One of the maybe most interesting developments is a revival of the idea that black hole evolution might just not be unitary. Recall, if one takes Hawking's semi-classical calculation of black hole evaporation one has a hard time explaining how information that falls into a black hole can come out again. (And if you don't recall, read this.) There is the option to just accept that information doesn't come back out. However, this would be in conflict with unitarity, one of the sacred principles of quantum mechanics. But nothing really is sacred to a theoretical physicist with a headache, so why not do without unitary? Well, there is an argument dating back to the early 80s by Banks, Susskind and Peskin that this would go along with violation of energy conservation.

Each time this argument came up I recall somebody objecting. Personally I am not very convinced that's the right way to go, so I was never motivated enough to look into this option. But interestingly, Bill Unruh has now offered a concrete counter-example showing that it is possible to have decoherence without violating energy conservation (which you can find on the arXiv here), that seems to have gone some way towards convincing people it is possible. It seems to me quite likely at this point that non-unitary black hole evaporation might increase in popularity in the next years again, so this is a good time to tell you about neutral Kaons. Stay with me for some paragraphs and the link will become clear.

Black hole evaporation seems non-unitary when taking Hawking's calculation all the way to the end stage because the outcome is always thermal radiation no matter what one started with - it's a mixed state. One could have started for example with a pure state that collapsed to a black hole. Unitary evolution will never give you a mixed state from a pure state.

But what if we'd take it seriously that black hole evaporation is not unitary? It would mean that if you take into account gravity it might be possible to note decoherence in quantum systems when there shouldn't be any according to normal quantum mechanics. Everything moves through space-time and, in principle, that space-time should undergo quantum fluctuations. So it's not a nice and smooth background, but it is what has become known as "space-time foam" - a dynamic constantly changing background, a background in which Planck scale black holes might be produced and decay all the time.

This idea calls for a phenomenological model, a bottom-up approach that modifies quantum mechanics in such a way as to take into account this decoherence induced by the background. In fact a model for this has been proposed already in the early 80s by Ellis et al in their paper "Search for Violations of Quantum Mechanics." It is relatively straight forward to reformulate quantum mechanics in terms of density matrices and allow for a non-unitary additional term for the Hamiltonian. As usual for phenomenological models, this modification comes with free parameters that quantify the deviations. For quantum gravitational effects, you should expect the parameters to be a number of order one times the necessary powers of the Planck mass. (If that doesn't make sense, watch this video explaining natural units.)

This brings us to the question how to look for such effects.

A decisive feature of quantum mechanics is the oscillation between eigenstates, which is observable if the state in which a particle is produced is a superposition of these eigenstates. Decoherence is the loss of phase information, so the oscillation is sensitive to decoherence. Neutrino oscillations are an example of an oscillation between two Hamiltonian eigenstates. However, neutrinos are difficult to observe - it takes a lot of patience to collect enough data because they interact so weakly. In addition, at the typical energies that we can produce them with the oscillation wavelength is of the order of a kilometer to some hundred kilometers, not really very lab friendly.

Enter the neutral Kaons. The Kaons are hadrons; they are composites of quarks. The two neutral Kaons have the quark content of strange and anti-down, and down and anti-strange. Thus, even though they are neutral, they are not their own anti-particles. Instead, each is the anti-particle to the other. These Kaons are not however eigenstates of the Hamiltonian. Naively, one would expect the CP eigenstates, that can be constructed from them, to be the eigenstates of the Hamiltonian. Alas, the CP eigenstates are not Hamiltonian eigenstates either because the weak interaction breaks CP invariance.

The way you can show this is to construct the CP eigenstates to the eigenvalues +1 and -1 and note that the state with eigenvalue +1 can decay into two pions, which is the preferred decay channel. The one with eigenvalue -1 needs (at least) three pions. Since three is more than two, the three pion decay is less likely, which means that the CP -1 state lives longer.

Experiment shows indeed that there is a long lived and a short lived Kaon state. These measured particles are the mass eigenstates of the Hamiltonian. But if you wait for the short lived states to have pretty much all decayed, you can show that the long lived one

*still*can do a two pion decay. In other words, the CP eigenstates are not identical to the mass eigenstates, and the CP +1 state mixes back in. This indirect proof of CP violation in the weak interaction got Cronin and Fitch the Nobel Price in 1980.

