摘要：Superdeterminism makes sense of the quantum world by suggesting it is not as random as it seems, but critics say it undermines the whole premise of science. Does the idea deserve its terrible reputation?

I’VE never worked on anything so unpopular!” Sabine Hossenfelder, a theoretical physicist at the Frankfurt Institute for Advanced Studies in Germany, laughs as she says it, but she is clearly frustrated.

The idea she is exploring has to do with the biggest mystery in quantum theory, namely what happens when the fuzzy, undecided quantum realm is distilled into something definite, something we would experience as real. Are the results of this genesis entirely random, as the theory suggests?

Albert Einstein was in no doubt: God, he argued, doesn’t play dice with the universe. Hossenfelder is inclined to agree. Now, she and a handful of other physicists are stoking controversy by attempting to revive a non-random, “deterministic” idea where effects always have a cause. The strangeness of quantum mechanics, they say, only arises because we have been working with a limited view of the quantum world.

The stakes are high. Superdeterminism, as this idea is known, wouldn’t only make sense of quantum theory a century after it was conceived. It could also provide the key to uniting quantum theory with relativity to create the final theory of the universe. Hossenfelder and her colleagues aren’t exactly being cheered on from the sidelines, however. Many theorists are adamant that superdeterminism is the most dangerous idea in physics. Take its implications seriously, they argue, and you undermine the whole edifice of science.

So what is the answer? Does superdeterminism deserve its bad reputation or, in the absence of a better solution, do we have little choice but to give it a chance?

Quantum theory describes the behaviour of matter at its most basic, the atoms and their constituent particles. It was conceived to make sense of the observed behaviour of atoms, and resulted in physicists claiming that particles behave like waves and can appear to be in several different states at once, known as being in a superposition. The idea is that only when we observe those particles directly do they assume definite properties.

Erwin Schrödinger came up with an equation to capture the fuzziness of the quantum realm, showing that it could be represented by a mathematical entity later called a wave function. This gives the probability that a quantum object will manifest as a particular state or place upon measurement. But it can’t say for certain.

In fact, we only get agreement between theory and experiment when we average out the results of lots of measurements of identical quantum objects. That leads to the assumption that each individual outcome occurs at random, and thus that, at the most fundamental level we know, the universe is indeterministic – governed by chance.

That is hard to swallow for many people because we experience a world in which effects always have a cause. Some have tried to fix the situation by suggesting that the simultaneous different states of an atom in superposition are a reflection of different realities occurring in separate universes. Or by saying that the atoms just don’t have any properties and don’t really exist when they aren’t being observed.

But none of these interpretations make sense to Hossenfelder. All of them contain contradictions, she says, which is why she is working to explore superdeterminism.

Broadly speaking, this is the idea that the outcome of any measurement is due to factors involved in the measurement, such as the measuring apparatus and its settings. What we see is determined by all these factors, including, perhaps, factors that are hidden from us.

To get to grips with the concept, first you have to understand an idea put forward by physicist John Bell in the 1980s. Bell proposed a scheme for testing whether there was merit to another of Einstein’s reservations about quantum theory, this time about “spooky action at a distance”, as Einstein dubbed it, in which measurements of one particle seem to influence the outcome of measurements of another, spatially distant particle.

“The resulting theory could have all the consequences of quantum mechanics, but none of the weirdness”

Bell’s scheme concerned the statistical outcome of a series of measurements on two particles with quantum properties that are “entangled” with each other because of some interaction in the past. He showed that if these non-local correlations aren’t real, then there is a minimum probability with which you should get a particular outcome, such as the same result from both measurements. It can be greater than or equal to this value, but it can’t be lower. In mathematical terms, it is known as an inequality. If you find you are getting the outcome of interest less often than you would expect, “Bell’s inequality” is being violated – and you know the results are being skewed by a non-local correlation between your particles.

Forbidden choices

Experiments have demonstrated that it is possible to violate Bell’s inequality. This seems to prove that the spooky action is real, in spite of Einstein’s objections. But the proof depends on an assumption about the measurement.

Specifically, Hossenfelder questions the assumption that the experimenter is entirely free to choose the “basis” of any given measurement. Given a collection of gloves, say, you might choose to compare them on the basis of their size, handedness or colour – or a combination of these. But what if certain measurement choices are forbidden by some as-yet-unknown law of physics? What if, for instance, the universe won’t let you measure the colour of a right-hand glove independently of measuring its size? If that were the case, you might get a strange result when you tried to do it. And if you didn’t know about that law, you might conclude that some fundamental weirdness exists in the world of gloves.

