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I Implications of validating loop quantum cosmology

  1. Aug 29, 2017 #21

    Urs Schreiber

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    The HOTW-paper explicitly discusses that FDM does fit "core aspects" of dwarf galaxies (search the article for this keyword). That's the point.

    The trouble with MOND is that while it is an equation that gives an excellent fit for a class of phenomena in a small range, it is completely inconsistent if promoted to a fundamental law of nature. As such it breaks relativity, conservation laws (besides giving ridiculous predictions outside that small range, as highlighted in Dodelson's "The real problem with MOND" ). If faced with this problem, people usually point out that MOND may be embedded into Bekenstein's tensor-vector-scalar gravity theory. But as the name suggests, "tensor-vector-scalar gravity" is standard gravity with... extra fields added, which must be argued to be otherwise unobserved. So it's just another kind of "dark stuff" theory, after all.

    A good historical analogue of the MOND formula is the Rydberg formula. At the time when it was proposed, it was the best formula in fitting certain atomic spectra while existing physical theory could not explain any of this. Still, the Rydberg formula is not a fundamental law of nature, instead it is an effect of a more fundamental theory, even if that fundamental theory was discovered only much later.

    While it may be fun to speculate that for the MOND formula that more fundamental theory is a de Sitter version of AdS/CFT, this argument is almost as hand-wavy as the argument for LQC from LQG. As long as there is no argument with a minimum of mathematical decency, something living up to the standards of 20th century theoretical physics, we can have endless speculation, but no conclusion.
     
  2. Aug 29, 2017 #22
    I have been very interested in Justin Khoury's attempt to obtain MOND from "axion-like particles" that form a galactic superfluid. In Berezhiani and Khoury 2015, the MOND law comes from phonons in the superfluid that couple to baryons, while in Khoury 2016, it just comes from the gravity of the superfluid.
     
  3. Aug 29, 2017 #23

    Urs Schreiber

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    Thanks for the pointers. I hadn't looked at these. That's of course another example of a fuzzy dark matter model that I was referring to above (there is a plethora of more or less synonymous terms for this idea, also "BEC dark matter" or "wave dark matter"). Lee's recent review mentions them all, though he does not seem to cite Khoury.
     
  4. Aug 29, 2017 #24
    do you have any theoretical objections then to a research program in which researchers stay with Ashtekar variable, then quantize them in a way you find acceptable. If "polymer quantization" is the wrong way to quantize Ashtekar variables, what would be the "correct" way to nonpertubative quantize Ashtekar variables? Is there a way to nonpertubatively quantize Ashtekar variables that is related to known physics.

    or formulating a theory of gravity say in terms of a gauge theory that reproduces GR in 4D, then quantizing that, quantizing in a way that is physically related to known physics.
     
  5. Aug 30, 2017 #25

    Urs Schreiber

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    That's the right question!

    Remember, as I mentioned a few times before, that not a single interacting field theory in dimensions 4 or higher has been non-perturbatively quantized yet. It's a major open problem. For the case of gauge theory (Yang-Mills theory) this problem is one of the "Millenium Problems" of the Clay Institute. So the same question for gravity might well be a "10^4 year problem". But every journey starts with the first step in the right direction, and so it's good to at least ask the right question.

    At least the problem description is understood:

    The usual perturbative quantum field theory in terms of formal power series of Feynman graphs is now known (due to Collini 16) to be the (Fedosov) formal deformation quantization of the covariant phase space induced by the given Lagrangian density (at least under favorable circumstances).

    This suggests that the non-perturbative quantization is what is called the "strict deformation quantization" of this covariant phase space (with gauge invariance etc. properly taken into account).

    This may or may not exist. If string theory is right, it probably does not exist for gravity, because in this case non-perturbative gravity is not a local field theory (possibly some string field theory, though). But it would be good to prove a theorem that this does or does not exist.

    Presently essentially nothing is known about this. It's a hard problem, but also essentially nobody has really looked into it. (LQG drew loads of attention away from the real problem.)