The same process can be used to find signs of decoherence. That's because the additional, decoherence inducing term in the Hamiltonian enters the prediction of the observables, eg the ratio of the decay rates in the two pion channel. The relevant property from the neutral Kaons that enters here is the difference in the decay widths which happens to be really small, of the order 10

^{-14}GeV, times the CP violating parameter ε

^{2}which is about 10

^{-6}, and we know these are values that can be measured with presently available technology.

This has to be compared to the expectation for the size of the effect if it was a quantum gravitational effect, which would be of the order

*M*

^{2}/

*m*

_{Pl}, where

*M*is the mass of the Kaons (about 500 MeV) and

*m*

_{Pl}is the Planck mass. If you put in the numbers, you'll find that they are of about the same order of magnitude. There's some fineprint here that I omitted (most important, there are three parameters so you need several different observables) but roughly you can see that it doesn't take a big step forward in measurement precision to be sensitive to this correction. In fact, presently running experiments are now on the edge of being sensitive to this potential quantum gravitational effect, see eg this recent update.

To come back to the opening paragraphs, the model that is being used here has the somewhat unappealing feature that it does not automatically conserve energy. It is commonly assumed that energy is statistically conserved, for example Ellis et al write "[A]t our level of sophistication the conservation of energy or angular momentum must be put in by hand as a statistical constraint." Mavromatos et al have worked out a string-theory inspired model, the D-particle foam model, in which energy should be conserved if the recoil is taken into account, but the effective model has the same property that individual collisions may violate energy conservation. It will be interesting to see whether these models receive an increased amount of attention now.

I like this example of neutral Kaon oscillations because it demonstrates so clearly that quantum gravitational effects are not necessarily too small to be detected in experiments, and it is likely we'll hear more about this in the soon future.

## 34 comments:

"It would mean that if you take into account gravity it might be possible to note decoherence in quantum systems when there shouldn't be any according to normal quantum mechanics."Is this in any way related to Penrose's idea that the influence of gravity is the reason why macroscopic mixed states are not observed?

Have you said 1) the vacuum has a trace parity-odd chiral background; 2) rigorous angular momentum conservation is questioned; 3) only quarks and leptons participate; and 4) gravitation is coupled to it? Test to 1.2x10^(-16) sensitivity (active mass fraction of loaded mass) in a 90-day geometric parity Eötvös experiment. Contrast chemically and macroscopically identical, single crystal test masses in enantiomorphic space groups:

P3(1)21 (right-handed) versusP3(2)21 (left-handed) alpha-quartz.The Eot-Wash group's torsion pendulum measures only Equivalence Principle violation nulls. A net violation output explains dark matter, SUSY failure, quantum gravitation unphysicality. 1) This is not the solution we are seeking, 2) There is no precedent for the experiment, and 3) The experiment seeks to falsify rather than validate theory. Yes! Do it.

Hi Phillip,

I haven't followed this very closely, but Penrose I believe has in mind a specific form for the collapse inducing term I think. I don't know what he has to say about the decoherence time of neutral Kaons, I never saw any specific prediction. I think his idea is more closely related to this one, also in terms of phenomenology. The collapse/decoherence is supposed to be induced by the gravitational field of the particles themselves and not, as it's the case here, by the fluctuations of the background. (Which reminds me though that I meant to look up what's the status of his predictions, thanks.) Best,

B.

I think Bill Unruh's example of non unitarity with energy conservation is fascinating. And I think he's right. Energy is required in the precession of spin while not strictly increasing the magnitude of angular momentum. Think of a swiveling wheel suddenly coming in contact with a directional force. In the instant of first contact with the force thr angular momentum does not increase but only serves to align the angular momentum with the force.

Since the quantum world is generally considered time reversible it would be like this rotating wheel acting in reverse. There would suddenly be a decrease in angular momentum with energy being released randomly at different angles and a concomitant change in the direction of the angular momentum spin vector. But if true reversibility was in effect there would be instants where there is a disconnect between conservation of the "magnitude" of the angular momentum while still maintaining energy conservation through the process of precession.

