Tuesday, March 25, 2014

Does nature hide strong curvature regions?

Quantum gravitational effects are strong when space-time curvature becomes large, so large that it reaches the Planckian regime. Unfortunately, space-time around us is barely curved. For all practical purposes, you sit in a flat space-time. This is why you don’t have to worry about post-post Newtonian corrections if you ask Siri for directions, but also why it takes some experimental effort to detect the subtle consequences of Einstein’s theory of General Relativity – and that’s the classical case. In the almost flat background around us, quantum effects of gravity are hopelessly small.

But space-time curvature isn’t small everywhere. When matter collapses to a black hole, the matter density and also the curvature become very large, and eventually, long after you’d been spaghettified by tidal forces, reach the regime where quantum gravitational effects are sizeable. The problem is that this area, even though it almost certainly exists inside the black holes that astronomers watch, is hidden below the black hole’s horizon and not accessible to observation.

Or is it? Could there be strong curvature regions in our universe that are not hidden behind event horizons and allow us to look straight onto large quantum gravitational effects?

The “Cosmic Censorship” conjecture states that singularities which form when matter density becomes infinitely large are always hidden behind horizons. But more than 40 years after this conjecture was put forward by Roger Penrose, there is still no proof that it is correct. On the contrary, recent developments, supported by numerical calculations which were impossible in the 1970s, indicate that singularities might form without being censored. These singularities might be “naked”, and yes that is the technical expression.

It has been known for a long time that General Relativity admits for solutions that have naked singularities, but it was believed that these do not form in realistic systems because they require special initial conditions which are never to be found in nature. However, today several physically realistic situations are known to result in naked singularities. Now that we cannot rule out naked singularities on theoretical grounds, we are left to wonder how we could detect them if they exist for real. And if this means strong curvature regions are within sight, what is the potential for observational evidence of quantum gravity?

It turns out these questions are more difficult to answer than you’d expect. Evidence for black hole horizons comes primarily from not seeing evidence of the surface of a compact object. A naked singularity however also doesn’t have a hard surface, so these observations are not of much use. If matter collapses and heats up, it makes a difference for the emitted radiation whether a horizon forms or not. This difference however is so small that it cannot be detected.

This has lead researchers to look for other ways to distinguish between a black hole and a naked singularity. For example by asking how a naked singularity would act as a gravitational lens in comparison to a black hole. However, the timelike naked singularities considered in this work is not of the type that has shown to be created in physically realistic collapse.

The so far most promising study is a recent paper by a group of physicists located in Morelia, Mexico
    Observational distinction between black holes and naked singularities: the role of the redshift function
    Néstor Ortiz, Olivier Sarbach, Thomas Zannias
    arXiv:1401.4227 [gr-qc]
In this paper, the authors have studied if one can distinguish between black holes and naked singularities not by the light that is emitted from the object itself during collapse but by light from a different source that travels through the collapse region. They find that the luminosity curves of the two cases differ on a timescale that, for a stellar black hole, is about 10-5s. In this work the authors do not evaluate if it is feasible to detect the difference with presently existing technology, but the signal does not seem hopelessly small.

The space-times that are considered in the above have a Cauchy-horizon, which is an interesting but also somewhat troubling concept which the cosmic censorship conjecture is supposed to avoid. The presence of the Cauchy-horizon basically means that after a certain moment in time you need additional initial data. You could interpret this as a classical instance of indeterminism. However, quantum gravity is generally expected to remove the singularity anyway, so don’t get too much of a headache over this. More interesting is the question if not the difference between the presence and absence of the horizon would be easier to detect if quantum gravitational effects were taken into account.

I am sure we will hear more about this in the soon future. Maybe we’ll even see it.


  1. Sorry, kind Off topic: Sabine what are the implications of BICEP2 on QG phenomenology (and the on different models)? I mean basically people observed (indirectly) the quantum fluctuations of gravitons!
    Are you planning a review post or a paper oriented on QG phenomenology aspects?

