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by zachf
1145 days ago
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This is one of those things that laymen often misunderstand, actually. (I don’t blame you, it’s often not well explained.) General relativity is easy to make into a QFT. There’s an action and you can easily derive amplitudes from it. And it works well, as long as you don’t ask questions of what happens at arbitrarily high energies. That’s what “nonrenormalizable” actually means: it only answers questions up to some energy scale, after which it stops being predictive. But believe it or not, physics has been here before, so we’re not totally clueless what to do! Fermi’s theory of beta decay [0] had the exact same problem. And the moral there was that there was something new that had been missed in Fermi’s theory that was only important at high enough energy. The theory was correctly predicting its own limitations. In fact we figured out what was missing. Fermi didn’t know about the W boson, and at the energy where W boson exchange becomes important, that’s where the old theory breaks down! But Fermi’s theory works well up to that scale. It’s like how Einstein’s relativity didn’t mean that everything in Newtonian physics was totally wrong, but just that you need it if you want to think about really fast moving objects. Newton’s theory is still an outstandingly good approximation. So if history is any guide, we don’t need to change the low energy theory of GR (at least not much), that works just fine. We just have to find out what’s the high energy phenomenon that we’re missing. That’s stuff that comes into play with black holes and very high energy collisions. Anyway we have some guesses here, too. In string theory, that’s the stringyness of the strings, their 2D nature, that fixes the problems automatically. (This was not by design, it was completely unexpected! You start playing with dimensions and it just falls out.) In LQG it’s about the fuzziness or discretization of space (which sounds appealing, although it’s really tough in practice to make this work). See also [1]. [0] https://en.m.wikipedia.org/wiki/Fermi%27s_interaction [1] https://en.m.wikipedia.org/wiki/Effective_field_theory |
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