In effect there would random changes in the direction of spin of the black hole with the emission of photons in random directions. Maybe Stephen Hawking was wrong that in bh evaporation the photons only radiate perpendicularly to one set spin vector. Maybe there is a constant wobble that emits photons in all directions that correlates with each instantaneous wobble?

"... which would be of the order M^2/m_{Pl}"That

can'tbe right. No quantum gravity effect should depend on thesquare rootof Newton's constant.At best, the effect (if it exists at all) goes like M^3/m_{pl}^2, which is

way too smallto measure.Oops. If you looked at a spin vector like you look at an angular momentum vector that vector would always be perpendicular to the plane of the spin. So in Stephen Hawking's version the photon emission is in the direction of the spin vector. But he might be wrong about that. That is, the photon emission would always be coincident with the instantaneous change in the vector angular momentum of the black hole. But that direction of the instanteous angular momentum would not be constant. Therefore, from an outside reference frame the photons would be emitted in all directions.

Distler,

It's not a perturbative effect. I agree that it's not particularly plausible, but difficult to exclude in lack of the fundamental theory. Best,

B.

Hi Bee,

Nice piece which forms to be one of those whose implications I will now have my radar up for. If nothing else it’s had me aware there is more than one colliders results that should be paid attention to.

Best,

Phil

"It's not a perturbative effect."It's certainly a

weak(effective) coupling effect.So you need to explain

why you thinkit should go like the square-root of Newton's constant. Why not the 4th root? (Or some other positive power?)"I agree that it's not particularly plausible, but difficult to exclude in lack of the fundamental theory. Best,"I disagree.

At weak effective coupling, I

don't believe you(regardless of the fundamental theory) that there's a mechanism which produces effects that scale like the square-root of the effective coupling.Maybe you could convince me by giving an example, in some other theory, where such an effect arises.

Saying that we "don't have a fundamental theory" merely compounds the implausible assertion --- that the alleged effect exists at all --- with the even more implausible assertion that the effect appears with a strength

19 orders of magnitude largerthan one expects for a weak coupling effect.Hi Distler,

How is the formation and evaporation of Planck scale black holes a perturbative effect? You don't have to believe me anything, I've just summarized the papers that I linked to. Maybe read Mavromatos' papers, then you can pick around on that. If I thought it was a promising effect to look for, I'd probably we working on it. Best,

B.

"How is the formation and evaporation of Planck scale black holes a perturbative effect?"It's not. So, rather than scaling like a (positive integer) power of the effective coupling, I would expect it to be

exponentially suppressed(like an instanton effect) at weak effective coupling.Which means that

it would be even more unobservablethan a perturbative effect would be."Maybe read Mavromatos' papers..."This was suggested by Nick Mavromatos? Ah. Well that explains it.

No, it wasn't originally suggested by Mavromatos. Maybe read my post.

"No, it wasn't originally suggested by Mavromatos."It

reallydoesn't matter to mewhofirst suggested that there's an effect in the neutral kaon system that goes like M_k^3/m_{Pl}. That strikes me asobvious nonsense.Evidently, you disagree, so I'm curious as to why.

"Maybe read my post."I did. Which is why I am asking the questions I am asking.

Obviously, you think the above assertion is

plausible enoughto write a whole blog post about. So I'm asking you to share your insight as to why.Well, evidently your "reading" was so attentive that you missed both the reference to Ellis et al as well as the reference to Mavromatos, as well as the explanation about black holes and their evaporation to begin with. So excuse me for suggesting that you actually read what I wrote.

Yes, in fact I think it's plausible enough. Everybody who seriously believes to know enough about the UV completion of quantum gravity to claim that effects to first order in M/m_pl are "obviously nonsense" has lost touch to reality. Go prove it and write a paper and then come back. Until then, I think it's plausible enough to parameterize effects in a power series with unknown coefficients, though maybe not plausible enough for me to spend my time on it. Best,

B.

Dear Jacques, I understand that by doing perturbative expansions involving the Einstein-Hilbert action and even higher-derivative terms of that kind, you get integer powers of G = 1/m_{Planck}^2.

And I agree about your statements that the nonperturbative effects (like instantons) are even smaller than the perturbative ones, exponentially suppressed, and so on.

