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I Recent paper Asymptotic safety in quantum gravity

  1. Sep 19, 2016 #1
    Quantum gravity on foliated spacetime - asymptotically safe and sound
    Jorn Biemans, Alessia Platania, Frank Saueressig
    (Submitted on 15 Sep 2016)
    Asymptotic Safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which controls the scaling of couplings and correlation functions at high energy. In this work we use a functional renormalization group equation adapted to the ADM-formalism for evaluating the gravitational renormalization group flow on a cosmological Friedmann-Robertson-Walker background. Besides possessing the UV-non-Gaussian fixed point characteristic for Asymptotic Safety the setting exhibits a second non-Gaussian fixed point with a positive Newton's constant and real critical exponents. The new fixed point alters the phase diagram in such a way that all renormalization group trajectories connected to classical general relativity are well-defined on all length scales. In particular a positive cosmological constant is dynamically driven to zero in the deep infrared. Moreover, the scaling dimensions associated with the universality classes emerging within the causal setting exhibit qualitative agreement with results found within the ϵ-expansion around two dimensions, Monte Carlo simulations based on Lattice Quantum Gravity, and the discretized Wheeler-deWitt equation.

    Seems like Asymptotic safety in quantum gravity is making good progress, apparently progressing faster than either strings or loops, as a predictive theory. i.e prediction 126 gev higgs mass, 4 dimensions, no SUSY, etc. What are the implications if Asymptotic safety in quantum gravity is the final theory of quantum gravity?

    Asymptotic safety in quantum gravity seems to avoid many of the issues of string theory reliance on higher dimensions and thus far unobserved supersymmetry. it also seems to avoid issues of LQG with semiclassical limit and lorentz invariance and coupling to SM QFT fields.
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  3. Sep 21, 2016 #2


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    I think the AS assumes 4 dimensions rather than predicting them; I don't think that dimensionality is an emergent property in AS. Progress on the cosmological constant is encouraging. I would look to see a chart demonstrating the running of the coupling constants in the SM with and without AS.

    Not implicating supersymmetry or extra dimensions are strong points. Predicting the Higgs mass isn't bad but also shouldn't be overstated since there were so many efforts and other predictions (even in the same group) predicting the Higgs mass using AS methods were way off the mark.

    What I haven't seen any clear explanation of, however (which is not to say that it doesn't exist), is how AS resolves what is arguably the biggest problem with QG, the non-renormalizability of a naive QG theory. Maybe I'm being an idiot here and the asymptotic safety (i.e. not allowing the UV part of the theory to run to infinity) is precisely what makes that possible, but I had thought that there was more to it. I had also thought that doing any quantum gravity calculations was even tougher than doing calculations in QCD which scientists have spent a generation bringing to the point where those calculations can have 1% precision, which would imply that even if AS was correct that it would be pretty much useless except for qualitative predictions and a few highly stylized calculations.

    I would argue that the coupling to SM QFT fields are not, in fact, a serious problem with LQG and instead is something that flows pretty naturally from LQG relative, for example, to string theory or other TOEs where reproducing the SM is real challenges that spoil the prize of getting a theoretically consistent theory of quantum gravity.

    Formulating a space-time based quantum gravity like LQG or causal sets or what have you without breaking Lorentz invariance is a serious issue, although I think that there might be some natural way of addressing it that integrates the crazy mystery that a proper path integral for the propagation of a photon in QED requires consideration of paths across which the particle is propagating at c+ϵ and c-ϵ for all possible values of ϵ, albeit with a weighting in the total calculation that becomes vanishingly small the larger that ϵ becomes. This would be consistent with an LQG-like space time in which points in space-time are not perfectly continuous and local, because there are some non-local connections (whose probability of existing declines with classical distance) because in LQG models, both dimensionality and locality are emergent rather than fundamental properties of space time.

    Also, ultimately, it may be that an LQG-like theory needs to make distance traveled by a particle in its own reference frame discrete, rather than making space-time itself discrete. In other words, it might make sense for the LQG space-time quanta themselves to be something that Lorentz transformations modify in some mathematically sensible manner.

