Monday, June 17, 2013

Phenomenological Quantum Gravity

Participants of the 2012 conference on 
Experimental Search for Quantum Gravity.
The search for quantum gravity and a theory of everything captures the public imagination like no other area in theoretical physics. It aims to answer three questions that every two-year old could ask if they would just stop being obsessed with cookies for a minute: What is space? What is time? And what is matter? We know that the answers we presently have to these questions are not fundamentally correct; they are merely approximately correct. And we want to know. We really really want to know. (The cookies. Are out.)

Strictly speaking of course physics will not tell you what reality is but what reality is best described by. Space and time are presently described by Einstein’s theory of general relativity; they are classical entities that do not have quantum properties. Matter and radiation are quantum fields described by the standard model. Yet we know that this cannot be the end of the story because the quantum fields carry energy and thus gravitate. The gravitational field thus must be compatible with the quantum aspects of matter sources. Something has to give, and it is generally expected that a quantization of gravity is necessary. I generally refer to ‘quantum gravity’ as any approach to solve this tension. In a slight abuse of language, this also includes approaches in which the gravitational field remains classical and the coupling to matter is modified.

Quantizing gravity is actually not so difficult. The problem is that the straight-forward, naive, quantization does not give a theory that makes sense as a fundamental theory. The result is said to be non-renormalizable, meaning it is a good theory only in some energy ranges and cannot be taken to describe the very essence of space, time, and matter. There are meanwhile several other, not-so-naïve, approaches to quantum gravity – string theory, loop quantum gravity, asymptotically safe gravity, causal dynamical triangulation, and a handful of others. The problem is that so far none of these approaches has experimental evidence.

This really isn’t so surprising. To begin with, it’s a technically hard problem that has kept some of the brightest minds on the planet occupied for decades. But besides this, returns on investment have diminished with the advent of scientific knowledge. The low hanging fruits have all been picked. Now we have to develop increasingly more complex experiments to find new physics. This takes time, not to mention effort and money. With that, progress slows.

And quantum gravity is a particularly difficult area for experiment. It’s not just a weak force, it’s weaker than the weak force! This grammatical oxymoron is symptomatic of the problem: Quantum effects of gravity are really, really tiny. Most of the time when I estimate an effect, it turns out to be twenty or more orders of magnitude below experimental precision. I’ve sometimes joked I should write a paper on “50 ways one cannot test quantum gravity”, just to make use of these estimates. It’s clearly not a low hanging fruit, and we shouldn’t be surprised it takes time to climb the tree.

Some people have claimed on occasion that the lack of a breakthrough in the area is due to sociological problems in the organization of knowledge discovery. There are indeed problems in the organization of knowledge discovery today. We use existing resources inefficiently, and I do think this hinders progress. But this is a problem which affects all of academia and is not special to quantum gravity.

I think the main reason why we don’t yet know which theory describes gravity in the quantum regime is that we haven’t paid enough attention to the phenomenology.

One reason phenomenological quantum gravity hasn’t gotten much attention so far is that it has long been believed experimental evidence for quantum gravity is inaccessible to experiment (a belief promoted prominently by Freeman Dyson). The more relevant reason is though that in the field of theoretical physics it’s a very peculiar research topic. In all other areas of physics, researchers share either a common body of experimental evidence and aim to develop a good theory. Or they share a theoretical framework and aim to explore its consequences. Phenomenological quantum gravity has neither a shared theory nor a shared set of data. So what can the scientist do in this situation?


The phenomenology of quantum gravity proceeds by the development of models that are specifically designed to test for properties of the yet-to-be-found theory of quantum gravity. These phenomenological models are normally extensions of known theories and are developed with the explicit aim of testing for general features. These models do not aim to be fundamental theories on their own.

Examples of such general properties that the fundamental theory might have are: violations or deformations of Lorentz-invariance, additional space-like dimensions, the existence of a minimal length scale or a generalized uncertainty principle, holography, space-time fluctuations, fundamental discreteness, and so on. I discuss a few examples below. If we develop a model that can be constrained by data, we will learn what properties the fundamental theory can have, and which it cannot have. This in turn can serve as guidance for the development of the theory.