But just to be sure: how do you rule out the possibility that the effective action has, for example, h^5/M_{Planck} where h is the physical Higgs field? I agree it would be huge, unexpected, but is there really a solid proof that QG can't generate huge non-renormalizable terms of this kind in the effective action?

Again, I am just asking, thinking it is plausible that you have such a proof and it may be just a simple extra realization added to the proof obvious to me that one doesn't get it from the actual effective QFT including the Einstein-Hilbert action and other things.

"But just to be sure: how do you rule out the possibility that the effective action has, for example, h^5/M_{Planck} where h is the physical Higgs field?"Why start there? If you're going to entertain the possibility that quantum gravity can induce large corrections to the effective potential, why not start by asking about M_{Planck} h^3?

In terms of the electroweak fields, such terms look like

(H^† H - v^2)^{n/2}

where v is the electroweak symmetry-breaking scale. (Obviously, the n=2 and n=4 terms can be reabsorbed in a redefinition of the cosmological constant, v^2, and the quartic Higgs self-coupling, which is why I suggested starting with n=3.)

The problem with such terms, were they present, is that they would lead to bad behaviour of scattering amplitudes at energies

way belowthe Planck scale. Presumably, you (if not Bee) would find that objectionable, on physical grounds.Moreover, once you start entertaining such terms, there's no particular reason to restrict yourself to

integern. Why not(H^† H - v^2)^a

for arbitrary a?

Dear Jacques,

you wrote: Why start there? If you're going to entertain the possibility that quantum gravity can induce large corrections to the effective potential, why not start by asking about M_{Planck} h^3?

LM: I think that you think that you are asking a rhetorical question but I think that this "Why" question of yours has a very good answer. MPlanck.h^3 doesn't vanish in the G=0 limit so it is ruled out but the 1/MPlanck terms do vanish in the limit.

There's also a difference between your random fractional powers and my h^5/MPlanck: the latter is polynomial in the fields. It may be a fractional power of Newton's constant but this constant isn't a dynamical observable.

I don't consider your comment a proof I asked you for. By quoting a different possible term that *may* be proved to be wrong and saying that they're "analogous", you're not proving anything because the question is moved to the question whether they're really analogous. One may show - and I have shown - reasons to say that they are not analogous and the answers to questions about their validity may be different.

Moreover, I didn't mean any subtraction of v. The discussion whether 1/MPlanck is allowed surely depends on the precise quantity one studies. For example, the neutrino mass term, in the seesaw Ansatz, is schematically

psi.psi.m_H^2/m_GUT

so it does have the first and not second power of 1/m_GUT, doesn't it? It's because the mass term for fermions is linear and not quadratic in the mass.

Considering the GUT physics to be a part of the broader quantum gravity regime, this pretty much falsifies the claim that "all" terms in the effective action only have integer powers of G. So I think that to support your claim, you must first refine it and say which terms must have integer powers of G. It's apparently not the neutrino mass terms.

Also, dimensions of various operators are non-integer in the full theory - anomalous dimensions etc. - so they are naturally multiplied by coefficients that are not simply integer powers of scales, either. And the fractional part of anomalous dimensions doesn't have to be tiny - it may boil down to substantial couplings such as the Standard Model gauge couplings.

While I can prove that the K0 effective Hamiltonian doesn't have big terms of order 1/MPlanck from quantum gravity, at least starting from an effective theory with the EH action, and maybe even from a reasonable string starting point, I don't know what to do with a more general claim that there is never G^{1/2} in "any terms".

BTW in M-theory, G is length^9 but there is a similarly natural claim to yours that natural objects always have integer powers of G^{1/3}. For example, the M2-brane and M5-brane tension is Mplanck^3 and MPlanck^6, respectively. Other powers are "unnatural". But they're not necessarily integer powers of G and the absence of other powers than integer powers of LPlanck^3 may be due to a higher symmetry.

