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What I am interested to see are specific examples/reasons why gravity should be quantized. Something more than "well, everything else is, so why not gravity too". For example, isn't it possible that a quantum field theory on curved space-time would be the way treat QFT and gravity in questions where the effects of neither can be ignored?

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Hasn't this been covered in previous question(s)? –  user346 Mar 15 '11 at 19:07
    
Possibly, I couldn't find it. I can delete this one if someone can show me the questions. –  MBN Mar 15 '11 at 19:09
    
I didn't bother looking either, so I'll take your word for it ;) Right now, its the retrodiction question that's hot and heavy, so back to it! And back to yours later I'm sure. –  user346 Mar 15 '11 at 19:17
    
I might have missed it. I didn't search too much although I hate when people repeat questions and are too lazy to check. So it that is the case sorry. It is not urgent, whenever you have the time. –  MBN Mar 15 '11 at 19:26
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I think it is precisely because "everything else is" ;) As soon as one accepts that our world is inherently quantum, there is just no other way. And I think this has been accepted for quite some time now (well, by scientists at least)... –  Marek Mar 15 '11 at 19:37

8 Answers 8

Gravity has to be subject to quantum mechanics because everything else is quantum, too. The question seems to prohibit this answer but that can't change the fact that it is the only correct answer. This proposition is no vague speculation but a logically indisputable proof of the quantumness.

Consider a simple thought experiment. Install a detector of a decaying nucleus, connected to a Schrödinger cat. The cat is connected to a bomb that divides the Earth into two rocks when it explodes. The gravitational field of the two half-Earths differs from the gravitational field of the single planet we know and love.

The nucleus is evolving into a superposition of several states, inevitably doing the same thing with the cat and with the Earth, too. Consequently, the value of the gravitational field of the place previously occupied by the Earth will also be found in a superposition of several states corresponding to several values - because there is some probability amplitude for the Earth to have exploded and some probability amplitude for it to have survived.

If it were possible to "objectively" say whether the gravitational field is that of one Earth or two half-Earths, it would also be possible to "objectively" say whether the nucleus has decayed or not. More generally, one could make "objective" or classical statements about any quantum system, so the microscopic systems would have to follow the logic of classical physics, too. Clearly, they don't, so it must be impossible for the gravitational field to be "just classical".

This is just an explicit proof. However, one may present thousands of related inconsistencies that would follow from any attempt to combine quantum objects with the classical ones in a single theory. Such a combination is simply logically impossible - it is mathematically inconsistent.

In particular, it would be impossible for the "classical objects" in the hybrid theory to evolve according to expectation values of some quantum operators. If this were the case, the "collapse of the wave function" would become a physical process - because it changes the expectation values, and that would be reflected in the classical quantities describing the classical sector of the would-be world (e.g. if the gravitational field depended on expectation values of the energy density only).

Such a physicality of the collapse would lead to violations of locality, Lorentz invariance, and therefore causality as well. One could superluminally transmit the information about the collapse of a wave function, and so on. It is totally essential for the consistency of quantum mechanics - and its compatibility with relativity - to keep the "collapse" of a wave function as an unphysical process. That prohibits observable quantities to depend on expectation values of others. In particular, it prohibits classical dynamical observables mutually interacting with quantum observables.

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Wow, that's a great answer. I never thought about it that way. –  Keenan Pepper Mar 16 '11 at 0:15
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This is just an explicit proof ... it is no such thing. In fact the line of reasoning that you use has been used previously by Penrose and is that at basis of his proposal on wavefunction collapse due to gravitational effects. It is one thing to create a superposition of a state of a single, or even multiple, qubits. It is quite another thing altogether to claim that you can create a superposition of a gravitationally massive body such as the earth. In fact I spoke to Penrose once (lucky me) and as he said this is precisely the situation where the argument fails ... –  user346 Mar 16 '11 at 0:24
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... So unless you can explain or describe what the superposition of the gravitational field of a massive object in two separate locations should look like, your thought experiment doesn't really stand. This is, in fact, not just another possibility but one that is actively under investigation. See the PRLs on "Towards quantum superpositions of a mirror" ref1, ref2 –  user346 Mar 16 '11 at 0:29
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@MBN: apologies, but again, there can't be any inequivalent answer because the incompatibility of classical evolution with the quantum evolution is the only (but very important) possible reason why classical gravity can't be added to a quantum world. If you wanted to avoid infinite exchanges with Deepak, you should have therefore avoided asking this question altogether. –  Luboš Motl Mar 16 '11 at 6:57
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@Deepak: your bold proposition - that macroscopic objects could avoid quantum mechanics - is even much worse than the proposition in this very question, namely that gravitational fields could avoid quantum mechanics. Arbitrarily large pieces of a solid (e.g. crystal or metal), to pick an example, follow the laws of quantum mechanics. Ask any condensed matter physicist who study these very questions all the time. You may try to defend your nonsensical propositions by the authority of a British mathematician but because he has no clue how QM works, this ad hominem argument is very weak. –  Luboš Motl Mar 16 '11 at 7:00

Reasons for why gravity should be amenable to "quantization":

  1. Because everything else or as @Marek puts it because "the world is inherently quantum". This in itself is more an article of faith than an argument per se.