The idea that nature forbids certain choices might seem far-fetched, but quantum theory itself was built on a far-fetched restriction. Max Planck only discovered it through what he called “an act of desperation”: conjecturing that atomic stuff comes in definable lumps of energy, with certain energies forbidden. What’s more, we have since discovered that atomic structures such as two electrons can’t occupy the same quantum state inside an atom, which is known as the Pauli exclusion principle. “In that case, no one asks, ‘how is it that I can’t put these electrons in the state that I want to?'” says Hossenfelder. “You just say it’s a law of nature: that’s just how it is.”

To move the idea along, Hossenfelder is creating a model of reality that forbids certain combinations of quantum states from existing. She is hoping that the resulting idea will have all the consequences of quantum mechanics, but none of the weirdness.

She isn’t the first to lean in this direction. Physics Nobel laureate Gerard ‘t Hooft at Utrecht University in the Netherlands has proposed something along these lines. And Tim Palmer, a physicist at the University of Oxford, is joining their ranks. Palmer used to work at the European Centre for Medium-Range Weather Forecasts, and his experience with the physics of chaotic systems like weather has led him to formulate a chaos-based superdeterminism idea that he thinks might explain the quantum world.

In chaos theory, systems such as weather patterns evolve in a way that is extremely sensitive to their initial conditions. Tiny changes in the set-up lead to huge divergences in the later characteristics of the system. At the same time, some chaotic systems will always converge towards a particular set of characteristics. This can be captured in a mathematical entity called a chaotic “attractor”, which maps their movement through all the possible states towards these almost inevitable outcomes. The attractor has a curious, often-ignored property, however. In any chaotic system, there are states and situations that are just off-limits. The attractor’s blank space defines which states are impossible to access.

Palmer has been investigating what it would mean if our universe were subject to the same constraints. “I imagined that the universe is a chaotic system evolving on its own attractor,” he says. Then he pictured conducting a Bell experiment in this chaotic universe. The experimenters would still make choices about the measurement basis, but Palmer thinks that certain combinations of quantum states could be unattainable, implying that some experimental choices defy the laws of physics. “These gaps in state space, the places the system is not allowed to go, give you the wiggle room you need to be able to violate Bell’s inequality without having to fall back on indeterminacy or non-locality,” says Palmer.

He plans to put his ideas to the test, starting with an experiment that has to do with the number of quantum objects that can be entangled together. In standard quantum theory, there is no limit, but in Palmer’s scheme that number is finite. “After a certain number of entanglements, you’ll just go back to classical correlations,” he says. In February, with Jonte Hance and John Rarity at the University of Bristol, UK, Palmer published a range of experimental designs that are aimed at finding the limit, if it exists.

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Hossenfelder is even further along. Her design involves performing a set of repeated measurements on a quantum system. “A general prediction of superdeterminism is that the outcome of measurements is actually determined, not random. So you test it by checking whether quantum measurements are really random,” says Hossenfelder.

In her design, each initial set-up should be an exact copy, as far as is possible, of the one before. If the universe is ultimately deterministic, the results should be more or less identical. But if probabilistic quantum mechanics really is fundamental, there would be easily discernible changes in the outcome of each run.

That is harder than it sounds: you have to make sure you don’t introduce randomness through the measurement device, so the smaller it is and the lower the temperature it operates at, the better. “You also have to do the measurements in as fast a sequence as possible because the more time passes, the more likely it is that something wiggles,” says Hossenfelder.

A vast conspiracy?

The good news is that Siddharth Ghosh at the University of Cambridge has just the sort of set-up that Hossenfelder needs. Ghosh operates nano-sensors that can detect the presence of electrically charged particles and capture information about how similar they are to each other, or whether their captured properties vary at random. He plans to start setting up the experiment in the coming months.

All of which sounds exciting. And yet a large number of philosophers and physicists scoff at the prospect, insisting that we don’t need to do experiments to rule out superdeterminism. Howard Wiseman at Griffith University in Queensland, Australia, pretty much sums up the objections when he says the idea would imply there is a “fine-tuning” conspiracy behind the laws of physics, meaning you have to input initial conditions by hand and choose them very precisely to make sense of observations. And that’s just for starters. Wiseman adds that superdeterminism would also undermine the notion of human free will and make the whole idea of doing science pointless. “I’m not a fan,” he says.