Best regards

LM

"I think that this "Why" question of yours has a very good answer. MPlanck.h^3 doesn't vanish in the G=0 limit so it is ruled out but the 1/MPlanck terms do vanish in the limit."If you're going to entertain quantum gravity corrections to the effective action which are

largerthan expected (atweakeffective coupling), then you should not out-of-hand exclude terms which violate the (equally-naive, or equally sensible) expectation that they should vanish in the decoupling limit."Moreover, I didn't mean any subtraction of v"That was in inessential (and, apparently, confusing) nicety. The terms is question look like

(H^† H)^{n/2}

Such non-analyticities in the potential, at points in field space which can be probed at accessible energies (and H=0 is certainly probed at energies above the electroweak symmetry-breaking scale, but well-below the Planck scale) signal the breakdown of the effective field theory.

There's nothing wrong, per-se, with such a breakdown. It just indicates that new physics must enter at this energy scale. I'm happy to entertain the prospect of new Physics. But, barring some large-extra-dimension scenario, I would hesitate to call that new physics "quantum gravity", unless the energy scale really was the Planck scale.

Most of your examples are of exactly that sort, so I will take just one to illustrate the point.

"

For example, the neutrino mass term, in the seesaw Ansatz, is schematically"psi.psi. H^2/M

Here, "M" (and not its square or its square-root) appears directly as the mass of the singlet fermion that you integrated out to obtain this dimension-5 term in the effective action. This is a perfectly sensible (in fact, perturbative) contribution to the effective action.

"

And the fractional part of anomalous dimensions doesn't have to be tiny..."Indeed. At strong coupling, anomalous dimensions can be large, and none of what I said holds. My claim was

entirelypredicated on the assumption that the effective gravitational coupling wasweak."Considering the GUT physics to be a part of the broader quantum gravity regime"Doing

thatintroduces a whole host of new parameters into the theory, some of which could easily masquerade as "G^{1/2}".Bee was talking about "pure" quantum gravity effects (virtual blackholes or some-such), not "what possible terms can be induced in a completely general effective field theory (with or without gravity)?"

You may or may not think that's a

sensiblequestion to ask. But (I claim) it is one that admits a more restricted set of possible answers.You seem to want me to make a more general statement than I think is warranted (or even possible).

Sorry to disappoint you ...

It is a disappointment, indeed, Jacques. But without such a broader statement, I don't consider your disagreement with Sabine to be truly justified.

The neutrino mass term with the squared Higgs is a dimension 5 operator. So such operators clearly exist. They influence various things and if they're induced by the Planck-scale physics, they scale like 1/M_Pl. If the neutrino squared field had a vev, it would give a potential correction for the Higgs that does scale like 1/M_Pl.

There are various reasons why I think that without a well-defined proof, one should be open-minded about the scalings. Let me give you another major one. Closed string perturbation theory adds g_{closed}^2 to every loop and you could similarly claim that there can't be any nonperturbative objects with masses lighter than 1/g_{closed}^2. But voila, there are D-branes one may suddenly discover whose tensions scale like 1/g_{closed} only - exactly the forbidden intermediate power. For that reason, the breakdown of the resummed perturbation series is twice as fast as expected, the nonperturbative corrections are analogously higher, and there are new fields with terms that have a natural scaling 1/g instead of 1/g^2. One discovers that the elementary coupling at vertices is really "g_open" which is sqrt(g_{closed}).

This could be not just an analogy but a specific construction of a counterexample to your statement that you haven't quite made because G_{Newton} *is* proportional to g_{closed}^2.

Moreover, I think that you were slightly cheating in the last comment when you confused the gravitational couplings with other couplings. The effective gravitational coupling is probably tiny at low energies but there are other couplings, like the electromagnetic one or the larger stronger one, which are of order one and they produce significant O(1) anomalous dimensions even at experimentally accessible energies. The coefficients therefore can't be described as products of simple integer powers of the Planck scale and other scales.

I am not saying that I am further from your viewpoint than from Sabine's, that's surely not the case and I do not believe that any mundane experiment of this sort may be sensitive to QG ie Planck scale physics, but one must be careful not to try to replace proofs by screaming "implausible, implausible".

I suspect that the problem we have here is that you and I (and possibly Bee) mean something

differentwhen we talk about "G_{Newton}".So let me be very clear about what

Imean.The low energy theory is characterized by a finite number of relevant/marginal operators, and the corresponding coupling constants. When I speak of the latter, I mean the

renormalizedcouplings, defined in terms ofphysical observables. So, when I talk about "G", I mean thephysicalNewton's constant, defined in terms of some Cavendish experiment (or whatever).When I talk about the "decoupling limit", I mean: tuning the short distance theory so that the renormalized G (and, to be pedantic, the cosmological constant, too) go to zero, while the other relevant/marginal couplings are held fixed.