  2. Giotis,

    Not anytime soon. I prefer to let the dust settle, then things will become clearer. We're having the ESQG meeting in early September and I'm sure this will be one of the main discussion topics, so maybe I'll write something after that. Best,


  3. Would you agree that the issue is whether the boundary of "strong curvature regions" is spacelike or not?

    With timelike boundaries and non-predictable physics along the boundary one will run in to Cauchy horizons, but the strong curvature region will not be hidden.

  4. Hi Bee,

    Ahem....only "a woman" could think of such comparisons? :)

    Your post is quite helpful to me about what is happening now within the CMB while making use of the all sky map.

    So thanks.


  5. Sorry for being off-topic myself, but I just need to answer Giotis on

    "what are the implications of BICEP2 on QG phenomenology"?

    There aren't any! At least no obvious ones. Internet is full of clueless comments that BICEP2 has probed quantum gravity, which is just unfounded hype.

    The gravitational waves observed by BICEP2 are two or three orders of magnitude away from any QG effect, and fall completely within the ordinary general relativity. If anything, the data supports the validity of Einstein's GR up to the scales of order 10^16 GeV.

    This is in complete analogy with the fact that discovery and initial measurements of electromagnetic waves had absolutely no consequence for quantum electrodynamics, but were only a support of validity of Maxwell's classical electrodynamics.

    HTH, :-)

  6. A singularity is a point where the known laws of physics breakdown. This entity does not exist per se but is another way of saying we do not know what happens at this level of spacetime curvature. Most physicists are comfortable with admitting that only a self consistent quantum theory of gravity will explain the physics beyond the event horizon.So talking of naked singularities is tantamount to discussing a speculation of a speculation.

  7. Cauchy horizons certainly a lot of talk lately where the wiki articles cited mentions there are issues.

    Why should Penrose keep only the Big Bang born naked singularly? So what are the hidden depths of inflation,

    The space and time SR reversal is what at the instant or interval of change? Partial differentiation. Or multiple integration where uncertainty and certainty meet in obscurity or transparency?

    I found it surprising in early drawings by Descartes that a hyperboloid can be used as focusing of light as well as lenses of more spherical approximations. Lenses van be flat too.

    In the hyperbolic case the partial view of space is two dimensionally Lorentz symmetrically invariant.

    The simple analogy of the equivalence principle, a ship circumnavigating an island finding excess angles (Euclidean) could interpret this as forces drawing it to the island. But what angles of what distances from some imagined singularity or center would we need to surround a flat, say triangular region, that folding the excess I could assemble them into a sphere again? Would this not be there such radii partials as if an onion structure. Gravity with a sort of generations concept?

    My thoughts seem far too simple though hard to reach save in retrospect which is the case of inquirey so transparent at theory's frontiers that our haunting new horizons seem to vanish yet boost us to ask the why of hidden dreams.

    Only the Higgs excepted as singularity giving mass save to itself - this in stark transparency an end not reduced to gravity as closed and censored standard theory as imagined multiverses do not necessarily balance with local regions of quantum many -world phenomenology and math is not powerful enough yet between the curves of free fall or force as expoTentistion.

  8. Gals, guys, and string theory pad their assets as business plans until investors lock in. They are then revealed to be fantasies. Investors can be disappointed.

    Extreme spacetime curvature internally obtains through violent acceleration (Einstein's inertial elevator, but Unruh radiation) or by degenerate mass concentration. Ashtekar chiral spacetime torsion is mathematically simpler than achiral curvature (arXiv:1112.1262, Section 5.5). Nobody proposes a closed trefoil knot of gravitation. Curvature and torsion have indistinguishable outcomes if the target is achiral or racemic, but possibly not identical if geometrically chiral or sufficiently spinning.

