Is it possible that there is no theory of quantum gravity?

Question

{{Under Construction}}

Short question: What published works and what research groups are investigating the possibility of non-existence of gravity at quantum level?

Long question: I am no physicist, but of what I read and understand of the subject, no-one has been able to fit the graviton into the standard model, it seems that the equations won't re-normalize, thus it would be useless for predictions. Gravity also is undetectable at the quantum level, it seems because the force is too small. Also, about every book about the subject traces a strong distinction between "quantum level" and "classical level", almost if they were different worlds that obey different laws of nature, and how they relate to each other is an open question. Finally, at least two sources I have seen state that Einstein's General Relativity is the most well verified theory of all physics, because of something related to pulsars.

Thus there are two distinct "worlds": in one gravity is pretty much settled, while in the other, it is neither detectable nor mathematically explainable in the most successful model. From that, the most logical and simple explanation I can have is that simply there is no such thing as quantum gravity, and that it is a purely classical phenomenon that arises from whatever may be the relation between both "worlds".

I like to imagine that space coordinates of both worlds are not quite the same, although very similar locally, thus, if classical world emerges from a projection of the quantum world, like a shadow, gravity is bumps in the surface where that shadow is projected (holographic principle comes in my mind now).

It doesn't seems to be the mainstream view of the problem, with millions of dollars spent in trying to find the mythical graviton (that is what a physicist of INPE, Brazilian's spacial research institute, told me yesterday). Thus, I want to know, what are the works, and what people shares with me this view of the problem?

Answer 1

The theory was put forward that semiclassical gravity (a classical gravitational field generated by quantum matter) was indeed the correct theory, something of the form

$G_{ab} = \langle T_{ab}\rangle$

With $G$ the Einstein tensor and $\langle T\rangle$ the expectation value of the stress energy tensor of the matter. It's a theory that works fine enough, but you encounter the following weirdness :

Get some matter in some state $\frac{1}{\sqrt{2}} |1\rangle + \frac{1}{\sqrt{2}} |2\rangle$ , where the state 1 is an energy distribution in some region of space, and state 2 is another energy distribution in a second region of space. The gravitational field will be that of half the energy in region one and half in region 2, or something along those lines.

Now perform a measure. The state collapse to $|1\rangle$, and now all the energy is in region 1. You just created a discontinuity in the gravitational field.

This by itself isn't enough to discard the possibility, but it is certainly suspiscious.

I seem to recall that some kind of experiment was performed in the 70's that involved a mass and torsion balance that would change depending on the result of a quantum measurement, and the experiment did not yield any result in favor of semiclassical gravity.

You might want to check those things, too :

http://backreaction.blogspot.fr/2012/01/real-thought-experiment-that-shows.html

http://papers.rqgravity.net/EppleyHannah.pdf

Edit : Also http://motls.blogspot.fr/2012/01/why-semiclassical-gravity-isnt-self.html

Answer 2

One may have many science fiction or fantasy projections of how physics might be. In the real world physics and physicists use mathematical theories as tools to model experimental observations.

Two landmarks guide the modelling of data at present .

1) The validation of Quantum Mechanics as the underlying framework that describes with great accuracy the microcosm of elementary particles and predicts with great accuracy future behavior in new experiments.

2) The formulation and validation, to a great extent, of the Standard Model of particle physics.

Number 1) has lead to the realization, in contrast to your hand waving shadows science fiction scenario, that all classical theories are emergent from the quantum mechanical level of fields and particle interactions. This emergence can be rigorously derived using mathematics, not words. Even before quantum mechanics it had been mathematically shown that Thermodynamics, a beautiful classical theory with its differential equations and postulates, emerged from statistical mechanics, the mechanics of large number of particles, again in a well derived mathematical manner.

Number 2) is within quantum mechanic and quantum field theory, but in addition the standard model uses the mathematics of symmetries arising from group transformations and gauge invariance. These symmetries under transformations exist in classical electrodynamics , but find their great usage in quantum electrodynamics and the behavior of elementary particles in forming the standard model of particles.

The success of the standard model and the symmetries it obeys guides the thinking of most physicists about General Relativity ( a classical theory) which also has similar symmetries . The goal is to have one unified model for all interactions at the quantum level, thus the proposal and search for the graviton as the corresponding particle to the photon of the gravitational interaction.

So it is the mathematical consistency of the validated experimentally models that describe the elementary particles that leads to the expectation of a quantized gravity. Call it a beauty postulate.

Another strong reason to expect quantization of General Relativity is that classically it has infinities, like the Big Bang and the black holes, singularities where values predicted to be measured go to infinity. This problem for electrodynamics was solved by quantum mechanics: the 1/r behavior of the potential between two charges lead to infinities/singularities which disappeared with the quantum mechanical formulation of quantized energy states. One may say that the classical "nature abhors a vacuum" has been transformed to "nature abhors infinities". In general terms it is the Heisenberg Uncertainty Principle connected to the probabilistic formulation of quantum mechanics that is the tool to control infinities. Thus one expects that a quantization of General Relativity will dispense with infinities/singularities.

For all these reasons I do not know, am not aware, of serious physicists working with assumptions of the order you imagine. There already exists a mathematical framework that accommodates both the group structures of the standard model and a quantized general relativity , string theories. In plural because as yet no unique successful model exists to be chosen out of a plethora of possibilities, but theorists are working on the problem. There do exist less popular researches on gravity which still quantize it but asking for discrete space time ( as loop quantum gravity) or 't Hooft's deterministic model but I believe anybody working with gravity accepts some form of quantization, mainly for the reasons stated above.

Answer 3

Following the link on Mitchell Porter comment, I found that there are at least 2 research branches followed by physicists (or maybe one is a generalization of the other) that deals with gravity as an emergent force from the interaction of the particles, and not a fundamental force itself:

• Induced Gravity
• Entropic Gravity

From both Wikipedia's articles and the reactions to this question, it seems that this idea faces strong resistance from physics community. Coincidence or not, the reaction seems pretty much like what Boltzmann faced in his time when upholding that entropy was a statistical thing, and that matter was made of molecules.