Gödel’s finding was first connected to the physical world in 1936, by British mathematician Alan Turing. “Turing thought more clearly about the relationship between physics and logic than Gödel did,” says Rebecca Goldstein, a US author who has written a biography of Gödel.
Turing reformulated Gödel’s result in terms of algorithms executed by an idealized computer that can read or write one bit at a time. He showed that there are some algorithms that are undecidable by such a ‘Turing machine’: that is, it’s impossible to tell whether the machine could complete the calculations in a finite amount of time. And there is no general test to see whether any particular algorithm is undecidable. The same restrictions apply to real computers, since any such devices are mathematically equivalent to a Turing machine.
Since the 1990s, theoretical physicists have tried to embody Turing’s work in idealized models of physical phenomena. But "the undecidable questions that they spawned did not directly correspond to concrete problems that physicists are interested in”, says Markus Müller, a theoretical physicist at Western University in London, Canada, who published one such model with Gogolin and another collaborator in 2012.
“I think it’s fair to say that ours is the first undecidability result for a major physics problem that people would really try to solve,” says Cubitt.
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