    Can spacetime be twisted? Magnetic field B is the curl of a vector function. Pulsars' extreme magnetic fields and possibly observed magnetars (10^12 - 10^15 gauss), are not pathological. A 10^14 gauss field is 4.0×10^25 J/m^3, E/c^2 mass density exceeding 104 times solid lead (but nowhere near nuclear density). Ta-180m has a nuclear spin of 9- (units of h-bar). No strange claims. 1.74 solar-mass 465.1 Hz PSR J1903+0327 has ~11% of lightspeed equatorial spin velocity. GR perfectly predicts the binary system's orbit, periastron precession, and gravitation radiation orbital decay. A naked singularity on a bench top (and keeping it there) is a poser.

  9. /* Does nature hide strong curvature regions? */

    It depends. When they're of positive curvature (jets of pulsars and black holes) it exposes them instead. I dunno how it could be related to the perex illustration - but at least it does provide some clue...

  10. "For all practical purposes, you sit in a flat space-time."

    Then what is holding me down in my chair? Or maybe that is not a practical purpose.....

  11. Giotis,
    you may want to have a look at this paper:

  12. General Relativity (GR) == wrong !?
    GR + cosmic censorship (i.e. no NS's) + energy conditions + chronology protection == right !?
    Isn't that weird ? What else are we missing ?

  13. Stuart,

    I tend to agree with you, see the last paragraph in the above blogpost. However, it makes sense to first ask the question whether one could distinguish the two classical cases. I'll admit though that it is not a priori clear to me that the signature of a qg region replacing the naked singularity would have a similar signature. Best,


  14. Giotis, vmarko,

    I don't think it's clear what BICEP2 means for qg pheno. Re the question of quantization per so, it's basically what we discussed here, ie it isn't clear to me that one can exclude it wasn't quantized. Regarding certain qg pheno models, it will take a while for that to be sorted out. Best,


  15. I completely agree with your statements in the post you linked Sabine and I'm impressed on how accurate your statements are.

    We need to make a distinction between QG (and QG effects) and the theory that UV completes QG.

    A provocation: GR is a theory of QG in the former sense, meaning it is an *effective* *quantum* field theory of massless spin two particles perturbatively valid up to Planck scale (or compactification/String scale if you believe in String theory).

    Now if BICEP2 gravitational waves are of quantum origin (our best hypothesis so far is that this is the case and we have a concrete calculation in our hands) then they just validate the above statement up to the inflation scale. Basically this confirms what we already knew, it's like having experimental proof of Hawking radiation. The result doesn't say much for the theory that UV completes QG (non perturbatively or via new dof)

    My question was whether there are any pheno models/theories that advocated something different and thus they are excluded? Or models that are excluded due to the new large inflation scale E.g. models with large extra dimensions come to my mind.

    Another question for example is that SUSY will be broken at inflation scale. What are the broader implication of this?

  16. Giotis,

    Yes, I agree with you regarding perturbative QG. It would still be good to have proof for that because there are some theories (think Schrödinger-Newton) that would be ruled out - but these are arguably not particularly popular, for not to say not plausible, anyway.

    Regarding the UV completion, yes there have been predictions from pheno QG models. I collected some of them in this paper, section 3.3. Now keep in mind that this paper is 3 years old already, so this isn't very up to date, and the list is also not exhaustive. (Even writing this short review took up an exceedingly long amount of time, not something I'm likely to do again!) To accurately tell which models can be ruled out though, I think we'll have to wait for more detailed data fits. I expect that it won't be more than a month or two until it becomes clear who wins and who loses. Best,