What we are discussing is how the coefficient of some other (typically, irrelevant) operator behaves in this limit.

You've brought up numerous examples which may be interesting, in their own right, but which don't seem to be relevant to the issue at hand (at least, as I understand it).

It was nice to see the exchange.

Bee it is common for some people in marirage to have both names...so this would make you and Stefan identifiable apart from the other Scherer.

So have all three, Bee, Jacques and Lubos come to a understanding? Can you three say absolutely from "their perspective" that a constructive pattern can be established?

If so would such collaboration have said....?

Best,

Dear Jacques, I am confident that your very accurate recent description allows me to say that we mean exactly the same thing by G, at least the two of us. ;-)

It's the renormalized coupling (1/16.pi.G) in front of the Ricci scalar term in the Einstein-Hilbert action that may be reconstructed by actual long-distance measurements.

Now, this G suggests that there is a scale, M_Planck, where this EH term becomes as important as loop corrections such as Riemann^3 terms, to avoid the mostly trivial Riemann^2 terms.

The question is whether other terms induced by the same Planck-scale physics may have coefficients that go like 1/M_Planck. I would agree that if they were obtained just from loops involving vertices from the EH term, the coefficients would be integer powers of 1/G.

But to take this assumption, one has to assume that the field-theory description is already kind of fundamental even at the Planck scale. If it is not, the EH term itself may easily be imagined as something produced out of 2 more fundamental vertices, if you wish, and there may be other corrections that only scale as sqrt(G).

Dear Plato, I and Jacques have the same guesses. We seem to disagree on whether or not we have a proof that there can be sqrt(G)-scaling corrections to K3 mesons' mass matrix elements (do you agree with this description Jacques)? I am confident that we would ultimately agree on whether or not we have such a proof and if there's one, if the proof has to assume something that isn't certain.

Sabine has provoked this whole exchange and she may be watching. While one could agree with Jacques' suggestion that Sabine's takes the possible existence of sqrt(G)-scaling terms too uncritically, I am afraid that Jacques' certainty that such things can't occur e.g. in the K0 mesons' Hamiltonian may be comparably premature.

Would you agree with this description of the situation, SH and JD?

All the best

LM

Hi Lubos,

The question for me is about phenomenological approach.

If one seeks clarity "about assumptions" then one would want to be clear on how to approach such experimentation.

So for me, this clarity would indeed need to be seen as some basis amongst principals collaborators as to develop that approach.

I would like to see how Bee feels with your response to Jacques.

Best,

Oh Lubos,

While I do not have the educational background of the three does not mean I was unaware of the arguments that have taken place over the years:)

Phenomenological approaches and development.

What rests in the valley may be of "theoretical design." This did not mean what should come out of "first causes" would not have been of interest to me:)

Best,

"

I am confident that your very accurate recent description allows me to say that we mean exactly the same thing by G..."Good, because that was not clear, from some of your previous comments.

"

Now, this G suggests that there is a scale, M_Planck, where ..."Here, again, a possible confusion may arise, so I want to be

really clearon what we are talking about.I am certainly assuming that there is a valid effective field theory description, valid on length-scales longer than some cutoff scale, L. The precise choice of L is unphysical, and no physical quantity depends on L (which is why, for clarity, I want to express the statement we want to examine in terms of renormalized couplings, defined by physical observables).

While the choice of L is immaterial, it cannot be chosen completely arbitrarily. There's some minimum value, L_0, below which no effective field theory description is possible, and effective field theory must be replaced by something else.

The asymptotic-safety people claim that L_0=0 (i.e., there's always an effective field theory description). Whether or not their claims should be taken seriously, this raises an important point relevant to our analysis.

You alluded to the standard argument that says that L_0≳G^{1/2}. We are interested in the decoupling limit, where G→0 (holding particle physics scales, like the QCD scale, fixed). One needs to say what happens to L_0 in the decoupling limit.

Is the theory such that L_0 also scales to zero, in the decoupling limit, or do we need to hold L_0 fixed?

