andrew
11.8K posts

andrew
@andrewbaums
theoretical physicist (strings ➡️ bio) | professional poser | he/him






Speaking of mathematical consistency. While you want a physical theory to be mathematically consistent, it's not necessary for it to be useful. The standard model without the Higgs eg violates unitary beyond a certain energy. That's not consistent. It's still a useful theory to very good approximation below that energy. And just because a theory is mathematically consistent doesn't mean it has anything to do with reality. There is nothing specifically wrong, for example, with gravity in 1+1 dimensions -- it's even quantizable -- it just doesn't describe the world that we live in. Hence, mathematical consistency is neither necessary nor sufficient for a physical theory. That said, as I explained in my book "Lost in Math", mathematical consistency has historically been a good guide in theory development. If you look at the cases where breakthroughs have been made on theoretical grounds, these came from resolving inconsistencies. Eg: General Relativity, the Dirac Equation, the Higgs-Boson! Still, you need experiment after that because there are always many ways to achieve mathematical consistency. The problem with research in quantum gravity has been that for decades they focused exclusively on consistency and neglected the need for experimental test. (Interesting in itself, as one may ask why that happened.) That is changing now, which is an excellent development that gives me much hope. So, brief summary: Consistency is neither necessary nor sufficient, but it's useful.



Speaking of mathematical consistency. While you want a physical theory to be mathematically consistent, it's not necessary for it to be useful. The standard model without the Higgs eg violates unitary beyond a certain energy. That's not consistent. It's still a useful theory to very good approximation below that energy. And just because a theory is mathematically consistent doesn't mean it has anything to do with reality. There is nothing specifically wrong, for example, with gravity in 1+1 dimensions -- it's even quantizable -- it just doesn't describe the world that we live in. Hence, mathematical consistency is neither necessary nor sufficient for a physical theory. That said, as I explained in my book "Lost in Math", mathematical consistency has historically been a good guide in theory development. If you look at the cases where breakthroughs have been made on theoretical grounds, these came from resolving inconsistencies. Eg: General Relativity, the Dirac Equation, the Higgs-Boson! Still, you need experiment after that because there are always many ways to achieve mathematical consistency. The problem with research in quantum gravity has been that for decades they focused exclusively on consistency and neglected the need for experimental test. (Interesting in itself, as one may ask why that happened.) That is changing now, which is an excellent development that gives me much hope. So, brief summary: Consistency is neither necessary nor sufficient, but it's useful.

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