Sunday, June 29, 2014

The Inverse Problem. Sorry, we don’t have experimental evidence for quantum gravity.

The BICEP collaboration recently reported the first measurements of CMB polarization due to relic gravitational waves. It is presently unclear whether their result will hold up and eventually be confirmed by other experimental groups, or if they have screwed up their data analysis and there’s no signal after all. Ron Cowen at Nature News informs the reader carefully there’s “No evidence for or against gravitational waves.”

I’m not an astrophysicist and don’t have much to say about the measurement, but I have something to say about what this measurement means for quantum gravity. Or rather, what it doesn’t mean.

I keep coming across claims that BICEP is the first definite experimental evidence that gravity must be quantized. Peter Woit eg let us know that Andrew Strominger and Juan Maldacena cheerfully explain that quantum gravity is now an experimental subject, and Lawrence Krauss recently shared his “Viewpoint” in which he also writes that the BICEP results imply gravity must be quantized:

“Research by Frank Wilczek and myself [Lawrence Krauss], based on a dimensional analysis argument, suggests that, independently of the method used to calculate the gravitational wave spectrum, a quantum gravitational origin is required. If so, the BICEP2 result then implies that gravity is ultimately a quantum theory, a result of fundamental importance for physics.”
We previously discussed the argument by Krauss and Wilczek here. In a nutshell the problem is that one can’t conclude anything from and with nothing, and no conclusion is ever independent of the assumptions.

The easiest way to judge these claims is to ask yourself: What would happen if the BICEP result does not hold up and other experiments show that the relic gravitational wave background is not where it is expected to be?

Let me tell you: Nobody working on quantum gravity would seriously take this to mean gravity isn’t quantized. Instead, they’d stumble over each other trying to explain just how physics in the early universe is modified so as to not leave a relic background measureable today. And I am very sure they’d come up with something quickly because we have very little knowledge about physics in such extreme conditions, thus much freedom to twiddle with the theory.

The difference between the two situations, the relic background being confirmed or not confirmed, is that almost everybody expects gravity to be quantized, so right now everything goes as expected and nobody rushes to come up with a way to produce the observed spectrum without quantizing gravity. The difference between the two situations is thus one of confirmation bias.

What asking this question tells you then is that there are assumptions going into the conclusion other than perturbatively quantizing gravity, assumptions that quickly will be thrown out if the spectrum doesn’t show up as expected. But this existence of additional assumptions also tells you that the claim that we have evidence for quantum gravity is if not wrong then at least very sloppy.

What we know is this: If gravity is perturbatively quantized and nothing else happens (that’s the extra assumption) then we get a relic gravitational wave spectrum consistent with the BICEP measurement. This statement is equivalent to the statement that no relic gravitational wave spectrum in the BICEP range implies no perturbative quantization of gravity as long as nothing else happens. The conclusion that Krauss, Wilczek, Strominger, Maldacena and others would like to draw is however that the measurement of the gravitational wave spectrum implies that gravity must be quantized, leaving aside all other assumptions and possibly existing alternatives. This statement is not logically equivalent to the former. This non-equivalence is sometimes referred to as “the inverse problem”.

The inverse problem is finding the theory from the measurements, the inverse of calculating the data from the theory. Strictly speaking it is impossible to pin down the theory from the measurements since this would imply ruling out all alternative options but one, and there might always be alternative options - unknown unknowns - that we just did not think of. In practice then solving the inverse problem means to rule out all known alternatives. I don’t know of any alternative that has been ruled out.

The so-far best attempt at ruling out classical gravity is this paper by Ashoorioon, Dev, and Mazumdar. They show essentially that it’s the zero-point fluctuations of the quantized metric that seed the relic gravitational waves. Since a classical field doesn’t have these zero-point fluctuations, this seed is missing. Using any other known matter field with standard coupling as a seed would give a too small amplitude; this part of the argument is basically the same argument as Krauss’ and Wilczek’s.

There is nothing wrong with this conclusion, except for the unspoken words that “of course” nobody expects any other source for the seeds of the fluctuation. But you have practice now, so try turning the argument around: If there was no gravitational wave background at that amplitude, nobody would argue that gravity must be classical, but that there must be some non-standard coupling or some other seed, ie some other assumption that is not fulfilled. Probably some science journalist would call it indirect evidence for physics beyond the standard model! Neither the argument by Ashoorioon et al nor Krauss and Wilczek’s for example has anything to say about a phase-transition from a nongeometrical phase that might have left some seeds or some other non-perturbative effect.