In practice, these phenomenological models quantify deviations from general relativity and/or quantum field theory. One expects that the only additional dimensionful scale in these models is the Planck scale, which gives a ‘natural’ range for the expected size of effects in which all dimensionless constants are of order one. The aim is then to find an experiment that is sensitive to this natural parameter range. Since most of these models do not actually deal with quanta of the gravitational field, I prefer to speak more generally of “Planck scale effects” being what we are looking for.

Example: Lorentz-invariance violation

The best known example that demonstrates that effects are measureable even when they are suppressed by the Planck scale are violations of Lorentz-invariance. You expect violations of Lorentz-invariance in models for space-time that make use of a preferred frame that violates observer-independence, for example some regular lattice or condensate that evolves with some special time-slicing.

Such violations of Lorentz-invariance can be described by extensions of the standard model that couple to a time-like vector field and these couplings change the predictions of the standard model. Even though the effects are tiny, many of them are measureable.

The best example is maybe vacuum Cherenkov-radiation: the spontaneous emission of a photon by an electron. This process is normally entirely forbidden which makes it a very sensitive probe. With Lorentz-invariance violation, an electron above a certain energy will start to lose energy by radiating photons. We thus should not receive electrons above this threshold from distant astrophysical sources. From the highest energies of electrons of astrophysical origin that we have measured we can thus derive a bound on the possible violation of Lorentz invariance. This bound is today already (way) beyond the Planck scale, which means that the natural parameter range is excluded.

This shows that we can constrain Planck scale effects even though they are tiny.

Now this is a negative result in the sense that we have ruled out certain properties. But from this we have learned a lot. Approaches which induce such violations of Lorentz-invariance are no longer viable.

Example: Lorentz-invariance deformation

Deformations of Lorentz-invariance have been suggested as symmetries of the ground state of space-time. In contrast to violations of Lorentz-invariance, they do not single out a preferred frame. They generically lead to modifications of the speed of light, which can become energy-dependent.

I have explained a great many times that I think these models are flawed because they bring more problems than they solve. But leaving aside my criticism of the model, it can be experimentally tested. The energy dependence of the speed of light is tiny – a Planck scale effect – but the measurable time-difference adds up over the distance that photons of different energies travel. This is why highly energetic photons from distant gamma ray bursts are presently receiving a lot of attention as possible probes of quantum gravitational effects.

The current status is that we are just about to reach the natural parameter range expected for a Planck scale effect. It is presently a very active research area.

Example: Decoherence induced by space-time foam

If space-time undergoes quantum fluctuations that couple to all matter fields, this may induce decoherence in quantum mechanical oscillations. We discussed this previously in this post. In oscillations of neutral Kaon systems, we are presently just about to reach Planck scale sensitivity.

Misc other examples

There is no lack of creativity in the community! Some other examples of varying plausibility that we have discussed on this blog are Craig Hogan’s quest for holographic noise, Bekenstein’s table-top experiment that searches for Planck-length discreteness, massive quantum oscillators testing Planck-scale modified commutation relations, and searches for evidence for a generalized uncertainty in tritium decay. There is also a vast body of work on leftover quantum gravitational effects from the early universe, captured in various models for string cosmology and loop quantum cosmology, and of course there are cosmic (super) strings. There are further proposed tests for the idea that gravity is just classical (still a little outside the natural parameter range), and suggestions to look for dimensional reduction.

This is not an exhaustive list but just to give you a sense of the breadth of the topics.

Demarcation issues

What counts and what doesn’t count as phenomenological quantum gravity is inevitably somewhat subjective. I do for example not count the beyond the standard model physics of grand unification, though, if you believe in a theory of everything, this might be relevant for quantum gravity. I also don’t count applications of AdS/CFT because these do not describe gravitational systems in our universe, though arguably they are examples for some quantized version of gravity. I also don’t count general modifications of quantum theory or general relativity, though these might of course be very relevant to the problem. I don’t label these phenomenological quantum gravity mostly for practical reasons, not for ideological ones. One has to draw the line somewhere.