    There is one hint: Hawkins 06 has shown that plausible candiates of strict deformation quantizations of finite-dimensional phase spaces are nothing but the convolution algebras of the higher pre-quantized symplectic groupoids induced by the covariant phase space. My students Bongers and Nuiten have shown that this, in turn, is equivalently holography for the non-perturbative PSM topological string (master thesis Bongers and master thesis Nuiten). There is a subtlety with defining the symplectic groupoid relevant in field theory. If that could be solved, there would be a road towards non-perturbative quantization of field theory.
     
  6. Aug 30, 2017 #26
    Urs
    ever thought about writing a resesarch paper to this effect?

    if a research group were to successfully strict deformation quantizations of gravity expressed as Ashketar variables,
    1- what would be some qualitative features you would expect to see in a strict deformation quantizations of gravity expressed as Ashketar variables
    2- would you take it as a serious candidate theory of planck scale physics
    3- would certain issues such as resolving the semiclassical limit be easier to arrive at?
    4- how would strict deformation quantizations qualitative features be similar or different from the current polymer quantization?

    would you prefer LQC to also be done as a strict deformation quantizations?
     
  7. Aug 31, 2017 #27

    Urs Schreiber

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    Sure, when it's done I am going to claim the million dollar prize money ;-)

    Regarding your other questions: Beware, as I said, that it is not clear that strict deformation quantization of gravity will exist as an "non-perturbative effective field theory", but it would be very interesting to investigate the existence in its correct and precise form, something which has received almost no attention yet. If it exists, it should be independent of which variables are used to describe the phase space, though it might have more convenient expressions in one choice of variables or the other.

    You seem to be asking whether quantum gravity could be a serious candidate theory of planck scale physics. This sounds like a tautology to me, or else I am misunderstanding what you are after here.

    That's built into the very definition of "strict deformation quantization": This is a continuous deformation, parameterized by the value of Planck's constant, which interpolates continuously between the classical theory and the non-perturbative quantum theory at some finite value of Planck's constant (if it exists, that is).

    The concept of strict deformation quantization is a mathematically precise formalization of ordinary/standard/established/observed quantum theory. It's standard established physics, just phrased in precise enough terms to guarantee that everything makes sense and we don't trick ourselves into thinking we have found a quantization while in reality we didn't. That "polymer quantization" instead is an example of the latter error.

    What is called LQC is nothing but the proposal that the differential equation that describes FRW-like cosmological models is to be replaced by a finite difference equation. That this is the quantization of anything is a conjecture without any evidence.

    While we are waiting for non-perturbative quantization theory to develop, the next thing that should be done in quantum cosmology is probably clean discussion of perturbation theory of quantum fields (gravity plus other fields) on a classical curved background, as in BFHPR 16 . For instance I am being told that presently there is still a gap in the derivation of the nature of Hawking radiation of gravitons themselves.
     
  8. Aug 31, 2017 #28
    In context, i was asking if a "strict deformation quantization" of Ashketar variables could be a serious candidate theory of planck scale physics, since the discussion was that you regard polymer quantization to be unrelated to known physics, and that if Ashketar variables could be successfully quantized using "strict deformation quantization" instead of polymer quantization, what would be its qualitative features.

    would there still be spin networks, area and volume operators in "strict deformation quantization" of Ashketar variables?
     
  9. Aug 31, 2017 #29

    Urs Schreiber

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    Regarding the area operators in LQG polymer quantization: Their specific nature is directly connected to the polymer-style prescription, with a disconnected copy of SU(2) associated wiith each edge of a spin network, each being quantized separately.

    If you are looking for solid results that support the wide-spread intuition that quantum gravity will reveal that the nature of spacetime itself becomes fuzzy/quantized on small scales, I recommend
    which works out in technical detail how string field theory retains causal locality macroscopically albeit this being manifestly broken on the string scale.
     
    Last edited: Aug 31, 2017
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