There are more things in heaven and earth, Horatio, than annihilation and creation operators for spin-two fields.

The argument by Krauss and Wilczek uses only dimensional analysis. The strength of their argument is its generality, but that’s also its weakness. You could argue on the same grounds for example that the electron’s mass is evidence for quantum electrodynamics because you can’t write down a mass-term for a classical field without an hbar in it. That is technically correct, but it’s also uninsightful because it doesn’t tell us anything about what we actually mean with quantization, eg the commutation relations between the field and its conjugate. It’s similar with the Krauss’ and Wilczek argument. They show that, given there’s nothing new happening, you need an hbar to get the dimensions work out. This is correct but in and by itself doesn’t tell you what the hbar does to gravity. The argument by Ashoorioon et al is thus more concrete, but on the flipside less widely applicable.

Don’t get me wrong there. I have no reason to doubt that perturbatively quantized gravity is the right description at weak coupling, and personally I wouldn’t want to waste my time on a theory that leaves gravity unquantized. But the data’s relevance for quantum gravity is presently being oversold. If the BICEP result vanishes you’d see many people who make their living from quantum gravity backpedal very quickly.


  1. quantizy space and time is the main trouble. To me looks a non sense.
    From the other side if matter is so strongly interact with space time, there must be a solution.
    My question is: is it possible to build up a quantum theory without space and time ?

  2. "There are more things in heaven and earth, Horatio, than annihilation and creation operators for spin-two fields."


  3. Repeat the observation outside objections. Reality is not a peer vote (re 1957 Yang and Lee versus 1928 Cox - same observation, different outcomes). OPERA at Gran Sasso reported transluminal muon neutrinos. arXiv flooded with theoretical models. Bleeding edge physical theory missed a loose fiberoptic connector.

    40 years' failure of quantum gravitation, SUSY, and dark matter say "empirically defective postulate." Postulate-validated observation cannot discover postulate violation. Falsifying experiments must offend physics while being consistent with all prior observation. Chemistry offers five heretical tests of vacuum symmetry toward hadronic matter: chiral Eötvös experiments, chiral enthalpies of fusion, chiral microwave rotation temperature, chiral pawnbroker rotation, chiral Galilean drop. Look for the loose connection, not the next epicycle.

  4. I suppose that the experiment are the only track that it is possible to follow if you wish to understand the Nature rules

  5. Bee, IMHO there is a flaw in your argument.

    You say:

    “But you have practice now, so try turning the argument around: If there was no gravitational wave background at that amplitude, nobody would argue that gravity must be classical, but that there must be some non-standard coupling or some other seed, ie some other assumption that is not fulfilled.”

    Nobody will argue such things. Gravitational waves originated during inflation are detectable only if inflation occurred at very high energies close to GUT scale.

    Thus if gravitational waves are not detected people we’ll just say that presumably inflation took place at lower energies.

    So the inverse does not exist in this case i.e. detection of gravitational waves is evidence for perturbative QG (since this is the most clean prediction of inflation and is the best theoretical explanation we have up until now)but the inverse is not true.

  6. Excellent points!

  7. Things we don't understand: Black holes, big bang and quantum gravity. Historians in the future will obviously say: What an obscure, violent and unrefined culture!!

  8. /*If the BICEP result vanishes you’d see many people who make their living from quantum gravity backpedal very quickly*/

    Isn't it a phenomenological nonsense? The BICEP2 people claimed the observation of gravitational waves, which are general relativity prediction, not quantum gravitational one. At second, the subject of quantum gravity is every phenomena between the quantum mechanics and general relativity scales (including Bee, real bees and other things moving around us), at third the gravity is already quantized in observable way in form of common photons (and another particles mediating mass).

    So I don't quite understand the outcome of this particular article at all (and I used diplomatic language intentionally here)...

  9. @Giotis: Are You sure that inflation theory will work for energy lower than GUT scale? (I am assuming that soon after GUT, something has to start producing particles.)

  10. So when we look into a mirror and try to reason it out, and decide some things are possibly beyond our current experiments we can admire our muscles - rather than asking which way is it to the beach and if we had enough spinach behind our theories?