I often get asked which approach to quantum gravity I believe in. When it comes to my religious affiliation, I’m not only an atheist, I was never Christianized. I have never belonged to any church and I have no intention to join one. The same can be said about my research in quantum gravity. I don’t belong to any church and have never been Christianized. I have on occasion erroneously been called a string theorist and I have been mistaken for working on loop quantum gravity. Depending on the situation, that can be amusing (on a conference) or annoying (in a job interview). For many people it still seems to be hard to understand that the phenomenology of quantum gravity is a separate research area that does not built on the framework of any particular approach.

The aim of my work is to identify the most promising experiments to find evidence for quantum gravity. For that, we need phenomenological models to quantify the effects, and we need to understand the models that we have (for me that includes criticizing them). I follow with interest the progress in various approaches to quantum gravity (presently I’m quite excited about Causal Sets) and I try to develop testable phenomenological models based on these developments. On the practical side, I organize conferences and workshops to bring together theoreticians with experimentalists who have an interest in the topic to stimulate exchange and the generation of new ideas.

What I do believe in, and what I hope the above examples illustrate, is that it is possible for us to find experimental evidence for quantum gravity if we ask the right questions and look in the right places.


  1. "And quantum gravity is a particularly difficult area for experiment. It’s not just a weak force, it’s weaker than the weak force! This grammatical oxymoron is symptomatic of the problem: Quantum effects of gravity are really, really tiny."

    Unless the "strong force" is really atomic scale gravitation partially disguised, partially understood and almost completely misinterpreted.

    When the best minds have spent decades on a problem and yet have not achieved experimental success, it is usually because there is some fundamental assumption in their reasoning that is incorrect but they cannot break free from it.

    Mass is "quantized" at all fundamental scales of nature's hierarchy and nature's scaling includes discrete dilation invariance. This radically modifies the coupling constants like G.

    Robert L. Oldershaw
    Discrete Scale Relativity/Fractal Cosmology

  2. "Straight-forward, naive, quantization does [...] give a result [which] is said to be non-renormalizable".

    If I remember correctly the Wilson approach to renormalization group, being renormalizable for a quantum field theory means that it can keep its form (in term of interaction operators) up to any scale in order to describe the phenomenology, by simply adjusting the coupling constant values (so called 'running' of the renormalized coupling constants). Not being renormalizable, on the other hand, means that the theory needs new (dimensionful) operators when approaching the ultraviolet renormalization cutoff.

    Classic example: Fermi's four-fermion theory for the weak interaction was non-renormalizable, and in fact it was pointing to the W/Z bosons of the electroweak theory.

    So my question is: does the non-renormalizability of naive gravity quantization points to any intriguing energy scale? to any intriguing whatever?

  3. This two-year old says that space is what the matter that makes up cookies occupy in the time before I eat them :)

  4. Project Earth's surface onto a flat map without distortion, cuts, or folds. This
    fundamentally cannot obtain, then the Shroud of Turin. Gravitation demands obvious symmetries, then photon detection contradicts fermionic matter application. Violations get corrections. A rigorously derived axiomatic system cannot be internally falsified.

    Continuous geometry relativity works, but must be defective. Quantized spacetime has zero empirical validation. Vacuum isotropy is as weak as Euclid’s triangles, for both. Interrogate spacetime geometry with test mass geometry, not photons. Oppose self-similar single crystal enantiomorphic atomic mass distributions in an otherwise unremarkable Eötvös experiment. The worst it can do is succeed, violations being revealed as diagnostics. Rewrite gravitation given the inelegant, inescapable empirical footnote.

  5. Why to quantize gravity? Is the gravity quantized somewhere in our Universe - or the theorists just want to violate observations at any price from solely masochist reasons?

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  9. Energy does not gravitate. It condenses a portion of the finite total energy through the strong force. Because protons are confined through the strong force the large majority of gravity around standard matter is simply due to low energy density around standard matter making up for the condensed energy in matter. Whatever it is you want to call energy, its limited stuff.

