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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.

Law Without LawThe 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.