    Explaining the Casmir force for example can have several equivalent descriptions of which it seems a little pointless to point out the other position is in error. Feynman's cloud is as valid as say point electrons and so on.

    If a vacuum is filled, the zero point idea is zero and things are positive - where does the inverse begin if it ever does? The problem is with our theory not with the universe.

  11. Giotis,

    You say the detection of primordial grav waves is evidence for pert qg. Yes, true, but 'evidence for' is a rather weak statement because it could be evidence for other things too. That's what the inverse problem is all about. What I am saying you need to show is that the observation it is evidence *against* everything else (everything else that we know of). Eg, now you have show me that there is no way to produce the (potentially) observed spectrum without pert qg. Best,


  12. George,

    The question is not whether or not you can have tensor perturbations, but whether these have to be quantized. The measurement of the CMB polarization is/would be evidence for tensor perturbations, but a priori not for them being quantum perturbations (see the Ashoorioon et al paper, they are very clear on this). Now we do not have any direct evidence for them having quantum properties - this doesn't play a role for the CMB imprint. It does play a role for the generation of the spectrum, but that brings up the problem of how do you show there is no other way to generate the spectrum - and this generation depends on the model. Best,


  13. Zephir,

    You should read my earlier post and think about it. I am using diplomatic language intentionally here. Best,


  14. George,

    The problem is that gravitational waves can be produced also by other (more exotic) mechanisms during inflation.

    Check for example this nice paper by Eva Silverstein et al for such alternative mechanisms.

    Quantum fluctuations of the metric though is the most plausible theoretical explanation.

    @Bee I agree with that you say but that was not my point

  15. The next time we twins can not reach consensus we will call in Uncle Al.

    Twins don't have an inverse problem.

    "Repeat the observation outside objections. Reality is not a peer vote..."

    That's right. We don't have a say in the course of what nature does.
    Or what twins do.

    Taking advantage of nature's or twins' knowledge for any benefit
    is confirmation bias.

    Great Blog. Great posts.

    All the best.

  16. Giotis,
    Ok, sorry, then I misunderstood. Whether or not fiddling with the inflation scale makes the theory fit with the data depends on the data (which might contain other observations too), so my prediction about what people would or wouldn't argue in the light of different is rather vague and might not be correct, I agree on that. I assure you I have no intentions to become a psychologist ;) Best,


  17. Fraternal (sororal) twins, identical twins (and mirror-image twins, re Gregory and James Benford), polar body (half-identical twins), chimeras, superfecondation twins, superfetation twins.

    There is nothing wrong with a rigorously derived theory assuming all swans are white, including reduction to practice, mostly. The "mostly" requires perturbation treatment...

    ...that miserably fails, thus supporting more studies rather than a repaired founding postulate.

  18. To summarize a bit:

    Indeed strictly speaking the BICEP2 result (assuming holds as it is) is not a “smoking gun” neither for inflation nor for QG effects.

    It is not a smoking gun for inflation because the GW can be generated by mechanisms not related to inflation but to Big Bang itself (e.g. cosmic strings); the interested reader can read for example the introduction of this paper by Baumman et al. on how we can distinguish the two mechanisms:

    But even if we take inflationary origin for granted the BICEP2 result is not a “smoking gun” for QG effects. This is because within inflation there are other mechanisms that could source the GW and produce the same BICEP2 results.

    As I said above a relevant paper, explaining such alternative mechanisms *within inflation*, is for example:

    As the authors indicate in the abstract we could have similar effects (i.e. production of similar GW by the alternative mechanisms) even if the inflationary potential is low. So now we assume that the inflationary energy is high and the origin of the GW is vacuum fluctuations of the metric (this is because the magnitude of the metric tensor perturbations set the scale of inflation) but it might be the case that the inflationary potential is low and the GW are produced by the alternative mechanisms (but of inflationary origin)and not by QG effects.

    Having said that I think the consensus is that such alternatives are implausible; if you hear a barking you will assume that a dog is barking; of course there might be other explanations but this is the most plausible one.

  19. The quacking ducks or ducking quacks as we try to evolve or domesticate our theories. Given a flat honeycomb we remove a node and connecting edges to get a round finite but not necessarily unique finite system of convex symmetries. Can the same be said for any node in concave hyperbolic lattices? This simple Euclidean model as reasoning seems to me a more general question of what we mean by unique.
    Deeper than what ideas we make inverses or mirrors.
    Certainly, the subtle evidence of spin differences and new chiralities can address dynamics unto ultimate states. But then what in our tower and inflating complexities? A photon may be seen as continuous but we can only experience its vanishing as discrete.

