A quantum technique highlights math’s link to physics
Science News said:It has long been a mystery why pure math can reveal so much about the nature of the physical world.
Antimatter was discovered in Paul Dirac’s equations before being detected in cosmic rays. Quarks appeared in symbols sketched out on a napkin by Murray Gell-Mann several years before they were confirmed experimentally. Einstein’s equations for gravity suggested the universe was expanding a decade before Edwin Hubble provided the proof. Einstein’s math also predicted gravitational waves a full century before behemoth apparatuses detected those waves (which were produced by collisions of black holes — also first inferred from Einstein’s math).
Nobel laureate physicist Eugene Wigner alluded to math’s mysterious power as the “unreasonable effectiveness of mathematics in the natural sciences.” Somehow, Wigner said, math devised to explain known phenomena contains clues to phenomena not yet experienced — the math gives more out than was put in. “The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and … there is no rational explanation for it,” Wigner wrote in 1960.
But maybe there’s a new clue to what that explanation might be. Perhaps math’s peculiar power to describe the physical world has something to do with the fact that the physical world also has something to say about mathematics.
In an enormously complicated 165-page paper, computer scientist Zhengfeng Ji and colleagues present a result that penetrates to the heart of deep questions about math, computing and their connection to reality. It’s about a procedure for verifying the solutions to very complex mathematical propositions, even some that are believed to be impossible to solve. In essence, the new finding boils down to demonstrating a vast gulf between infinite and almost infinite, with huge implications for certain high-profile math problems. Seeing into that gulf, it turns out, requires the mysterious power of quantum physics.
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