Are there any theories of quantum gravity that don't incorporate gravitons?
No, there aren't any theories of quantum gravity that don't incorporate gravitons, but that's just because there aren't any theories of quantum gravity
Basically there are pretty generic arguments to the effect that it's not possible to couple classical and quantized fields to each other. E.g., Bohr wanted the atom to be quantized and the electromagnetic field to be classical, but that really doesn't work; you'd be able to violate conservation of energy because without quantum-mechanical correlations more than one atom could absorb the energy from the same light wave.
It's conceivable that if you're creative enough, you could get around this: Carlip, "Is Quantum Gravity Necessary?," Class.Quant.Grav.25:154010,2008, http://arxiv.org/abs/0803.3456
How about if we consider quantum gravity as an effective field theory (just like QED)? Something like http://arxiv.org/abs/gr-qc/9512024 or http://relativity.livingreviews.org/Articles/lrr-2004-5/ [Broken]?
That part was a joke, hence the emoticon. I was emoting, really ... visualize me as William Shatner and that'll be about right.
I think LQG-ers are starting to refer to LQG as a "theory" now. Not sure if string "theory" really deserves the name yet -- maybe it should be called "string framework."
On a tangentially related topic, even though gravitons presumably exist, there is essentially zero chance of ever detecting them directly: http://arxiv.org/abs/gr-qc/0601043
Well. that's what you get for making a subtle comment:) I missed the "don't" on first reading.
Sometimes people talk implicitly about QG as meaning a bona fide "quantum
theory" of the gravitational field, ie. like the name suggests "quantum gravity". So the question becomes, to quantize or to not quantize.
But the interesting part is wether a "bonafide quantum theory" including gravity is possible, or rather what is MEANS? QG also means unifiying two frameworks. In this context, the question of gravitons seem superficial.
If a graviton is a quantum of the gravitational field, you need a background context to define it. This is how things are always done in regular QFT. You need somehow a controlled background that allows asymptotically controlled properties. In bonafide quantum theory this background is classical. And it's similarly obvious that the quantum theory itself, depends on this split.
> it's not possible to couple classical and quantized fields to each other.
I think somehow, the relation between classical and quantum is what we don't understand. Somehow, it seems to me they MUST couple, right - but how? To do away completely with the "classical part" means doing away with the background and this is not possible because then we also do away with the defining context of measurement theory in the first place. Measurements are supported by the background. Instruments and information are encoded in a classical environment in any bonafide quantum theory.
What are the arguments for the case of the gravitational field? For the electromagnetic field, they are relatively easy and clear, but for gravity I have not seen anything convincing. I even asked the question elsewhere but didn't get any useful answers. In fact I was accused of being a non-believer in quantum gravity)
I apologize if we're on different pages but for example, this problem is manifested in string theory as the topology change where one can trade in gravitons relative to a background, for a different background. However the possible physics beyond such background independent forumlation in ST is still unclear to me.
So it's not that the background dependence of gravitons that is the question (this seems obvious), it's more how to wrap up the picture where you can use this process to adapt excitations in the background, and understand the evolution in such a picture.
In such a picture, indeed the classical and quantum somehow mix, but we don't understand how. Note that this duality between classical and quantum and exciting the background isn't dependent on string theory. One can talk about this in general terms (which I aim at here).
It's the same argument.
E&M version, in more detail: Suppose a classical EM wave carries a certain amount of energy. The wave sweeps across both atom A and atom B. Let's say that the intensity of the wave is such that A and B each have 50% probability of absorbing the wave. With 25% probability, both A and B absorb the wave, which violates conservation of energy. To preserve conservation of energy, you need quantum-mechanical correlations in the wave that cause A not to absorb it if B did.
The gravitational version is exactly the same. Just change "EM wave" to "gravitational wave."
I'm pretty sure that physicists incorporate gravitons because the other three forces all have particles that transmit their energy. (sorry that's worded poorly).
Ex. E&M is transmitted by photons
The obvious difference is that EM, weak and strong are defined relative to a background geometry/space.
But since gravity "is" space/geometry this same trick only works when you make an artificial split between what one may call asymptotic geometry and local geometry which is treated as a perturbation on the asymptotics. This works when you study a small subsystem, and you have a controlled environment which effectively encodes the asymptotic properties. This subsystem assymmetry we always have in cases where SM is tested. The interaction domain is small (< molecular scale).
Now, partly one can imagine this trick also for stuff like microscopic black holes, which are then defined as local distortions relative to the ambient field. But this does introduce an artificial split between background and disturbance.
Given this difference, it's not clear that it's conceptually sound to think of bonafide quantization of gravity the same way as we do with other fields. The formal similarity when you quantize a perturbation doesn't IMO mean it makes sense.
Are you arguing that a graviton may not need to exists (gravitational field doesn't need to be quantized), or that we need to look at quantization differently?
The latter - we should look at quantization differently.
This logic applies to photons and any other particles for that matter not just gravitons. In the presence of strong gravitational fields particles of all types lose their meaning. Fields are fundamental not particles. Quantum theory does predict that fields will exchange energy in discrete quanta though. Also when the gravitational force enough gets weak then the particle interpretation of quantum field theory always presents itself so gravitons will emerge at least as low energy effective degrees of freedom.
In the end though a full non-perturbative sum over all histories and geometries is how QFT is defined with no special role played by any background field. So taking this as a starting point for quantum gravity as is done in CDT and AS approaches does not require that we need to invent a new quantisation. At least not for these reasons.
I do agree that we have to look at quantisation differently. But QFT is a powerful framework which has not yet been fully explored non-perturbativly. So QFT itself is not sick only some of the preferred tools for studying it e.g. perturbation theory IMHO.
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