I know which I mean, but which do you mean?

Dear Jacques, I haven't used the symbol L_0 in this thread before so I can't tell you what I meant by it. ;-)

If L_0 is the cutoff distance where the effective theory breaks down, it may be longer (i.e. closer to accessible energies which are low) than the 4D Planck scale sqrt(G) (e.g. if there are large extra dimensions) but it can't be shorter, I think. So sqrt(G) is the lower bound on L_0. So L_0 cannot be fixed if G is scaled to zero. If G goes to zero, then L_0 goes to zero, too. That's my answer to your question (second sentence from the end of your comment).

In the musings above, I implicitly assumed that we care about the gravitational part of the effective theory and indeed, L_0 is proportional to G. There's some physics at the Planck scale that causes various things. The question is whether it may produce terms of the form L_0.Op5 where Op5 is a dimension 5 operator, besides the term (R/16.pi).L_0^2, the Einstein-Hilbert term, and I don't see why the discussion whether the two scales are linked to each other should be relevant for that.

If L_0 (where a low-E theory breaks down) is longer than sqrt(G) where G is the long-distance-measured Newton's constant, then naturally, the corrections that the new physics at L_0 generates could be even stronger at low energies, right? However, if there are no large extra dimensions and similar stuff, then L_0 isn't a purely gravitational scale if it deviates from sqrt(G), so L_0.Op5 corrections are not purely quantum gravitational ones...

Best, LM

Absolutely there could be corrections to the effective action which are

strongerthan G (or, as Bee would have it, G^{1/2}).You gave a bunch of examples of such corrections.

The distinguishing feature is that the strength of those corrections doesn't vary as you vary G (i.e., as you take the decoupling limit).

If you wish, there are lots of potential sources of new physics at short distances, but we don't want to call all of those "quantum gravity" effects. The ones we want to call "quantum gravity" are the ones which vanish in the decoupling limit (defined above).

Dear Jacques, it's hard to understand your point. You don't question that e.g. the neutrino mass terms in GUT theories' seesaw mechanism scale like 1/M_{GUT} and they *do* arise from GUT-scale physics, do you?

And you do not question that if G is sent to zero, sqrt(G) goes to zero, too, do you?

I'm merely trying to make sure that we agree on the distinction between the first type of effect (of which you have written at considerable length) and the second.

The latter (if they exist) might reasonably be called quantum gravity effects; the former --- I would maintain --- should not.

If you don't agree with that distinction, then there's little point in pressing on to discuss would-be G^{1/2} effects if they can't be distinguished, unambiguously, from other sources of new physics at short distances.

thanks for sharing.

Dear Jacques, I don't think you have offered evidence that there is any distinction between "two types of effects".

Dimension 5 operators may be suppressed by the GUT scale much like by the Planck scale. In the former case, the effects are an order of magnitude or two stronger but there is no qualitative difference between the two.

The effective interactions one may produce from an action including the EH term which goes like 1/G go like (1/G)^n to integer powers but there may still be more general terms and the EH term itself may have a non-minimal dependence on G.

All the best

LM

"Dimension 5 operators may be suppressed by the GUT scale much like by the Planck scale. In the former case, the effects are an order of magnitude or two stronger but there is no qualitative difference between the two."I suggested a way to, qualitatively, distinguish the two. If you don't agree, then there's not much to say.

The GUT scale is only "by accident" a few orders of magnitude below the Planck scale. We could just as easily have new physics as 10^5 GeV as at 10^{15} GeV. It would be utterly meaningless to "estimate" the strength of such effects, in powers of G.

Since there's no point in further discussion, if you don't accept my basic premise (that "quantum gravity" effects can, in a large class of theories, be distinguished from other sources of new physics), let me --- at least --- reiterate the question that started this discussion.

Bee estimated that a certain effect goes like (G M^2)^{1/2} M. One could equally-well assert that the effect goes like (G M^2)^a M, for some other positive real number, a.

I think you agree that positive integer values for "a" have a somewhat different status (though exactly what that is, remains a source of disagreement).

My question is: once you admit that non-integer powers are allowed, why do you object to a=1/4 or a=0.0015?

Don't mind me Bee. Just doing a little background :)

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