  20. Giotis,

    I agree with what you say. I have another reference to add which I found very clearly written:

    "Is the Spectrum of Gravitational Waves the "Holy Grail" of Inflation?"

    It remains to be added though that none of these scenarios actually intends to not quantize gravity in some way. Best,


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  22. Markus,

    Not a naive question, it's the right question. The point of the whole argument of Wilczek and Krauss is that the so-generated perturbations, while existent, would be way too small in magnitude. As I said above, you need to do something 'non-standard' to get the perturbations be large enough if you want to seed them differently than normally assume. Best,


  23. This comment has been removed by the author.

  24. Could you reduce the Inverse square problem even further while qualitatively speaking?

  25. Looking back toward the B-modes that had been talked about, was a selective way with which to "recognize early universe results" so why not look at what was gained from looking toward the CMB as one might given a Penrose theory of cyclical nature as to identifying a pattern. This, so as to suggest other things going on when looking at the map.

    Does it fit with the suggestion of some gravitational spectrum? Qualitatively, you must have an answer?

  26. r = 0.20+0.07

    the amount of power present in gravitational waves compared to the amount of power present in other scalar density perturbations in the very early universe

  27. Sabine,

    I have a question about the term standard model (SM of particles I understand.) Is the standard model considered that of inflation and that is what you mean by non-standard methods needed?.

    From my combinational notations I try to choose standards such as the order of axes drawn or some alphabetical order. Conway has a standard model involving surfaces which came out in Scientific American after I communicated my inversion model to Martin Gardner.

    It seems the usual method in the description of these things is a three by three matrix times a tensor to describe standard particles.

    The occasion of this question is a small realization that if a particle (well a coordinate in spacetime, perhaps a point) cannot distinguish if it is in four or three dimensions, yet is logically connected to the three space phenomena such as "stresses" "perturbations" "density" and so on, there are more such symmetry patterns that amounts to a slightly larger non-standard model.

    As I come here I see Plato's next to his last post and I think this suggests an answer for his question. As well as the general qualitative reason for such a wide difference in certain values of the forces, and so on.

    In a sense we cannot distinguish the standard from non-standard models yet in this local quasi certainty descriptions as quantitative may have traces, direct or indirect.

    I based this on one simple little passing idea so I am not certain how or why it is a good thought or that it reaches far to be so trivial... I did see yesterday that in QCD the gluons involved the number 8 and 36 for the quarks (actually as in uncle al's statements of 5 fold chirality the number is 30 for six distinct colors on a cube- which is Conway's (and mine, it was discussed on the net between the puzzle guys before publication I found out later). so six neutral ones. The six by six matrix as dominoes have unique features along with 2 fold things that no other such arrangements share in all this arithmetic.

    Can we declare the big bang as a standard model based on this or is it also nonstandard, are inflation or cyclic theories for that matter clearly reasoned out or ruled out?

    While there seems to be more I doubt say the otherworldly but intricate idea of SUSY can be justified as beautiful theory alone without linking them to what is of physical observation - that is it disqualifies itself as a nonstandard model. But that is a stray thought I am not that certain of unless such math somehow comes before the said big bang while not linked in a sense.

  28. A "point source" recognition while held to the belief that a geometric structure lies at the heart of this process, we may see this then as "some pattern" in the CMB(the authors belong to a persistent group?:).

    This may to some, reveal the telltale signs of that Platonist group view as some substructure detail as to this pattern of subsistence. So this then becomes a String theory confrontation? :)

    The point in in this theoretic view it already belongs in the wider view of accepted theoretical challenge beyond the phenomenological approach?


  29. Only two things...

    When you are all one hundred years of age - don't threaten me to depart before this age prematurely (barring accident!)

    You are NOT going to pull the crap that Alexander Grothendieck pulled on us... suddenly disappearing in 1991...

    "Nobody knew if he was alive or dead. His whereabouts or ultimate fate were the source of endless speculation in the mathematical community. However, it turned out that he became a hermit, and is living in seclusion because he's embarrassed by the fact that he can no longer understand advanced math papers currently being published in the field he helped create, since the field has advanced so much since he made his contribution."