    This may even verge into the research effort to see if it is possible to mere the SM into a semi-classical GR theory in a minimalist manner that resolves the theoretical inconsistencies between the SM and GR without actually making gravity itself a quantum theory. Maybe we can't formula quantum gravity because it does not and cannot exist for some reason.
  4. Sep 21, 2016 #3

    whats your fav approach to qg? btw

    your suggestion sounds a lot like this

    Emergence of string-like physics from Lorentz invariance in loop quantum gravity
    Rodolfo Gambini, Jorge Pullin
    (Submitted on 10 Jun 2014)
    We consider a quantum field theory on a spherically symmetric quantum space time described by loop quantum gravity. The spin network description of space time in such a theory leads to equations for the quantum field that are discrete. We show that to avoid significant violations of Lorentz invariance one needs to consider specific non-local interactions in the quantum field theory similar to those that appear in string theory. This is the first sign that loop quantum gravity places restrictions on the type of matter considered, and points to a connection with string theory physics.
    Comments: Honorable mention Gravity Research Foundation 2014, 7 pages
    Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
    Journal reference: International Journal of Modern Physics D 23, 1442023 (2014)
    DOI: 10.1142/S0218271814420231
    Report number: LSU-REL-061014
    Cite as: arXiv:1406.2610 [gr-qc]
    Last edited: Sep 21, 2016
  5. Sep 21, 2016 #4


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    Interesting paper.

    Forgive me for omitting detailed citations to this sprawling answer to your question as it would take many additional hours to do so and would probably exceed maximum comment size in this format as well.

    I am interested in many approaches to quantum gravity and I am more interesting in their consequences than the particular approaches used, a subject upon which I am largely agnostic. And, this is a useful stance to have when improving astronomy instrumentation from gravity wave detectors to space satellites, make it plausible that we'll have a lot more empirical data to inform our analysis even within my own lifetime and definitely within the lifetime of my children. This data will rule out all manner of speculative theories that anyone who wants to think about quantum gravity and modifications to classical gravity must consider today.

    I see pros and cons to graviton based approaches (like SUGRA and string theory), and to space-time based approaches (like LQG and causal sets). I see virtues to efforts to fit the SM into semi-classical gravity similar to GR and classical gravity modification theories such as f(R, T) theories. SUGRA and string theory end up in the dog house from my perspective mostly because they propose too many new particles that have not been observed, not because their approaches to the problem of quantum gravity itself are bad.

    I see how massive graviton theories can be fruitful, even though I don't really believe that gravitons are massive, because massive graviton theory can reproduce phenomena similar to those that would arise from including the energy of gravitons in the stress-energy tensor, even though the analogy isn't perfect, in a rigorous way that escapes the dogma and no go theories of standard GR for massless gravitons.

    I find the usefulness of renormalization in formulating asymptotic gravity theories suggestive. My intuition also suggests that the fact that the peak density of stellar sized objects (neutron stars and the smallest stellar black holes measured on a mass per volume within the event horizon basis) is on the same order of magnitude as the most dense atomic nuclei is a meaningful hint suggesting some sort of asymptotic limit in gravity. In particular, I am interested in formulations of quantum gravity or modified classical gravity theories in which objects with densities greater than the smallest possible stellar black holes are not just impossible to create in the modern era, but are actually fundamentally forbidden by the laws of nature for some reason (hence ruling out primordial black holes, a conclusion that leads to a lot of cosmology consequences in the early universe), something that would naively seem easier to incorporate in space-time based approaches. Density as opposed to energy scale seems like a natural way to formulate an asymptotic gravity theory, although it does make linking it to the SM a less obvious endeavor.

    Another interesting concept from space-time based approaches is the notion of particles as intensely interconnected packets of space-time, such that matter is part of space-time as opposed to something that exists in space-time. This too naturally melds well with space-time based approaches to quantum gravity. And, the notion that the number of dimensions in space-time and locality are both emergent in LQG type theories is also very alluring.

