ view. The photon in the double slit experiment is not in two places at once. There is no spooky action at a distance, either. Those are just shorthand descriptions that make sense of the mathematics of quantum theory — and quantum theory, as it currently stands, is not the final answer.

The big problem with superdeterminism is philosophical. It requires that science is an act of self-delusion because all the atoms of the universe are linked in a way that destroys human free will. You’re not free to choose how to tweak the emitter because the atoms in the neurons of your brain are also subject to those hidden threads. And, by extrapolation, scientists are not freely choosing the tasks they perform. We are just a part of the complex clockwork mechanism of subatomic physics. Think of yourself as a cog, with teeth that are enmeshed with those of another cog. If that cog turns, can you choose not to?

This idea has been labelled the ‘ultimate conspiracy theory’. One researcher once put it to me like this: ‘According to superdeterminism, you’re allowed to say about any experimental result: “Well, maybe that happened because of a giant, universe-wide conspiracy involving both the particles you measured and the atoms of your own brain — which allowed the particles to know in advance which experiment you were going to do and to get into just the right state, thereby fooling you into thinking that, had you chosen to do a different experiment (which is actually impossible, since you lack free will), you would’ve continued to see results consistent with standard physical theory. So it all looks like the standard physical theory is valid, but really it’s not.”’

It’s safe to say, he wasn’t a fan.

Gerard ‘t Hooft is unconcerned. His take on superdeterminism is that you can believe in the other interpretations if you like, but you won’t ever have a satisfactory explanation for what is going on. There’ll be inexplicable measurement-induced collapses, things in two places at once, and spooky action at a distance. With superdeterminism, you simply assume there’s more to the world than we can currently see — there is a God’s eye view — and that all the weirdnesses would have a perfectly good explanation if only our experiments were able to probe things down to the ultimate, fundamental scales of reality.

But even then we’d need to use our own brains and they are part of the conspiracy. The brain is a machine made of atoms that have particular properties, and those properties determine what our conscious state is at any moment. Those atoms weren’t always inside our skulls: they have been in stars and travelling through intergalactic space. They were part of a water molecule, perhaps, or once skirted the event horizon of a black hole on the other side of the universe. Ultimately, they can trace their origins to the moment after the Big Bang, when the universe first saw matter. And the imprints that one atom left on another back then continue to exert their influence now, even as carbon-based life forms attempt to construct stories about how the universe really works. Yet even ‘t Hooft doesn’t yet fully believe in superdeterminism. There are lots of holes, he admits — although in Vienna he did tell me that it’s the only explanation that he trusts. ‘I can’t help being disgusted by the Many Worlds interpretation,’ he said. ‘I want to know what is really going on …’

I’d tell you to make up your own mind. But, if ‘t Hooft’s suspicions are correct, you really can’t.

ψ

‘I like this idea,’ Jerome says.

Of course he does. If it’s right, nothing — his incarceration, the fate of his sons and his wife — is his fault. Everything is outside of his control. I’m tempted to point out that it also means his successes are nothing to glory in. His return from England, for example, gave him enormous satisfaction. He travelled through Europe a celebrated man. He effectively went on tour, invited to visit and be entertained by the most famous doctors, publishers, bishops, and philosophers of the continent in Bruges, Ghent, Brussels, Louvain, Michelin, and Antwerp. The procession continued to Aix-La-Chapelle, Cologne, Mainz, Worms, Speyer, Strasbourg, and Basel. From there he went on to Berne and Besançon, Zurich, and — finally — Milan.

Crowds had lined the streets of Milan in welcome, in stark contrast to Jerome’s long-forgotten return from Gallarate as a penniless pauper with a wife, a young baby, and a trolley of books. ‘Now they put up bowers for me to pass under and my treasure-boxes are great enough to be drawn on a cart flanked by guardsmen,’ he wrote of the occasion. ‘Where I was despised I am now the chief physician, where I was unknown my skills in medicine, numbers, the stars, wisdom and machines are everywhere discussed. Honours and awards have been flung at me till I grow weary of them. Sovereigns of church, palace and battlefield have summoned me to their aid.’

Such celebrated success must have been particularly galling for Nicolo Tartaglia, a man whose reputation had, thanks to Jerome, been in tatters for some years.