“I've often heard you say that we don't have a theory of quantum gravity yet. What would be the requirements, the conditions, for quantum gravity to earn the label of 'a theory' ?

I am particularly interested in the nuances on the difference between satisfying current theories (GR&QM) and satisfying existing experimental data. Because a theory often entails an interpretation whereas a piece of experimental evidence or observation can be regarded as correct 'an sich'.

That aside from satisfying the need for new predictions, etc.

Thank you,

Best Regards,

Noa Drake”

Dear Noa,

I want to answer your question in two parts. First: What does it take for a hypothesis to earn the label “theory” in physics? And second: What are the requirements for a theory of quantum gravity in particular?”

**What does it take for a hypothesis to earn the label “theory” in physics?**

Like almost all nomenclature in physics – except the names of new heavy elements – the label “theory” is not awarded by some agreed-upon regulation, but emerges from usage in the community – or doesn’t. Contrary to what some science popularizers want the public to believe, scientists do not use the word “theory” in a very precise way. Some names stick, others don’t, and trying to change a name already in use is often futile.

The best way to capture what physicists mean with “theory” is that it describes an identification between mathematical structures and observables. The theory is the map between the math-world and the real world. A “model” on the other hand is something slightly different: it’s the stand-in for the real world that is being mapped by help of the theory. For example the standard model is the math-thing which is mapped by quantum field theory to the real world. The cosmological concordance model is mapped by the theory of general relativity to the real world. And so on.But of course not everybody agrees. Frank Wilczek and Sean Carroll for example want to rename the standard model to “core theory.” David Gross argues that string theory isn’t a theory, but actually a “framework.” And Paul Steinhardt insists on calling the model of inflation a “paradigm.” I have a theory that physicists like being disagreeable.

Sticking with my own nomenclature, what it takes to make a theory in physics is 1) a mathematically consistent formulation – at least in some well-controlled approximation, 2) an unambiguous identification of observables, and 3) agreement with all available data relevant in the range in which the theory applies.

These are high demands, and the difficulty of meeting them is almost always underestimated by those who don’t work in the field. Physics is a very advanced discipline and the existing theories have been confirmed to extremely high precision. It is therefore very hard to make any changes that improve the existing theories rather than screwing them up altogether.

**What are the requirements for a theory of quantum gravity in particular?**

The combination of the standard model and general relativity is not mathematically consistent at energies beyond the Planck scale, which is why we know that a theory of quantum gravity is necessary. The successful theory of quantum gravity must achieve mathematical consistencies at all energies, or – if it is not a final theory – at least well beyond the Planck scale.

If you quantize gravity like the other interactions, the theory you end up with – perturbatively quantized gravity – breaks down at high energies; it produces nonsensical answers. In physics parlance, high energies are often referred to as “the ultra-violet” or “the UV” for short, and the missing theory is hence the “UV-completion” of perturbatively quantized gravity.

At the energies that we have tested so far, quantum gravity must reproduce general relativity with a suitable coupling to the standard model. Strictly speaking it doesn’t have to reproduce these models themselves, but only the data that we have measured. But since there is such a lot of data at low energies, and we already know this data is described by the standard model and general relativity, we don’t try to reproduce each and every observation. Instead we just try to recover the already known theories in the low-energy approximation.

That the theory of quantum gravity must remove inconsistencies in the combination of the standard model and general relativity means in particular it must solve the black hole information loss problem. It also means that it must produce meaningful answers for the interaction probabilities of particles at energies beyond the Planck scale. It is furthermore generally believed that quantum gravity will avoid the formation of space-time singularities, though this isn’t strictly speaking necessary for mathematical consistency.

These requirements are very strong and incredibly hard to meet. There are presently only a few serious candidates for quantum gravity: string theory, loop quantum gravity, asymptotically safe gravity, causal dynamical triangulation, and, somewhat down the line, causal sets and a collection of emergent gravity ideas.

Among those candidates, string theory and asymptotically safe gravity have a well-established compatibility with general relativity and the standard model. From these two, string theory is favored by the vast majority of physicists in the field, primarily because it has given rise to more insights and contains more internal connections. Whenever I ask someone what they think about asymptotically safe gravity, they tell me that would be “depressing” or “disappointing.” I know, it sounds more like psychology than physics.

Having said that, let me mention for completeness that, based on purely logical reasoning, it isn’t necessary to find a UV-completion for perturbatively quantized gravity. Instead of quantizing gravity at high energies, you can ‘unquantize’ matter at high energies, which also solves the problem. From all existing attempts to remove the inconsistencies that arise when combining the standard model with general relativity, this is the possibly most unpopular option.

I do not think that the data we have so far plus the requirement of mathematical consistency will allow us to derive one unique theory. This means that without additional data physicists have no reason to ever converge on any one approach to quantum gravity.

Thank you for an interesting question!

## 13 comments:

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agreement with all available data relevant in the range in which the theory applies" Empirically sterile models have excuses and testing prohibitions. "hard to make any changes that improve the existing theories rather than screwing them up altogether" Save science not face.Two gold-plated, externally identical, solid single crystal alpha-quartz balls locally vacuum free fall. Crystallographic space group P3(1)21 with all atoms in

right-handed three-fold helices opposes mirror image space group P3(2)21 with all atoms inleft-handed three-fold helices. Only symmetries diverge; chirality emergent volume is 0.113 nm^3. Does the Equivalence Principle fail? "This is not the answer we are seeking."Thank you for an interesting reply!

