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5 years ago in Mathematics , Physics By Mathew

Is there an equivalent of Gödel’s incompleteness theorem in physics?

My interdisciplinary work sits at the boundary of mathematical logic and theoretical physics. Gödel's theorems profoundly changed our view of formal mathematical systems. I'm curious if physicists have identified a truly analogous, provable limitation within our theories of nature a point where physics becomes "incomplete" or "undecidable" in a rigorous, Gödelian sense, not just due to practical complexity.

PhilosophyofPhysics TheoreticalPhysics GödelsIncompletenessTheorems

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By Neethi Answered 4 years ago

This is a profound and active area of inquiry. While there's no single, universally accepted exact analogue, I would point you to several compelling candidates. I've seen fascinating work on the uncomputability of certain outcomes in quantum field theory and the undecidable problems that can arise in lattice models. Some researchers argue that a final theory of quantum gravity might contain logical paradoxes for observers within the universe. The consensus, in my experience, is that computational irreducibility and undecidability appear in physics, but framing it exactly as a Gödelian "incompleteness" for physical law is still an open, meta-theoretical challenge.

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Is there an equivalent of Gödel’s incompleteness theorem in physics?

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