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Loop Quantum Gravity (LQG) is a theory of quantum space-time that attempts to describe the interconnection between general relativity and quantum mechanics. It's main postulate is the granularity of space on the quantum scale. Though, is there an experiment that can disprove it?

Some ideas of an experiment:

  1. How can we test for the granularity of space and is there any feasible experiment that can be able to test this hypothesis of LQG in the near future?

  2. Are there any consequences of LQG that have already been experimented with and exploited in that they can be potentially disproved with a similar subsequent experiment?

  3. What are some theories of quantum gravity that explore the same or similar framework as LQG, and are there any experiments that can disprove those theories which will also impact LQG?

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So, "phenomenological quantum gravity" is the particular field where we consider experimental tests of quantum gravity (with the hopes of winnowing the 3 dozen competing theories down to a handfull). To the best of my knowledge, Giovanni Amelino-Camelia pioneered the field (c.f., Amelino-Camelia's review article).

At any rate, when focusing on loop quantum gravity, there have been a few preprints. Most deal with the phenomology of loop quantum cosmology, but this one appears more general:

  • Florian Girelli, Franz Hinterleitner, Seth A. Major, "Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics". Eprint

I think it's precisely what the OP is looking for...

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First of all, Loop Quantum Gravity doesn't postulate the granularity of space: it's a logical consequence of the canonical quantization of Einstein's Lagrangian and it's associated whit the spectra of the Volume operator (for mathematical details take a look at these lectures https://arxiv.org/pdf/gr-qc/0210094.pdf). Now, a minimum length doesn't imply that Loop Quantum Gravity violates Lorentz symmetry: it's the same as saying that discrete eigenvalues for the angular momentum violate rotational invariance(!); so you can' t look for Lorentz violations in order to disprove the theory. Anyway, a lot of work has been done in order to derive results which can verify or falsify LQG. In LQC (the application of LQG to Cosmology) the factor scale of the FRW metric doesn't vanish leading to a bounce-phase which can in principle be detected today (see https://arxiv.org/pdf/1308.4348v2.pdf); not only this, applying LQG to black holes shows that they decay whit a life-time, emitting radiations which in principle can be detected. (be careful, it's a different process from Hawking radiation, for more see https://arxiv.org/pdf/1605.05268.pdf)

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Please correct me if I'm wrong, but I thought that no one had been able to show how General Relativity (GR) emerged from LQG in the semi classical limit ? In this context, it may make sense to ask for experimental manifestations but to me it would seem more important to make sure first that LQG gives in some limit a classical theory of gravitation before all.

String theory, which describes a theory of quantum gravity, treats short distances by means of so called dualities; if you try to probe distances smaller than some scale, you obtain the exact same physics as the one at larger scales (this is called T-duality). So it has a minimal distance, as you would expect somehow from quantum gravity, though it includes it in a continuous manner.

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  • $\begingroup$ 1)What deals string theory with this question? 2) The procedure of semi classical limit is not straightforward and needs a mathematical definition, what do you mean by it in the context of LQG? $\endgroup$ – Yildiz Jan 3 '17 at 23:45
  • $\begingroup$ @Yildiz: Point 3 in the question asked about other approaches to quantum gravity, which string theory is. By semi-classical limit the physicist means starting from a quantum model for gravity and showing that it implies in any way a classical smooth space-time (or semi-classical) with Einstein's equations. The spirit of my answer was simply that if you don't even know if a candidate theory of quantum admits gravity as a consequence in some way, then any experiment compatible with gravity naively disproves it. $\endgroup$ – picop Jan 11 '17 at 14:31
  • $\begingroup$ Personally I don' t understand why it's so important to have General Relativity as "semi-classical limit". Given a hypothetical theory of quantum gravity, It could be the same as trying to derive the Navier-Stoke equations for a fluid using only the Schroedinger equation, for every molecule in the fluid, as a fundamental law. I am working on Loop Quantum Gravity and it seems to me that this is the case; anyway there are many indications that LQG has GR in some proper limit, for example it has been derived the graviton propagator, see arxiv.org/abs/gr-qc/0604044 $\endgroup$ – Yildiz Jan 11 '17 at 14:46
  • $\begingroup$ It's not so simple to derive a semi-classical limit of a theory: in quantum mechanics you can't just set $\hbar$ to 0; not only this: I have never seen Maxwell equations derived from QED in a straightforward way, so does it mean that QED is wrong? No. $\endgroup$ – Yildiz Jan 11 '17 at 14:56
  • $\begingroup$ And honestly, in string theory you have extra dimensions while GR is formulated in four dimensions: a "conservative" could say that string theory hasn't GR has semi classical limit. $\endgroup$ – Yildiz Jan 11 '17 at 15:06

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