Mysterious Quantum Rule Reconstructed From Scratch

Mysterious Quantum Rule Reconstructed From Scratch

Ronaldo Barry

In other words, Born’s rule connects quantum theory to experiment. It is what makes quantum mechanics a scientific theory at all, able to make predictions that can be tested. “The Born rule is the crucial link between the abstract mathematical objects of quantum theory and the world of experience,” said Lluís Masanes of University College London.

The problem is that Born’s rule was not really more than a smart guess — there was no fundamental reason that led Born to propose it. “It was an intuition without a precise justification,” said Adán Cabello, a quantum theorist at the University of Seville in Spain. “But it worked.” And yet for the past 90 years and more, no one has been able to explain why.

Masanes and colleagues have now set out an argument that does not require Gleason’s assumptions, let alone many universes, to derive the Born rule. While the rule is typically presented as an add-on to the basic postulates of quantum mechanics, they show that the Born rule follows from those postulates themselves once you admit that measurements generate unique outcomes. That is, if you grant the existence of quantum states, along with the “classical” experience that just one of them is actually observed, you’ve no choice but to square the wave function to connect the two. “Our result shows that not only is the Born rule a good guess, but it is the only logically consistent guess,” Masanes said.

To reach that conclusion, we just need a few basic assumptions...

The work can’t answer the troublesome question of why measurement outcomes are unique; rather, it makes that uniqueness axiomatic, turning it into part of the very definition of a measurement. After all, Galley said, uniqueness “is required for us to be able to even begin to do science.”

Law Without Law

The project pursued here is one that has become popular with several researchers exploring the foundations of quantum mechanics: to see whether this seemingly exotic but rather ad hoc theory can be derived from some simple assumptions that are easier to intuit. It’s a program called quantum reconstruction. Cabello has pursued that aim too, and has suggested an explanation of the Born rule that is similar in spirit but different in detail. “I am obsessed with finding the simplest picture of the world that enforces quantum theory,” he said...

His approach starts with the challenging idea that there is in fact no underlying physical law that dictates measurement outcomes: Every outcome may take place so long as it does not violate a set of logical-consistency requirements that connect the outcome probabilities of different experiments. For example, let’s say that one experiment produces three possible outcomes (with particular probabilities), and a second independent experiment produces four possible outcomes. The combined number of possible outcomes for the two experiments is three times four, or 12 possible outcomes, which form a particular, mathematically defined set of combined possibilities.