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Operator algebras and the substructure of space and time
A 1930s-era breakthrough is helping physicists understand how quantum threads could weave together into a holographic space-time fabric.
Along the way, as a young man in 1932, von Neumann rewrote the rules of quantum mechanics, formulating the strange new theory of particles and their fluctuating, probabilistic behavior in the mathematical language used today. These methods, which involve powerful mathematics called tensor networks and quantum error-correcting codes, amount to, very roughly, tapping out patterns of ripples in the boundary sphere that correspond to measurements at specific locations in the bulk. Both the researchers hacking their way into black holes and those calculating the entropy from outside are using von Neumann algebras to tiptoe toward the ultimate goal: a theory of any space-time that can handle mild and violent quantum gravitational effects alike.
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