  17. Uncle Al,
    problem is that a trifold knot model can be thought of as minimal QM gravitational effects.
    This is to say that it is a degenerate case of a wider coordinate interpreted model background where we try to observe "eutactic shadow polytopes "(see Coxeter) as a centered point or not as a censored singularity or not for a region as lensing in odd or even "Euclidean" Dimensions.
    This is the origin of today's speculative confusions. The equivalent knot is but a Peano fractal linear dimension over the space to be filled or in the count of quantized bits a sponge hierarchy lipped or opened that force effects distinguish what we regard as material or empty holes as internal axes.
    Inflation is a point of view that is consistent but not really needed to explain the flatness barring issues of defects over causitive or casual connected local regions or issues of measure and conservation laws as horizon boundaries.
    At each point along this curvy loop where different parity signs show physical effects as we know them is in effect another such singularity and so on as we collide or super impose these curves as particles, or stack them say as nucleons.
    Thus it is the way we apply the theory if groups as to what twists on some generations shift level phase change. We may only combine five objects in successive duality two ways if we leave only a censored positive for our equations. Two of these remain hidden and pentagonal as we tie a strip into a granny knot.
    As to broken symmetry in this higher contiguous gravity, that is a much deeper question than when time begins or ends.

  18. Oh, now I see, this is actually an issue of terminology... :-)

    So one can make a distinction between a "The QG theory" (a UV completion, fundamental theory), and an "effective QG theory", which is the perturbative quantization of GR below the Planck scale.

    The effective perturbative quantization of GR is defined by its set of values for the counterterm coupling constants, none of which has been even sniffed by BICEP2. They would be certainly bragging around much more had they had such a result.

    As for the fundamental QG theories, there are two classes --- those whose semiclassical limit is equal to GR all the way up to Planck scale, and those which predict that a classical theory of gravity starts to deviate from GR at some scale lower than Planck. However, I must admit that I am not familiar with any examples of the latter type of theories. Such a theory would need to introduce an additional scale, between the Planck and currently observable scales, and my first question would be "But why?".

    However, disregarding my potential ignorance, I agree that any fundamental QG theory that predicts an additional scale below 10^{16} GeV, is now disfavoured by BICEP2 results. That is to say that BICEP2 confirmed the validity of GR up to that scale. I repeat --- I have never heard of any example of a QG model that falls into this disfavoured class.

    As for the fundamental QG models of the first class, those that do not have multiple scales but only the Planck scale (i.e. virtually all models that I've ever heard of), BICEP2 says absolutely nothing about them.

    So saying that "BICEP2 has probed quantum gravity" is an overstatement, and I'm just frustrated by the fact that it is being advertised so bluntly all over the media. In reality, the best BICEP2 can do is to put a new bound on the scale where we cannot see any QG effects.

    I hope this clears up my point.

    Best, :-)

  19. Bee wrote "The issue with what?"

    The issue whether nature hides strong curvature regions.

  20. "...Could there be strong curvature regions in our universe that are not hidden behind event horizons?..."

    Yes. See Geometry of Electromagnetic Systems by Baldomir and Hammond. Or for something immediate see The role of the potentials in electromagnetism by Percy Hammond and look at the sentence near the end-note: "We conclude that the field describes the curvature that characterizes the electromagnetic interaction."

    Perhaps I can illustrate via an analogy. Imagine you're standing on a headland looking out over the ocean. You notice a single wave, and you notice that its path is very slightly curved. This curved path relates to curved spacetime. Now look at the surface of the sea where the wave is. It's curved. And compared to the slightly curved path, it is rather more strongly curved. 10^39 times more strongly curved.

  21. Vmarko tou say:

    "As for the fundamental QG theories, there are two classes --- those whose semiclassical limit is equal to GR all the way up to Planck scale, and those which predict that a classical theory of gravity starts to deviate from GR at some scale lower than Planck. However, I must admit that I am not familiar with any examples of the latter type of theories. Such a theory would need to introduce an additional scale, between the Planck and currently observable scales, and my first question would be "But why?"."

    Sorry this this is a joke?

    If not then I guess you've never heard of a theory called String theory which introduces two new scales between Planck scale and the new inflation scale i.e. the String and compactification scales

  22. Goitis is correct in terms of pushing the timeline back and of course this is agreed upon that such a timeline has shown it to be more then the first three seconds of Steven Weinberg. That's the first connection in the inflation model.