    Have you been drinking the koolaid again, Bee? Sorry for amending my post so many times. I've come to realize that if I don't clarify terms you will wriggle out of a mistake by using a non-standard meaning for words like "gravitate".

  10. gravity, like all other forces comes as a pair: falling in we know from Newton's apple and spatial distention

    any object in motion carries gravitational-charge equivalent to its momentum(s)

    matter is a self-sustaining reaction of more fundamental motion forces

    there is no space and there is no time: space is merely the distance between objects and time is merely the distance between events (each requires an observer to denote what is an object and what is an event)

    - from my 1987 work The Fundamental Quanta

  11. Radii, I see no fundamental conflict with what you are saying and how I view it.

    Adding substance to my earlier quibble. If you use the word gravitate in the usual sense of "falling towards" then energy in its pure form would seem to act just the opposite of matter to matter or matter to photons.

    Before matter formed in the cosmos all evidence suggests the push was outward and acting the opposite of gravitating. Only when some of that energy combined in inelastic relationships through the formation of matter did gravity occur.

  12. God damn it! Every common sense thing I'm expressing seems to lead ineluctably to another common sense conclusion. Yet the final conclusion is completely different from what conventional wisdom says happens.

    If energy in its pure form before matter forms has no compensating pull of gravity before mass forms it would mean that the before the earliest form of mass occurs there would be no gravity. In other words, if the Higgs turned out to be the earliest form of mass then the unification of forces most likely occurs at that point, not at the Planck scale. Soooo, no heirarchy problem.

    I'll shut up now and let anyone who wants to find an error in my logic or assumptions.

  13. Hi Sabine,

    Are there any quantum gravity models that currently derive General Relativity and explain vacuum dragging effects such as the Thirring and Thirring-Lense effects and also make new predictions that can be tested experiment today?

    Cheers, Paul.

  14. The Holey Grail and its Dual: From String Theory to Strange Metals -


    The celebrated AdS/CFT correspondence makes it possible to deal with strongly coupled systems by mapping them to a weakly coupled gravitational system in a space-time with one more dimension. This is computationally more manageable, or at least one hopes so. So far, this correspondence, also called “duality”, between the gravity in the AdS space and the strongly coupled theory on the boundary of this space (thus one dimension less) is an unproved conjecture put forward by Juan Maldacena. However, it has been extensively tested for a few cases and many people are confident that it captures a deep truth about nature (though they might disagree on the extent to which it holds). We previously discussed this idea here and here.

  15. Hi Sabine

    You wrote:

    "Quantizing gravity is actually not so difficult. The problem is that the straight-forward, naive, quantization does not give a theory that makes sense as a fundamental theory. The result is said to be non-renormalizable, meaning it is a good theory only in some energy ranges and cannot be taken to describe the very essence of space, time, and matter."

    QED is renormalizable; this means that QED makes sense as a fundamental theory describing the electromagnetic interactions?

  16. Hi Eric,

    You're right, it's not energy that gravitates, it's energy density. Best,


  17. Hi hronir,

    Yes, it's the Planck scale that I keep talking about. Best,


  18. Hi Giotis,

    Well, I'd say renormalizability is a necessary but not a sufficient criterion as the theory can have other problems, like QED has a Landau pole. Or a theory might be renormalizable but violate unitarity. Or have some other disease that would make you doubt it's the last word. Best,


  19. Hi Paul,

    Pheno QG models don't normally 'derive' Einstein's field equations, they parameterize deviations. The only two example that I know that would fit your bill might be a) Verlinde's entropic gravity. I don't know though if people have looked at the Lense Thirring effect. It seems quite unlikely because the deviations would probably primarily be relevant at long distances. And b) there are Lorentz-invariance violating models (Jacobson et al) where the preferred frame field only couples to gravity and not to the SM particles. In these cases you generically have deviations from General Relativity, many of which have been calculated. I'm not following this part of the literature too closely though, so I recommend you look up the original references. It goes under the keyword 'Einstein-aether gravity'.