This last point comes from the fact that superdeterminism violates something known to philosophers of science as “statistical independence”. This is the idea that tweaking the input to an experiment shouldn’t change anything in the equipment set-up to detect the output. The free will problem arises because, in the Bell test, the experimenter has to be able to set the experiment up however they want to. Superdeterminism says this isn’t possible because there are hidden constraints.

But Wiseman thinks the fine-tuning argument is the most persuasive. He points out that experimenters have made deliberately ridiculous, random choices when performing Bell experiments – choosing sequences of binary digits from a digitised version of the 1985 movie Back to the Future to create the measurement settings, for example. Since superdeterminism explains Bell experiments through correlations between hidden variables in the quantum particles and the measurement settings, that would imply that the series of events and choices in the film’s production are correlated with the actions of the physicists carrying out the experiment.

“According to superdeterminism, the explanation for these particular Bell correlations is that it is impossible to have a universe in which the hidden variables in the experimental photons are the same, but Michael J. Fox’s smile was 1 millimetre wider in one frame of Back to the Future,” says Wiseman. “It’s the most bizarrely fine-tuned theory imaginable. The whole thing is a vast conspiracy: an insanely complicated universe with unimaginably fine-tuned initial conditions.”

Palmer rejects this argument. “It is most certainly not the case that superdeterminism says that there is any conspiracy,” he says. The problem, he says, is that people see fine-tuning because they are applying the wrong kind of mathematics. Physicists assume that the fundamentals of the universe evolve in a linear fashion, but they might well be chaotic, says Palmer. In which case, the linear equations we have won’t work.

In any case, the choice of Back to the Future was itself curious. That is because, according to Huw Price, a philosopher at the University of Cambridge, backwards-in-time causation is the one thing that can make superdeterminism plausible. Price argues that superdeterminism works if you take the “block universe” perspective of Einstein’s special theory of relativity, where past, present and future all co-exist in a big four-dimensional grid we call space-time.

In this scheme, time doesn’t run in any one direction. Time’s arrow isn’t fundamental to relativity – or to quantum theory, for that matter. And that means tweaking a detector’s settings to determine the properties of two entangled particles in a particular way can influence the properties those particles gained at what we would call an earlier time. “The setting that we chose has an influence on the particle all the way back to when it was first formed in some event that produced two particles,” says Price.

“If there is backwards-in-time causation, science and human free will can be rescued”

He believes this perspective has two advantages. First, it doesn’t require that the universe was set up in some precise, finely tuned way that gives the experiment its outcome. Second, it doesn’t undermine science and human free will. Emily Adlam, a philosopher of physics affiliated with the independent Basic Research Community for Physics, says she is willing to consider this idea. “An approach where the laws of nature apply all at once to the whole of history gives much less reason for concern.”

Wiseman remains unconvinced. It is all just too vague, he says. People have been suggesting that some kind of “retrocausality” might resolve our problems with quantum theory for nearly 100 years, he points out, but no one has ever embedded an idea that works this way into Einstein’s space-time.

And what would be the point? “I don’t see the motivation for wanting to deny the conclusion of Bell’s theorem,” says James Ladyman, a philosopher at the University of Bristol, UK. It isn’t the end of the world to accept the existence of a non-local phenomenon like entanglement, even if it does go against our metaphysical presuppositions.

The proponents of superdeterminism think there is a lot to be gained, however. For a start, it might open the door to new kinds of technology, says Hossenfelder. The limits to how well we can make measurements come from the noise that has its roots in quantum randomness. If the apparent randomness is actually the result of controllable processes, perhaps we could push down the quantum noise. “I think this would be important for quantum computing – the major issue that they have is the noise,” says Hossenfelder.

For Palmer, the benefits might lie in the quest to unite quantum theory with relativity to create a theory of quantum gravity. The usual approach is to modify relativity and leave the quantum stuff alone, but Palmer thinks that superdeterminism suggests this might be a mistake. “It’s going to require a lot more give from the quantum side than from the relativity side,” he says.

There is no agreement in sight, and progress is slow because there are so few people working on superdeterminism. Nonetheless, their proposal for answering the riddle of quantum theory is worth exploring, says Adlam. “I wouldn’t say superdeterminism is my preferred route, but I think it’s definitely reasonable, and it deserves a lot more attention than it has received.”