  2. Because QFT on curved spacetime (in its traditional avatar) is only valid as long as backreaction is neglected. In other words if you have a field theory then this contributes to $T_{\mu\nu}$ and by Einstein's equations this must in turn affect the background via:

    $$ G_{\mu\nu} = 8\pi G T_{\mu\nu} $$

    Consequently the QFTonCS approach is valid only as long as we consider field strengths which do not appreciable affect the background. As such there is no technical handle on how to incorporate backreaction for arbitrary matter distributions. For instance Hawking's calculation for BH radiation breaks down for matter densities $\gt M_{planck}$ per unit volume and possibly much sooner. Keep in mind that $M_{planck}$ is not some astronomical number but is $\sim 21 \, \mu g$, i.e. about the mass of a colony of bacteria!

    The vast majority of astrophysical processes occur in strong gravitational fields with high enough densities of matter for us to distrust such semiclassical calculations in those regimes.

  3. Well there isn't really a good third reason I can think of, other than "it gives you something to put on a grant proposal" ;)

So the justification for why boils down to a). because it is mandatory and/or would be mathematically elegant and satisfying, and b). because our other methods fail in the interesting regimes.

In the face of the "inherently quantum" nature of the world we need strong arguments for why not. Here are a couple:

  1. The world is not only "inherently quantum" but it is also "inherently geometric" as embodied by the equivalence principle. We know of no proper formulation of QM which can naturally incorporate the background independence at the core of GR. Or at least this was the case before LQG was developed. But LQG's detractors claim that in the absence of satisfactory resolutions of some foundational questions (see a recent paper by Alexandrov and Roche, Critical overview of Loops and Foams). Also despite recent successes it remains unknown as to how to incorporate matter into this picture. It would appear that topological preons are the most natural candidates for matter given the geometric structure of LQG. But there does not appear to be any simple way of obtaining these braided states without stepping out of the normal LQG framework. A valiant attempt is made in this paper but it remains to be seen if this line of thought will bear sweet, delicious fruit and not worm-ridden garbage!

  2. Starting with Jacobson (AFAIK) (Thermodynamics of Spacetime: The Einstein Equation of State, PRL, 1995) there exists the demonstration that Einstein's equations arise naturally once one imposes the laws of thermodynamics ($dQ = TdS$) on the radiation emitted by the local Rindler horizons as experienced by any accelerated observer. This proof seems to suggest that the physics of horizons is more fundamental than Einstein's equations, which can be seen as an equation of state. This is analogous to saying that one can derive the ideal gas law from the assumption that an ideal gas should satisfy the first and second laws of thermodynamics in a suitable thermodynamical limit ($N, V \rightarrow \infty$, $N/V \rightarrow$ constant). And the final reason for why not ...

  3. Because the other, direct approaches to "quantizing" gravity appear to have failed or at best reached a stalemate.

On balance, it would seem that one can find more compelling reasons for why not to quantize gravity than for why we should do so. Whereas there is no stand-alone justification for why (apart from the null results that I mention above), the reasons for why not have only begun to multiply. I mention Jacobson's work but that was only the beginning. Work by Jacobson's student (?) Christopher Eling (refs) along with Jacobson and a few others has extended Jacobson's original argument to the case where the horizon is in a non-equilibrium state. The basic result being that whereas the assumption of equilibrium leads to the Einstein equations (or equivalently the Einstein-Hilbert action), the assumption of deviations from equilibrium yields the Einstein-Hilbert action plus higher-order terms such as $R^2$, which would also arise as quantum corrections from any complete quantum gravity theory.

In addition there are the papers by Padmanabhan and Verlinde which set the physics world aflutter with cries of "entropic gravity". Then there is the holographic principle/covariant entropy bound/ads-cft which also suggest a thermodynamic interpretation of GR. As a simple illustration a black-hole in $AdS_5$ with horizon temperature $T$ encodes a boundary CFT state which describes a quark-gluon plasma at equilibrium at temperature ... $T$!

To top it all there is the very recent work Bredberg, Keeler, Lysov and Strominger - From Navier-Stokes To Einstein which shows an (apparently) exact correspondence between the solutions of the incompressible Navier-Stokes equation in $p+1$ dimensions with solutions of the vacuum Einstein equations in $p+2$ dimensions. According to the abstract:

The construction is a mathematically precise realization of suggestions of a holographic duality relating fluids and horizons which began with the membrane paradigm in the 70's and resurfaced recently in studies of the AdS/CFT correspondence.

