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Kyre comments on Crazy Ideas Thread - Less Wrong Discussion
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Use computers to discover the Theory of Everything.
(I am not a physicist, so what I say here is probably wrong or confused, but I am saying it anyway, so at least someone could explain me where exactly am I wrong. Or maybe someone can improve the idea to make it workable.)
As far as I know, (1) we assume that the laws of the universe are simple, (2) we already have equations for relativity, and (3) we already have equations for quantum physics. However, we don't yet have equations for relativistic quantum physics. We also have (4) data about chemical properties of atoms, that is, about electron orbitals. I assume that for large enough atoms, relativistic effects influence the chemical properties of the atoms.
The plan is the following: Let the computer explore different sets of equations that are supposed to represent laws of physics. That is, take a set of equations, calculate what would be the chemical properties of atoms according to these equations, and compare with known data. Output those sets of equations that seem to fit. Create a smart generator for sets of equations, that would generate random simple equations, or iterate through the equation space starting with the simplest ones. Then apply a lot of computing power and see what happens.
(Inspired by: Einstein's Speed, That Alien Message.)
Nitpick: we have equations for (special) relativistic quantum physics. Dirac was one of the pioneers, and the Standard Model for instance is a relativistic quantum field theory. I presume you mean general relativity (gravity) and quantum mechanics that is the problem.
In the spirit of what Viliam suggested, maybe you could do computational searches for tractable approximations to QFT for chemistry i.e. automatically find things like density functional theory. A problem there might be that you do not get any insight from the result, and you might end up overfitting.