    Without exception all of you will be explaining to me at one hundred years of age verbatim what work you are presently doing without the slightest lack of understanding.

    If not, you did something wrong.

    If Nature can repeat all her marvels at 13.8 (observable) years of age, you can at least repeat to me at a lapidary hundred years of age what you hold for a marvel of understanding.

    If what you think now is not simple enough to retain and understand with one hundred years of age, you are doing something wrong.

    Try p adic quantum mechanics.
    Fashionable right now.

    Oh, by the way, what did you say just 47 minutes ago?

    Of course you wrote that down with a time stamp.

    All the best,

  30. Hush,
    that link does not look too promising.
    why would we have to distinguish quantum from other possible p-adic models?
    I could post what I wrote about 47 minutes ago (time stamps are sometimes optional)on a physics fb page. Someone said gravons were modified gluons. Not sure what possessed me to say it but I had already thought of my comment in 1968 only now it rings even more true as I understand things better since then.

    Plato, John Barrows recent book "The Book of Universes" being more recent than one I read in 1995 or so, 2011 and his only book in the local library. Check it out, seems his ideas grew more firm over time also. And one early idea I had was proposed way before the twentieth century. Also Hoyle amounts to a form of Einstein's cosmological constant was shown later. I found it most interesting the difference in the way such physics was done in the USA and England (I was in the UK at the time, not as newsworthy in the states.) Not that mysterious I imagine to you after all these blog years so If you read it tell me what you think. I am not sure just what we mean by a point or a pure geometry the world Platonic or not.

    Best around...

  31. "why would we have to distinguish quantum from other possible p-adic models?" - Otto

    I'd dunno. Why?

    A model with no details left out has to be simple enough to recall on your hundredth birthday.

    No longer understanding what you created or no longer being able to follow what your model brings forth and entails with new understanding dovetailing into your model is not an option.

    Nor is seclusion or banning publication of all your work.

    Unless your name is Alexander Grothendieck.


  32. hush,
    interesting points and concept.

    OK...this is what I posted for what it is worth.

    L. Edgar Otto Gravity as such would be everything that is not a mulitdimentional complex of energetic gluons but not necessarily connected to everything that is not a muon so defining a wider neutral virtual pure space vacuum. There may be further levels of these physical photon analogies in our thereby most probable stable state in an imagined landscape of dynamic universes. 6 or 8 virtual gluons subdivide electrons logically.

    Also, it seems to me, a little bit lost reading Barrow among all the choices and ideas that lead to whole projects, a hundred years later, and my reading Leibinz and Einstein at the same time way back or and Russel in he mix (GUT is after all a theory we try to unify things by higher energy...but like the slowing of neutrons to fall into potential wells, even a charged particle energetic enough can pass thru walls and touch nothing.) In the book so many have published theories that were forgotten or done independently by others.

    Trying to suggest a theory of everything is like trying to copyright the idea of a sphere- But to know anything and it stick do we all not have to personally reinvent the wheel?

  33. Hush,
    Alexander Grothendiek... a typical story in many areas of thought reaching some frontier. That, by the way answers why, some issue or fad in very simple but profound models of fads suggesting truly new things beyond our day. How can the universe be so unreasonably uniform as if our experience of thought is a Bianchi model we get better at considering quantitatively? Said singularity thru layers of sheaves of dust into some limit of expansion then return to singularity again.
    Today I imagine everywhere but the black hole like walls. What limits the physics of such things if not the topology of thermodynamic limits in such symmetry? As there is now evidence of unexpected heat transfer outside taught models we can ask deeper where is the chaos in inflation or quantum theory.

  34. I suggest we ban the term "quantization" as it has become meaningless.

    Firstly, as I showed in 1991 you can "quantize" classical mechanics and get back clasical mechanics if by "quantize" you mean put an operator hat on all variables in sight.

    Secondly, as I showed later in 1994 there are ta least two theories of gravity in the classical Newtonian limit which gives different answers and have quantized eigenstates.

    Ergo... there is a lot of foolish dogma about what is or is not a quantized theory.

    If you mean a theory which uses fields in configuration space then the answer of what is or is not an entangled quantum theory is pretty clearly defined mathematically.

    However, talking about quantum versus classical theories by looking for "hats" and "operators" is just so much late 20thC drivel :-)

    It really is meaningless.


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