    The latest Cosmological Parameters are of course important here as they lead to the extended models. The WMAP parameters are also important in terms of correlations.

    ΔR2-Curvature fluctuation amplitude- 2.441^{+0.088}_{-0.092}\times10^{-9}, k0 = 0.002Mpc−1

  23. Bee, please forgive what will be for you a very naive, elementary question, but for me remains very puzzling, especially in the light of the recent claim for the discovery of gravitational waves that supposedly support cosmic inflation. If cosmic inflation actually did take place, and so I'm told, within a trillionth of a second of the Big Bang, then why do we need a Big Bang at all, why not simply inflation from an unknowable singularity, that at some point just slowed down for some reason to give us the expansion we now see?

    If our "window" into the past stops at inflation and we can't possibly see back any farther than that, then how can we claim that, prior to this inflation, there was an earlier "inflation" called the Big Bang? Please put me out of my misery and either explain this strange theory or else point me to some publication where it is explained. Thank you.

  24. Giotis,

    The fundamental string scale (the string tension) is usually taken to be equal to the Planck scale. The compactification scale is not predicted by ST, but is a free parameter, and one can always choose a convenient compactification scenario (from the landscape of 10^500 of them) such that the compactification scale is above 10^16 GeV.

    So no, string theory does not have a prediction for some scale which could be tested against the BICEP2 results. This is an example of a property that string theory critics usually call unfalsifiability of ST --- you can fit the theory to any given data.

    But we are getting way off-topic here. :-)

    Best, :-)

  25. vmarko,

    "The fundamental string scale (the string tension) is usually taken to be equal to the Planck scale"

    No, it is not.

  26. DocG,

    I'm not sure I understand the question. To begin with, nobody really believes that the universe indeed started with a singularity, see last paragraph of above blogpost which applies also to the cosmological case. Second, basically you use inflation to make something that appears difficult to obtain easy to obtain. You start with your cosmology and consider quantum fluctuations on that background. The problem is, these will not give you right away the universe we observe, you create several problems notably those known as the flatness problem the horizon problem and some related things. You use inflation to cure these issues and the result agrees well with observation. Best,


  27. I understand very well, Bee, what you say, and also the timeline and modeling pointed to by Plato -- thanks to both of you. I've actually read quite bit on that in the popular literature, but I remain puzzled.

    I guess what is bothering me is the necessity of a model that requires, first of all, an enormous explosion that sets the expanding universe in motion and then, very very shortly after that, yet another explosion that conveniently "corrects" the inadequacies of the first model. Of course, it's always possible that it happened that way, but compared with most scientific models this one seems particularly inelegant.

    In a nutshell, it looks like the Big Bang model was constructed to explain the evidence for the expansion of the universe, inflationary model was constructed as a kind of fudge to compensate for the inadequacies of the Big Bang -- and then of course the Multiverse model has been constructed as a fudge to compensate for certain problems associated with inflation.

    At least that's how it appears to a layman looking in at cosmology from the outside. Maybe I've been spoiled by all the elegant theories I've read about that fit Occam's Razor so neatly, so I must say the Big Bang cum Inflation cum Multiverse model looks really awkward to me and I wonder why so many physicists seem convinced by it.

