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First of all I, it is my understanding that the problems one encounters with the

ID: 1375262 • Letter: F

Question

First of all I, it is my understanding that the problems one encounters with the non-renormalizability of gravity are very similar (if not the same) as one encounters in any non-renormalizable theory. As long as you are doing your calculations well-below the scale that suppresses irrelevant operators your calculations should make sense. As you approach that scale that suppresses irrelevant operators there is new physics that comes in at that scale - if you try to push your effective theory to the scale of new physics, perturbation theory will break down. This to my knowledge is the story that underlies the failure of Fermi-theory that necessitates introducing W bosons, and the failure of the standard model with out a higgs that necessitates the introduction of a higgs.

My questions is, is gravity, a priori, any different then the above 2 scenarios? That is, we need new physics to come in at the planck scale to UV complete the theory (or, put it another way, unitarize graviton scattering), but could it be as simple as one to a few new particles? Or for other reasons does it have to be something as drastic as String Theory or Loop Quantum Gravity? By drastic I mean paradigm shifts where its not some small modification to the current theory consisting of a few new particles, but more of an complete overhaul.

Explanation / Answer

First of all, loop quantum gravity is a model inconsistent with the existence of the spacetime, gravity, and Lorentz invariance. It doesn't solve any problem with the non-renormalizability of general relativity, either. Instead, the problem of infinitely many counterterms reappears in the infinite number of ambiguities in the "canonical Hamiltonian". See e.g. this most cited loop quantum gravity paper of 2005 and a related paper from 2006:

http://arxiv.org/abs/hep-th/0501114
http://arxiv.org/abs/hep-th/0601129

So we're only talking about string/M-theory here because it's the only known and probably the only mathematically possible consistent quantum theory that includes gravity.

This was a rudimentary correction of a misleading statement in the original question.

Now, to answer the question, general relativity differs from Fermi's theory or a Higgsless theory of massive gauge bosons because in those QFT examples, a consistent short-distance completion that is a local quantum field theory itself exists. In both examples, one finds massive particles at a high scale