in 2015 a Nature paper literally titled “Undecidability of the spectral gap” showed that an important physical quantity—the difference in energy between ground state and the initial excited state of a material—is formally undecidable. It is also triggered by recursion (basically, they encode questions about spectral gaps into spectral gaps). [Quoted from Erik Hoel’s 2024 post on Consciousness as a Godel Sentence]
Worst case, our laws of physics seem to be turing-computable.
in 2015 a Nature paper literally titled “Undecidability of the spectral gap” showed that an important physical quantity—the difference in energy between ground state and the initial excited state of a material—is formally undecidable. It is also triggered by recursion (basically, they encode questions about spectral gaps into spectral gaps). [Quoted from Erik Hoel’s 2024 post on Consciousness as a Godel Sentence]