Interesting! By the way, in mathematical logic and theoretical computer science, the notions of theory and model are different from those you describe: there, a theory is essentially a set of formal propositions closed under deduction. A formal proposition would be some P like "(A implies B implies) implies (not B implies not A)" or "2 + 2 = 5". Or more complicated P, involving existential and universal quantifiers, modal operators, and so on. Rules of deduction would be things like "Every proposition declared to be an axiom is a theorem (= an element of the theory)". Or "If P1 and (P1 implies P2) are theorems, then so is P2" (closure under modus ponens). Or more exotic deduction rules depending on the logic at hand. A theory need not even be consistent! (Though consistency is a key desideratum.)

A model is a *mathematical* thing that (via some detours) maps propositions to truth values ("true" or "false") or more elaborate mathematical domains.

One then calls a theory "sound" if every theorem holds in every model, and "complete" if every proposition that holds in every model is a theorem.

I'm mentioning this for two reasons: firstly, because the ontologies are so strikingly different: in your view, *theories* mediate between models and the real world. In the logician's view, *models* mediate between theories and truth values (or more elaboratory mathematical domains). Secondly, because it's important to give the public consistent notions of "theory" and "model".

I'm not criticising your version though. I'm just realizing the hard sciences would do well syncing their views.

Sabine,

I wish to make a quick comment on your paper 1208.5874: in the equal time commutator (1) and (3), the delta function is singular at x=y and its product with the reduced Planck constant becomes ill-defined near the classical limit (h = 0). One may need to insert a smooth regulator of the form f (p^2/Lambda^2), where Lambda stands for the UV scale. This procedure should replicate the regularization used in the path-integral formulation of the axial anomaly (Fujikawa method).

Carsten,

Thanks, that's interesting, I didn't know that.

It's not so surprising though that there is a difference between math and physics when it comes to a 'theory'. While both agree on mathematical consistency being necessary, in physics you also need an identification of observables.

Yes, I agree that it would be good if we had a common terminology, but I don't see any way to get there. The second best I suppose is just to point out the different ways the word is used. Best,

B.

Ervin,

Yes, thanks. Whenever I use a delta-function, please understand it as some epsilon-to-zero limit of something else. The classical limit in this paper is \alpha to zero, not \hbar to zero. Best,

B.

Dear Sabine,

I love how you pointed out that GR and SM are inconsistent beyond Planck's mass,

"The combination of the standard model and general relativity is not mathematically consistent at energies beyond the Planck scale, which is why we know that a theory of quantum gravity is necessary. "

It seems to me that although technically correct such a phrasing is too subtle to be detected by most of the readership of popular science texts.

I find no other way to explain why looking back to Donoghue's papers from early '90s (there's probably even older stuff which I'm not aware of) you could find statements s.a. (I'm paraphrasing) "GR and QFT are compatible below Planck scale in the EFT sense and they lead to unambiguous, calculable quantum gravity effects", but even now, some 20 years later, in most of the pop-sci texts and videos everybody just keeps grinding on about how SM and GR are fundamentally incompatible.

I feel that this subtle message that you include in passing should actually be made much less subtle and maybe brought to the front. These are only concrete calulations in QG, these are the ones which can first be experimentally tested, and if ever possible these will be the ones to distinguish which QG theory is false and which may just be the "quantum theory of gravity".

I also have a question to make. I found it surprising that you do not include non-commutative geometry on your list of candidate theories. I'm wondering why this is so?

Best,

Vedran

Vedran,

Yes, you are right with this observation. I referred to this as a "paradigm shift that nobody noticed".

Do you mean Connes' non-commutative geometry? You're right, it should have been on the list. Sorry for the omission. It seems to have lost some popularity after predicting the Higgs-mass but not getting it right. Best,

B.

Trivial point. You write:

"In physics parlor, high energies are often referred to as “the ultra-violet” or “the UV” for short, and the missing theory is hence the “UV-completion” of perturbatively quantized gravity."

Should that be "parlance" not "parlor"?

A very clarifying elaboration, thank you Sabine.

GMHurley,

Yes, sorry about that, I've fixed it. Thanks for pointing out!

Hi Bee,

"There are presently only a few serious candidates for quantum gravity: string theory, loop quantum gravity, asymptotically safe gravity, causal dynamical triangulation, and, somewhat down the line, causal sets and a collection of emergent gravity ideas."

Could you point out among the candidates mentioned above, which ones make new predictions in physics that can be verified by experiment today or the near future (in the lab on earth)?

Cheers, Paul.

Captain InterStellar,

No existing approach to quantum gravity makes direct predictions. The search for experimental evidence for quantum gravity presently proceeds through phenomenological models, which are inspired by, but not strictly speaking derived from, the theoretical approaches. There is a large number of possible signatures which are being considered, from cmb non-gaussianities and tensor modes to unexplained decoherence to measuring the gravitational field of quantum oscillators. I write about these frequently on this blog. I am also presently organizing a conference on the topic, so sticking around will tell you more about this than you ever wanted to know. Best,

B.

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