  28. Sabine,
    Thanks for the link to your paper were you survey the state of cosmology at the time. Your comment mentions section 3.3... Such an effort as theory between peers and delayed before experimental evidence brings everyone to new questions including for the general public is not lost in the accretion of wisdom. Yes we should humbly see new areas to consider and science or philosophy involved as early baby steps as if baby universes in a multiverse of discource.
    I do not know of many contemporary scientists to attribute what is original or what commonly is understood. I see that conceptual wars are raging and many are disoriented when theories are surpassed, especially if not successfully defended assuming inquirey is symmetry in a zero sum all or nothing game. But I recognize your concerns cut through the tangled knots of chaotic inflation with X-ray vision. It is not necessarily the simple question where (in gravity issues especially) is chaos in QM theory.
    That said, some theories can be so clear as to be unnoticable or unobservable. My views are decidedly chemistry or biological in its philosophy of Nature. (to point this out for those who do not see this tradition or who would exaggerate and build on my lapses of reductionism.)
    At an existential or at a more general idea of spacious singularity that meet in a creative or empty place we tend to feel skeptical as we impose on the universe our model like a projection on a Creator of ourselves, or that that already a given image we the projection. So as a scientific description it seems equally absurd to suggest the universe has a mathematical body where humanoid bilateral form is the universal apex of creation. So much more so for the work of awareness and imagination.
    It would be an interesting social study in these speculative times to do alien autopsies of those with models in their death throes and testimonies as their swan song gives evidence at an end with doubt as their starship of dreams crashed down into reality.

  29. DocG,

    Well, I challenge you to come up with something more elegant. Best,


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  31. Yeah Sabine is right. If you take the String length equal to Planck length you won't be able to do perturbative string theory. String theory will be strongly coupled and we don't understand this regime. You typically take it an order of magnitude larger than Planck length.

    The compactification scale is not a free parameter, it can and should be stabilized (moduli stabilization) and thus is a new scale introduced. Typically it is larger than the String scale (meaning the volume is larger than the string length).

    If the above are not fulfilled you won't be able to reproduce the 4D Einstein-Hilbert action.

  32. Giotis said: "A provocation: GR is a theory of QG in the former sense, meaning it is an *effective* *quantum* field theory of massless spin two particles perturbatively valid up to Planck scale (or compactification/String scale if you believe in String theory). "

    I don't know why you call this a "provocation". It is in fact exactly how most people think about GR.

    And that's probably precisely why we have made zero progress in quantum gravity over the last 40 years....

  33. "And that's probably precisely why we have made zero progress in quantum gravity over the last 40 years...."
    LOL, I fully agree.
    IMHO the big misconception has been that the metric tensor is taken to be fundamental and should be quantized.
    Personally I find Connes' noncommutative approach where the Dirac operator is the fundamental object much much more promising (c.f. spectral geometry/action). In particular it shows the intricate (geometric) relationship of the Standard Model with gravity, which is the first thing I think one should try to understand before aiming higher.
    Let me cite Connes:
    "... in fact there is a temperature which is high enough and beyond which there is no geometry at all, there is no universe at all. What there is, is a type III1 chaotic quantum state on the space of all geometries which doesn't correspond to any specific geometry, it corresponds to a perfectly symmetrical state, and it's only when things are cooled down that it deposits and it chooses a specific geometry."
    (Note, that the Planck temperature is about 10^32 K - can we really expect to see generic quantum gravity effects at such a high temperature ?)

  34. MarkusM

    But what would seperate a geometrical
    or geometry free (perhaps non existing as well without curves and hidden)?

    I do not see this supports inflation or QG models decisively either.

    A universe could conceivably be filled with the background only that mass and gravity tensor like is all there is and scalar like but precipitate holes in the non local loops of expansion or extention.

    We may not make progress for another 40 years if we do not consider gravity continuous and inflation quantized where the role with QG and GR at the horizon of the unknown is interchanged.

    A class of finite universe is not necessarily a multiverse nor as generally quasifinite our models and measure an absolute unity in shifting contiguous groups and dimensions as prime. Geometry in its explaining physics is mathematical on natural levels yet we have to question if it is as simply equivalent to algebra as Euler's formulas show, at least for now.

  35. This comment has been removed by the author.

  36. MarkusM
    The history if those algebra theories was quite a workout. Of course it would take time to study the clear and vague assumptions and language. Some simple matrix ideas do make deep connections in the branches and methods of mathematics but not yet if ever to the deeper issue and topic question at hand.

    The issues viewed as thermodynamics, its extension of laws and verification of existing laws is needed. That would be especially needed for unanswered questions of symmetry in string theories.

