# Gravity as a non renormalizable theory

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malawi_glenn
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This makes me wonder just how fundamental and valid QFT as a framework really is, in general terms. I have only just begun studying QFT in recent weeks, so I'm still largely ignorant of the finer points and issues, but even in the most simplistic of textbook cases ( e.g. quantisation of Klein-Gordon fields ) there already seem to be fundamental issues and quite a bit of handwaving going on ("let's just subtract that infinity to fix that other infinity..."). I do not for a minute doubt or dispute the successes of the Standard Model in describing real-world physics, but the foundation this all stands on appears to me to be shaky and ad-hoc at best. Something just does not feel right about QFT to me; I can't put my finger on it, it's just a matter of intuition. I will keep learning, but there remains an itch that feels as if it badly needs to be scratched Am I the only one who feels that way ?
you have infinities in classical physics aswell. What is the potential energy for a system of two electrons positioned at the same point in space?

Could you give an observed example of such a system? It is an example beyond the scope of any kind of physics.

malawi_glenn
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Could you give an observed example of such a system? It is an example beyond the scope of any kind of physics.
why is it an example beyond any scope of physics?

If quantum mechanics is correct, then there is a nonzero probability that two electrons can occupy the same position in space.

In order to solve this - you introduce an electron-radius, two electrons can not occupy the same point in space due to their spatial separation.

In quantum field theory, you solve this problem differently. There you postulate that only the energy-difference is observable - you can not observe the "bare" energy. By considering energy differences only, the infinities are removed (renormalized)

In quantum field theory, you solve this problem differently. There you postulate that only the energy-difference is observable - you can not observe the "bare" energy.
Not true in GR.

Naive non-renormalisability is just one of many problems that arise if you try to quantise gravity. There are clashes between unitarity and locality at a deeper level. They manfest themselves for example in black holes. Naive approaches such as UV fixed points do not shed any light on these questions. This is naive QFT like thinking. You need to think broader than what you have learned from QFT textbooks.

What becomes more and more clear is that GR is an effective, emergent theory that should not be quantized as such. It does not make sense to stare at the GR lagrangian und agonise about how to quantize it and make sense of loops, etc. It should be the other way around: nature is intrinsic quantum, and sometimes, in some limits, there is a reasonably good classical approximation to it. It seems that eg in black holes, macroscopic (non-local) quantum effects play a crucial role, holography as well, and there is no obvious way to get to there from starting with the Einstein lagrangian, modifying it, guessing fixed points, discretizing it, etc.