  20. You see, the problem is in not yet solved renormalization program. If one manages to renormalize the equations exactly, from the very beginning, by subtracting the counter-terms, the resulting equations will be physical, see my toy model here:

  21. A Gravitational Explanation for Quantum Mechanics: There is no quantum theory of gravity. There is no graviton. Gravitational waves cannot exhibit quantum phenomena such as wave particle duality. Gravitational waves are not quantized.

  22. String theory is known to be inherently fuzzy already, i.e. leading to vast landscape of false vacui solutions. But string theory is quantum gravity theory and it can be proven, the same fuzziness is inherent obstacle for any other quantum gravity theory due the insintric inconsistency of postulated of both theories.

  23. Of course these insights were and will be ignored, because physical theorists are looking for ways, how to prolonge their research and how get as much grants for it as possible - not how to get their work nonsensical and ending prematurely. Quantum gravity theorists aren't an exception. We are living in era of physics driven with occupation criterions.

  24. Freeman Dyson's 2012 Poincare Prize Lecture discounts single graviton detection in part for requiring "a shield or a set of anti-coincidence detectors [made] out of some mythical material with super-high density." Muon/electron mass ratio is 206.7682843. To zeroeth order orbit radius, µ,µ-H_2 would be 1/(206.7683)^3 the atomic volume of H_2 (DOI:10.1126/science.1230016), or 8.84 million times denser than solid hydrogen at 0.086 g/cm^3. More localized ground-state wavefunction, shorter molecular bond length, and stronger lattice interactions promise even greater packing density.

    Be quick about assembly and measurement (2.2 µsec muon mean lifetime). Cooling a newly condensed shield (binding energy) to full density prior to measurement is left as an exercise for the alert reader.

  25. Highly relevant new post and discussion at Peter Woit's Not Even Wrong.


  26. The thread I was referring to is entitled "Farewell To Reality"

    Of special note is the comment on June 18, 2013 at 6:15 AM (somewhere around #45) by the author of the relevant book of the same title.

    Discrete Scale Relativity

  27. There is growing evidence that gravity IS renormalizable due to the existence of a (nontrivial) UV fixed point (Asymptotic Safety). It's just not nonperturbatively renormalizable, as are the other forces.


  28. Yeah, I would say that even if a theory is perturbatively non-renormilizable, it could well have an UV fixed point and thus defined on all scales (i.e. fundamental). So
    non-renormilizability is not a necessary condition for the UV completion of a theory.

  29. Markus, Giotis,

    Yes, as you can see, I mentioned asymptotically safe gravity in the above post. My point was simply this: Naively (read: perturbatively) quantized gravity breaks down at the Planck scale and isn't what we're looking for, so one has do to more than that. 'More' could be a non-trivial fixed point in the UV or it could be string theory or whatever. Loads of people have been working on that since decades. Be that as it may, we'll not know which approach describes nature unless we have experimental evidence. This isn't to say that understanding the theory is useless, just that theory alone doesn't make the physics. Best,


  30. Hi Bee,

    I've always favoured the agnostic approach whether it relates to philosophy or scientific theory, as it having hope able to keep one wanting to know more with giving due consideration to presented options, while having skepticism able to temper judgement respective of what one hopes for. Thus I find the phenomenological approach to quantum gravity more indicative of an agnostic’s mindset than that of an atheist, as enabling one to enjoy the benefits of having faith, while avoiding being restricted by the pitfalls of belief.

    ” Naive falsificationism takes it for granted that the laws of nature are manifest an not hidden beneath disturbances of considerable magnitude. Empiricism takes it for granted that sense experience is a better mirror of the world than pure thought. Praise of argument takes it for granted that the artifices of Reason give better results than the unchecked play of our emotions. Such assumptions may be perfectly plausible and even true. Still, one should occasionally put them to a test. Putting them to a test means that we stop using the methodology associated with them, start doing science in a different way and see what happens.”

    -Paul Karl Feyerabend, “Against Method”, p295-296

  31. Hi Phil,

    Agnosticism seems to me taking the position that we don't know, we'll probably never know, and who cares anyway. It's not an attitude that has any scientific spirit in it if you ask me, it's just a giant shoulder shrug. I definitely care what we'll find and as I said I am very convinced that we will find something, eventually.

