We are still searching for a non-probabilistic understanding of quantum mechanics

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Quantum mechanics’ probabilistic nature has puzzled researchers for more than a century. A new analysis shows that ridding the theory of this odd characteristic may be even harder than anticipated.

Infamously, quantum objects can exist in combinations of seemingly mutually exclusive states, such as in the Schrödinger’s cat thought experiment, where the animal is in a mix of states that makes it seem both alive and dead, and also neither. Left undisturbed and isolated, the cat remains mixed, but if it is observed – if an experimenter opens its box, say – it abruptly reduces to just one, unmixed state.

How exactly this happens – a question known as the measurement problem – is among the biggest unresolved questions about quantum mechanics. At its heart is a mathematical rule named after the physicist Max Born. Researchers have long tried to derive the Born rule from mathematical ingredients that could eliminate some of quantum mechanics’ probabilistic oddness. However, Jiaxuan Zhang at the University of Oxford has now found that some of the most influential among these derivations don’t fully accomplish this task.

The Born rule is a recipe for converting information about a quantum object into probabilities that tell us the likelihood of observing particular outcomes. The rule is also a postulate, which means the founders of quantum mechanics assumed its truth rather than deriving it. But it is a troublesome truth because it means that quantum mechanics cannot offer information firmer than the probability of something happening, such as Schrödinger’s cat being alive 30 per cent of the time you open its box.

Zhang wanted to know if past efforts to derive the Born rule from mathematical assumptions, instead of simply postulating it, introduced any probabilistic ingredients at the starting point. If no such ingredients are needed, it might be possible to place quantum mechanics on more deterministic ground – and so make it more understandable.

“I think that if we can find the origin of the Born rule, maybe we can also find the origin of quantum probability,” says Zhang. She spent about two years combing through five of the most influential derivations of the rule in an attempt to zero in on that origin.

These five derivations were motivated by a broad range of ideas about how to interpret the equations of quantum mechanics, drawing on arguments ranging from considerations about symmetry and quantum entanglement to decision theory for inhabitants of the quantum multiverse. Zhang assumed an interpretation-agnostic stance and paid attention solely to the maths.

But as she dug into the underlying assumptions, she found more probability. “For people who want to derive the probabilistic Born rule from only deterministic principles, my result for now doesn’t support that,” says Zhang.

For instance, she concluded that some version of a concept known as additivity is indispensable to all derivations of the Born rule in her analysis. Although it can be stated more generally and abstractly, additivity is simplest to understand when thinking about fair dice. Here, additivity means that the probabilities of rolling each number, from 1 to 6, always sum to 100 per cent.

“I find Zhang’s paper interesting because it addresses a fundamental question: where do quantum probabilities come from?” says Augusto Smerzi at the Shenzhen Technology University in China. He says that, by showing just how important additivity is, she brings clarity to a long-standing problem.

But Smerzi says that clearly identifying the assumptions underlying the Born rule shouldn’t be misunderstood as an explanation for why this rule in its postulated mathematical form describes our world so well. “Making assumptions explicit is essential, but understanding why nature obeys them is what gives a derivation its deeper physical meaning,” he says. “I would therefore not interpret Zhang’s conclusions as closing the door to a deeper explanation of quantum probabilities. Rather, they highlight the importance of continuing to search for such an explanation.”

Zhang says the work is nowhere near over because there are more derivations of the Born rule that she wants to analyse. She also doesn’t think that some mathematical surprise is fully out of the picture yet. While her work constricts the possibility, there is still a small chance that the Born rule could be put on deterministic foundations, she says.