# What are the remaining obstacles to low-energy quantum gravity?

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In a 2003 review Burgess outlined how the QFT perturbative methodology is being extended to gravity, and described some effective quantum gravity expansions that reproduce general relativity in the lowest order, and provide quantum corrections. My question is what were the developments during the last decade, and what remaining issues prevent including such effective quantum gravity into the Standard Model on the same terms as say QCD?

Of course, gravity is non-renormalizable, but after Weinberg renormalizability is considered a mathematical convenience rather than a must, it is nice to have, but... In both renormalizable and non-renormalizable theories it is the cutoff that removes the divergencies and blocks high energy degrees of freedom whose "true" theory is unknown. Burgess writes that "non-renormalizable theories are not fundamentally different from renormalizable ones. They simply differ in their sensitivity to more microscopic scales which have been integrated out".

One problem with the older semi-classical gravity was that when one couples quantum fields to the classical metric tensor of general relativity it becomes possible to track quantum observables through changes in the tensor, so the uncertainty principle is violated. Conservation laws are also violated, see e.g. Rickles (p.20). Does effective quantum gravity avoid these problems? Burgess also mentions that even the leading quantum corrections might be too small to detect. Is it still the case, and is that where the main problem is?

EDIT: Low Energy Theorems of Quantum Gravity from Effective Field Theory (2015) by Donoghue and Holstein seems to be relevant, it draws direct analogy to QCD:"In QCD at the lowest energies there exist only light pions which are dynamically active and the interactions of these pions are constrained by the original chiral symmetery of QCD. The resulting effective field theory — chiral perturbation theory — has many aspects in common with general relativity". But they only treat gravitational scattering.

This post imported from StackExchange Physics at 2016-02-11 14:37 (UTC), posted by SE-user Conifold

edited Feb 11, 2016
The point of renormalization is not simply to remove divergences but to gain a model that is described by a finite number of physically meaningful parameters. A model that can paint a duck in the detector today and a crocodile tomorrow is completely useless. If what you end up with at the end of the day is a forcefully regularized model with a cutoff, that's nothing else than the admittance that you have absolutely no idea what is really going on while you are shoehorning.

This post imported from StackExchange Physics at 2016-02-11 14:37 (UTC), posted by SE-user CuriousOne
@CuriousOne Nonetheless non-renormalizable theories are now routinely admitted, and even renormalizable ones are known to have non-renormalizable low-energy reductions, so there is no avoiding them. If I understand Cao and Burgess correctly restrictions on effective theories that make them physically sensible are far broader than renormalizability, and in EQG in particular the terms of perturbative expansions are more or less uniquely determined, it is no string theory.

This post imported from StackExchange Physics at 2016-02-11 14:37 (UTC), posted by SE-user Conifold
And by "admitted" you mean confirmed experimentally or just "admitted on the basis that they look mathematically interesting even though they don't tell us anything that we can compare with nature"? If it's the latter, I have to pass. As far as low energy is concerned... low energy physics is usually called chemistry, biology etc.. Absolutely nobody expects QFT to predict Darwinian evolution from first principles.

This post imported from StackExchange Physics at 2016-02-11 14:37 (UTC), posted by SE-user CuriousOne
Fermi's theory of CP violating weak interactions is non-renormalizable, it was experimentally confirmed. And "low energy effective theory" is a standard term in physics as you well know. Is there a point to this?

This post imported from StackExchange Physics at 2016-02-11 14:37 (UTC), posted by SE-user Conifold
Nothing stops you from fitting Newton's 1/r potential with a high order polynomial, either. Yeah... it does have real problems at large and small radii, but who cares? At least it almost works... in the middle, if we play with its 200 coefficients enough to fit the solar system orbital data for a couple of months. Wait... didn't they do something like that in the past? Wasn't that called "epicycles" or something?

This post imported from StackExchange Physics at 2016-02-11 14:37 (UTC), posted by SE-user CuriousOne
May I step in as a neutral referee (I've performed and published research calculations with renormalizable theories and with non-renormalizable theories). If you are looking for a final answer then wait for a renormalizable theory. That worked out very well for QED and QCD and the Standard Model to a lesser extent. If you are looking for something to do in the meantime then study effective theories. That is somewhat of a "shut-up and calculate" answer but there are times when it is necessary and not entirely meaningless.

This post imported from StackExchange Physics at 2016-02-11 14:37 (UTC), posted by SE-user Lewis Miller
@Lewis Miller I thought that people do not believe that renormalizable gravity is promising, both string theory and LQG are looking for a "final" theory not in QFT form. But so far they face a lot of issues, it seems that this low energy effective gravity might be a bridge to resolving some of them in simpler context.

This post imported from StackExchange Physics at 2016-02-11 14:37 (UTC), posted by SE-user Conifold
@Conifold I'm not going to disagree.

This post imported from StackExchange Physics at 2016-02-11 14:37 (UTC), posted by SE-user Lewis Miller

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