    Why, at some ultimate conception would nature distinguish symmetry from asymmetry?

    What do we gain in our treatment of unity or its roots and methods of operations if we do not face these still philosophic questions?

    But as physics I am suggesting there is at least a further generalization beyond our abstract conception of Hilbert spaces or the like.

    Perhaps Quantum is not a good term or is misleading. Is minimum quantization but a loop, a base ball curve drawn on a sphere? The models of inflation seem to be drawn with such simple pictures.

    Can 1 - 1 mean or equal anything even as an intrincally linear product let alone. What we mean by equality itself?

    Is this not like a faith in gods, or one god to another different in a multiverse of such beings to which god is on our side yet not necessarily the same god?

    "Statues made of match sticks crumble into one another ... She does not bother, she knows too much to worry or to judge. " Love Minus Zero

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  38. A map is always good, not just a sky map to help orientate perspective, where we are in the timeline as well as what parameters have been encounter with regard to that timeline. You use a framework to help extend the vision of the areas on the map that lie before 1 Planck time to encourage new extended formalizations of all current cosmological parameters already set.

    BICEP2 forces new constraints on models/frameworks chosen, as it must be and to eliminate others as it should do.

    The conception of time is forced back as well, and if you do not have a framework with which to answer that work given before 1 Planck time as too, the areas shown on the map, according to the time regime we are working on then we can safely assume, that such work could not be attached to any degree?

  39. MarkusM,
    I might add that "what drives the inflation field we do not know " assumes someone does not know or know from a little wider background thought ideally objective and independent. Some model makers assuming or beginning with principles of singularity as controversial models beyond current science are not ruled out and are intelligible in questions and conclusions although they tend to see new data as confirmation of the obvious should models evolve their way. Can we prove Poinclaire really?
    Imagine what it must sound to someone who has a better general idea who would think for inflation you do not see the obvious where the complications of two not even wrongs is but an artifact of simple arithmetic as ratios suggesting models right as the unknowns emerge at least consistently although the dust may not ever settle or the background never more in math description as a higher form of artifacts.

    Plato's comment on maps and Planck time does have its usefulness as a conceptual frame of reference. After all are we not interpreting a WMAP and trying to sort out that thermodynamic time may not explain the still deeper interpretations of what the heck is gravity? The map is or close to flat? The map is the landscape after all?
    Or must we also consider the grid that contains regions itself the question of delta-episilon stances on limits?
    We can find solutions to hidden symmetry of weights of identical shaped units provided we lable them in the process. But with conservation laws at stake it is not unreasonable to dowz a map to find water in the landscape.
    Moreover, in the simple count of Riemann multi-ply reintry over a region as we detect half unfoldings or unrollings of inflationary scales the simple count adds up as we divide the formalism as 3+1 embedded in general 4D. 48 of 96 monoverse unrollings which, although a paradox likewise, a quasic not simply a quantum inflation field source as is symmetry and the source of light. LQG is a simpler and superior theory to stringy chaos going where its phenomenology does not apply.

  40. L. Edgar Otto,
    "I do not see this supports inflation or QG models decisively either."
    In fact it does, see
    http://arxiv.org/abs/hep-th/0512169 for inflation and
    http://www.alainconnes.org/docs/bookwebfinal.pdf for QG.

    "Geometry in its explaining physics is mathematical on natural levels yet we have to question if it is as simply equivalent to algebra".
    At least in a sense it is, see Gelfand-Naimark theorem ...

  41. MarkusM
    My reply to you where your post was deleted and part reposted did address the Gelfand-Nalmark theorem context

    For more recent ideas which has long been blogged on my arithmetical and numerology as well as similiar work by Marni of her Arcadian Functor blogspot see: arxiv.org /1403.2099v3.pdf
    It says it applies to gravity without SUSY. But my recent thoughts on quasinflation might relate on a much higher level as part of the unified picture. If QM like in the main an intelligible universe tends to persist hovever inelegantly.


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