    The holographic principle is also fascinating although it is hard for me to discern how it could be traced back to mastering quantum gravity in a manner that discriminates between one approach and another.

    When you look at string theory, in which non-gravitational forces are confined to a 4-brane and the other 6 or 7 dimensions are accessible only to gravity, I see a pretty extravagant cheat whose main purpose is to cause gravity to be sufficiently weak, and I am highly skeptical that this is really necessary, even though I do grok to some extent the attractiveness of string theory as a quantum gravity solution. I also wonder if string theory isn't confounding the definition of dimensions as orthogonal degrees of mathematical degrees of freedom with a more conventional notion of the three dimensions of time and one of space. There are lots of quantities one can assign to an area of space in conventional physics (e.g. temperature, EM field strength) that allow you to assign many numbers to any given point in space-time that aren't obviously connected even though it turns out that many of these numbers that seem to be fundamental can actually be derived from something else if you go so deep into the fundamentals that concepts like temperature and EM fields as opposed to photons, become meaningless.

    My strong suspicion, a more respectable term would be a conjecture, is that a correct theory of quantum gravity will differ from general relativity in the weak field limit in a manner that explains dark matter phenomena (and perhaps some significant part of dark energy phenomena as well).

    I further suspect that this would arise in a quantum gravity theory primarily from the correct modeling of graviton-graviton interactions, and at a classical level, from a modification to GR that changes how a gravitational field interacts with itself in a class of theories that at their most general level are known as f(R, T) theories.

    Another class of modifications to classical GR that intrigue me as possible classical limits to GR are formulations that incorporate higher order derivatives (perhaps even infinitely) to classical GR. GR has only first and second derivatives in it and it seems highly plausible to to me that higher order derivative terms may be necessary to include in a more fundamental and accurate modification of classical GR that like f(R, T) could differ from classical GR primarily in the weak field limit.

    And, I'm also interesting in classical limits in the nature of Bekenstein and Moffat's gravity modifications, each of which involve a scalar, a vector and a tensor term, which, by design, reproduce dark matter phenomena.

    I think that one of the reasons that coming up with a quantum gravity theory has been so challenging is that almost all of them are designed to have GR as a classical limit, when I strongly suspect that dark matter phenomena are evidence that, in reality, the classical limit of quantum gravity is not GR, but some other classical limit that is significantly different in weak fields, while closely matching GR in medium strength and stellar to galactic scale black hole strength circumstances, although it might also differ significantly from the classical limit of GR at the extremely high energies present at the time of the Big Bang and shortly thereafter.

    To give just a few examples of why I suspect that this is the case, GR is formulated in a manner that observes the conservation of energy globally, but does make it possible to determine the energy of the gravitational field locally. Yet, any quantum gravity theory formulated in a manner that uses gravitons as carrier bosons for the gravitational force necessarily contradicts this qualitative feature of GR. Similarly, I think that the omission of the gravitational field from the stress-energy tensor of GR is probably a mistake, although in cases other than those where the gravitational fields of standard GR are very weak, the consequences of that omission are usually negligible.

    Another problem with integrating GR and the SM is that the SM assumes point particles, but in GR point particles give rise to black hole singularities if they have any mass or energy, which by definition, all particles do. There are multiple ways to overcome this, but string theory is notable for having an elegant solution to this problem although I am skeptical that it is truly a unique solution, as some of the assumptions that go into the claim that it is unique are not obviously and necessarily true.

    I also strongly suspect that integrating gravity with the other three SM forces influences materially the running of the SM coupling constants at high energies in a matter that might even lead to gauge unification of the SM forces (although, then again, it might not). Even if it doesn't the resulting modification of the running of SM coupling constants is still very interesting, as is the possibility that the UV-limit may be a metastable rather than a stable one as asymptotic gravity theorists have suggested.