    Maybe you'll find Eagleman's possibilism interesting :o) Best,


  32. Sabine, Giotis,

    sorry, I wanted to say: "It's just not PERTURBATIVELY renormalizable, as are the other forces.".
    This may have caused some confusion.

    So at least there is one theory demonstrating that renormalizability need not be the problem with gravity. But this is just a mathematical statement, if a theory matches physical reality is another thing.

    Is string theory really renormalizable ? (As far as I know a proof of its perturbative renormalizability is still lacking and a nonperturbative formulation is yet to be found).


  33. After (unfortunately from yesterday late) Wilson non re-normilizability wasn't really a problem for Gravity and for any other theory for that matter. It was understood that the perturbed QG is just an effective field theory like all QFTs and for its UV completion you need new degrees of freedom.

  34. Markus,

    Yes, I understand what you are saying. What I mean is if you perturbatively quantize it, you don't get what you want, and everything else needs more work and we don't yet really know how it works. Best,


  35. Hi Giotis,

    Yes, as I wrote, you can perturbatively ('naively') quantize it, and you get a theory, and that theory is just fine as an effective theory, but that's not what we're looking for. Best,


  36. Hi Sabine

    Yes, so I think we agree that renormalizability does not determine whether a theory is effective or not.

    It is neither sufficient nor necessary condition.

  37. Hi Sabine,

    Yes, I agree.

    "In November 1949, ... I met Pauli. I was hoping to spend some time as a postdoc at the ETH, so Pauli asked me what I was working on. I said I was trying to quantize the gravitational field. For many seconds he sat silent, alternately shaking and nodding his head (a nervous habit he had, affectionately known as die
    Paulibewegung). He finally said 'That is a very important problem - but it will take someone really
    - Bryce DeWitt -

    Extracted from "Quantum Gravity, Yesterday and Today", a very nice paper, by the way.


  38. Hi Bee,

    In the vernacular style of Richard Dawkins I find a Possibilian to be little more than a sexed up agnostic :-)

    ”Experience arises together with theoretical assumptions not before them, and an experience without theory is just as incomprehensible as is (allegedly) a theory without experience.”

    Paul Feyerabend, “Agianst Method”, pg 151



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  40. Hi Markus,

    While following down that most interesting quote of Dewitt’s you posted here , I came across another of his published in a book written by his son in his memory. Here he states that humans should “resist the temptation of believing that the universe exists for Man”; with this I totally agree. However I find it still interesting to consider if perhaps Man exists for the universe, as if for no other reason to enable it to have itself understood. Never the less, with such philosophical difference aside, I’m considering buying this book, as thinking it could prove interesting in telling the story of someone who spent much of his life projecting the goal for the universe that I propose as possible. Also thanks once again for putting me onto the contributions of Dewitt respective of the continuing development of a quantum gravity theory.

    “Theoretical physicists are the modern theologians. But they are amateurs. They are impressed, as anyone should be, by the scale and the astonishing properties of our universe, and they would like to see the face of God. When they are young they are set out, full of optimism, to discover how the universe ticks. Ultimately they learn, the words of Steven Weinberg, that “the more the universe seems comprehensible, the more it seems pointless.” At least it doesn’t point to any goal for human beings. It is certainly not incompatible with human beings, for they are part of it and can exploit it to their own advantage as far as they are able. But human beings must set their own goals. Among many worthy goals, one is to understand Nature. Another is to resist the temptation of believing that the universe exists for Man.”

    -Bryce DeWitt, from the book “The Pursuit of Quantum Gravity: Memoirs of Bryce DeWitt from 1946 to 2004”, written by Cécile DeWitt-Morette, Published by Springer.

  41. "... identify the most promising experiments to find evidence for quantum gravity." Look at Milgrom's MOND and the space roar. The space roar is supported by: (1) FIRAS & low-frequency radio data (2) ARCADE 2 & low-frequency radio data (3) ARCADE 2 & FIRAS.

  42. Hi Demian,

    It was certainly kind of you to refer to that as a small correction; many and my sincerest apologies are than due to his wife.




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