# What are the arguments for gravity not being a force? (in quantum gravity)

In quantum gravity the standard assumtion is that gravity is a force, although there is a small but persistent group of theorethical physicists who think otherwise.

What gives us the motivation to dismiss the graviton and go for the unortodox theories such as loop quantum gravity, causal dynamical triangulation or any emergent gravitation?

What is wrong with mass being a charge analoguosly to electromagnetism? To me it does not seem undesirable just yet. Is the non-renormalizability regarded as a technical issue or a fundamental one? Most importantly:

Is it reasonably proven(or assumed) that one cannot quantize gravity preserving Lorentz-invariance and the equivalence principle without introducing further non-quantum ugliness(such as compactified extra dimensions)?

reason for asking is:I am trying to learn the motivations for alternative theories of gravitation(those that do not contain a graviton at all)

• What are the orthodox theories of quantum gravity you contrast against? Regarding your question, as a first hint, I'm 100% sure StackExchange contains a list with Luboš reasons not to like blasphemous approaches like that. At first glance, I see a related link with 140 and one with 19 upvotes. – Nikolaj-K Dec 18 '13 at 18:34
• by ortodox I mean those that contain a massless spin-2 boson at some point, which is expected to reproduce GR, I'm asking, why would someone consider this undiserable after all? – Jani Kovacs Dec 18 '13 at 18:41
• @JaniKovacs: Because it isn't renormalisable? – John Rennie Dec 19 '13 at 10:28
• I thought it is just an everyday difficulty, like general relativistic n-body simulation etc. – Jani Kovacs Dec 19 '13 at 11:13
• If non-renormalizability indicates a fundamental inconsistency, that would be an answer. – Jani Kovacs Dec 19 '13 at 11:17

Gravity according to general relativity (classically) partially shapes the topology of the spacetime on which it exists. This is evident from the Einstein field equations, $R_{\mu\nu} - {\textstyle 1 \over 2}R\,g_{\mu\nu} = {8 \pi G} T_{\mu\nu}$, where I have used natural units, $c=1$. In quantum gravity, one expects a similar sort of relation to hold, i.e., the matter density $T_{\mu\nu}$ is quantized, and the Einstein field equation works for eigenvalues of the energy-density operator. Obviously, gravity is not a force in the normal sense. (Compare to the Maxwell tensor: $F:=\mathrm{d}A+A\wedge A$, which is modelled on the spacetime, not as an intrinsic property of spacetime itself). That is the reason quantum gravity theories are so difficult to come by. Another reason is that they are non-renormalizable.
As to the question of the graviton - I am not sure. There are many different approaches to quantum gravity, and while some predict a massless spin 2 boson, some don't. Example - string theory and loop quantum gravity respectively. My personal belief is in the nonexistence of a spin 2 boson, since I am a differential geometer and believe more in the geometrical aspects of GR than the force aspects. Of course, if GR is proved to be a gauge theory (such as LQG with the Yang-Mills gauge group $SU(2)$), then a massless gauge boson (of spin 2) would be needed in QG and I would be wrong.