    There is a fascinating little physics poster that suggests how gravitationally bound systems of leptons could give rise to weak force bosons, and while it may just be numerology, it is intriguing enough to deserve further study.

    While quantum gravity is absolutely critical to understanding a lot of cosmology questions like inflation, baryogenesis, leptogenesis, and why matter in the universe is arranged in a bubble-like web of filaments around very empty areas of space that have the size and structure that they do, to be perfectly honest, I'm not terribly interested in the cosmology of the very early universe. My natural inclination is to trace back the history of the universe as far as the laws of nature as they function here and now will comfortably take us without modification (which is remarkably far, on the order of seconds after the Big Bang or less and includes nucleosynthesis), and then to accept whatever the circumstances were that require 'new physics" before then to explain what we see as initial conditions, and then to move on to other more pressing issues.

    In part, my lack of interest arises because I suspect that the only possible solution to questions like the matter-antimatter imbalance in the universe requires consideration of stuff happening outside the Big Bang light-cone that is unobservable, and hence effectively unknowable (but please spare us the blasted multiverse of universes where the laws of physics are different in each one . . . ).

    There are a lot of modifications of classical GR that primarily focus on explaining inflation and/or dark energy. But, a simple cosmological constant is such a good approximation of dark energy that this doesn't seem like a priority, and honestly, while there are all sorts of good reasons to be interested in the fundamental physics of inflation and its relationship to quantum gravity and/or modifications to GR, I just find it terribly hard to get excited about it. There are catalogs of literally hundreds of inflation theories out there and none of them are all that interesting.

    I have seen papers that attempt to integrate gravity into the SM by means of a gravity-weak force unification, and by means of analogy to the strong force, which are quite interesting, and it seems plausible to me that if any SUSY/SUGRA predicted particles exist that a gravitino counterpart to the graviton that served as a singlet dark matter candidate with spin-3/2 would probably be the most likely to exist.
    Last edited: Sep 21, 2016
  6. Sep 22, 2016 #5
    in the KKLT paper, the 6 extra dimensions are planck scale size and carry energy, so shouldn't they collapse and form a black hole?
  7. Sep 22, 2016 #6
    ohwilleke, the above description about matter part of space-time as opposed to something that exists in space-time. May I know who are the physicists who study (or studied) them except Einstein (which is the basis for the Unified Field Theory in which matter is part of spacetime)?
  8. Sep 22, 2016 #7


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    My favorite paper on this issue is this one: http://fqxi.org/data/essay-contest-files/Dreyer_fqxi2012.pdf

    Not on but of.

    by Olaf Dreyer

    Essay Abstract
    In physics we encounter particles in one of two ways. Either as fundamental constituents of the theory or as emergent excitations. These two ways differ by how the particle relates to the background. It either sits on the background, or it is an excitation of the background. We argue that by choosing the former to construct our fundamental theories we have made a costly mistake. Instead we should think of particles as excitations of a background. We show that this point of view sheds new light on the cosmological constant problem and even leads to observable consequences by giving a natural explanation for the appearance of MOND-like behavior. In this context it also becomes clear why there are numerical coincidences between the MOND acceleration parameter a_0, the cosmological constant Lambda and the Hubble parameter H_0.

    Author Bio
    Olaf Dreyer is a theoretical physicist working at the university in Rome. He received a PhD in Quantum Gravity at the Pennsylvania State University and has worked at the Perimeter Institute, Imperial College, and the MIT, where he was supported by an FQXi grant.

    Twenty-five more papers by the same author can be found at: http://arxiv.org/find/all/1/all:+AND+Olaf+Dreyer/0/1/0/all/0/1
  9. Sep 22, 2016 #8
    Very good. Do you happen to have read any paper where locality is just a classical limit of a fully nonlocal universe? Or special relativity just a classical limit of a nonlocal manifold?
  10. Sep 22, 2016 #9


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    The former is the basic concept behind a lot of LQG papers. I don't recall ever reading a paper treating special relativity as a classical limit of a nonlocal manifold, at least, not using that kind of terminology.
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