To sum it all up let me quote from Jacobson's seminal 1995 paper:

Since the sound field is only a statistically defined observable on the fundamental phase space of the multiparticle sys- tem, it should not be canonically quantized as if it were a fundamental field, even though there is no question that the individual molecules are quantum mechanical. By analogy, the viewpoint developed here suggests that it may not be correct to canonically quantize the Einstein equations, even if they describe a phenomenon that is ultimately quantum mechanical. (emph. mine)


Standard Disclaimer: The author retains the rights to the above work among which are the right to include the above content in his research publications with the commitment to always cite back to the original SE question.

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Thanks for the effort, and it is probably morally wrong to complain, but it doesn't really answer the question the way I asked it. It seems that you only elaborate on the part I asked not be given as an answer. As I said in the comment above, there are reasons why electrodynamics should be quantized. Otherwise it leads to contradictions. And am hoping to see something along those lines. About QFTonCS you are right, but is there a reason to suspect that there cannot be a satisfactory formulation? Don't take this as a negative reaction I do like your not-exactly-answer, it's just as ... –  MBN Mar 15 '11 at 21:21
    
... a curmudgeon I have to say this. –  MBN Mar 15 '11 at 21:21
    
@MBN: there will be contradictions all over the place, I am sure you can think of many yourself. Are these simple Gedankenexperiments all you are looking for? –  Marek Mar 15 '11 at 22:28
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@Marek as I explain in comments to @Lubos' answer, his thought experiment regarding the superposition of two massive objects leads to the conclusion that gravity should trigger wavefunction collapse. Therefore, instead of providing support for the notion of "quantizing" gravity, this thought experiment requires us to answer why gravity should not be a factor in wavefunction collapse. That is one simple (on-its-face) argument that leads to a contradiction but not the sort you were hoping for :/ @MBN - LOL. Complaining is never morally wrong! The simplest reason for why the standard QFTonCS –  user346 Mar 16 '11 at 0:34
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@Marek, gedanken experiments would be fine. I am really interested only in the theory. What actually happens in reality is a concern for the physicists:)) –  MBN Mar 16 '11 at 3:56

I am very much surprised to see that apart from all the valid reasons (specially the argument, since everything else is quantum hence gravity should also be the same otherwise many inconsistencies will develop) mentioned by Lubos et. al. no body pointed out that one of the other main motivations to quantize gravity was that classical GR predicted singularities in extreme situations like big bang or black holes. It was kind of like the the instability of the Ratherford atomic model where electrons should have been spiral inward the nuclus as per the classical electrodynamics. Quantum theory saved physics from this obvious failure of classical physics. Naturally it occured to physicists that quantum theory should be the answer of the singularity problem of classical GR too. However experiences in the last 40 years have been different. Far from removing singularities it appears that our best quantum gravity theory is saying that some of the singularities are damn real. So obviously the motivation of quantization of gravity has changed to an extent and it is unification which is now driving the QG program in my humble opinion.

Some additional comments: @Mbn, There are strong reasons to believe that the uncertainty principle is more fundamental than most other principles. It is such an inescapable property of the universe that all sane physicists imho will try their best, to make every part of their world view including gravity, consistent with the uncertainty principle. All of the fundamental physics has already been successfully combined with it except gravity. That's why we need to quantize gravity.

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@sb1 that is a very good point. +1. –  user346 Mar 16 '11 at 11:57
    
A good point, but why do you take that as 'gravity needs to be quantized' and not as QFT needs to be done on a curved spacetime. –  MBN Mar 16 '11 at 15:09
    
@MBN: The bottom line is that there is gravity which should have a quantum description for consistency with all other phenomena in nature and which must produce finite (divergence free)answers. –  user1355 Mar 16 '11 at 15:24
    
That is exactly my question. What are there reasons to think that for consistency gravity has to be quantized? Saying it is the bottom line isn't enough for me. I would like to see the lines above the bottom. –  MBN Mar 16 '11 at 15:58
    
@MBN: I don't understand your comment at all. Either I am not understanding you or you are just playing with words without any specific goal. –  user1355 Mar 16 '11 at 16:09

For the sake of argument, I might offer up a plausible alternative. We might have some quantum underpinning to gravitation, but we might in fact not really have quantum gravity. It is possible that gravitation is an emergent phenomenon from a quantum field theoretic substratum, where the continuity of spacetime might be similar to the large scale observation of superconductivity or superfluidity. The AdS/CFT is a matter of classical geometry and its relationship to a quantum field theory. So the $AdS_4/QFT$ suggests a continuity of spacetime which has a correspondence with the quark-gluon plasma, which has a Bjorken hydrodynamic scaling. The fluid dynamics of QCD, currently apparent in some LHC and RHIC heavy ion physics, might hint at this sort of connection.

So we might not really have a quantum gravity as such. or if there are quantum spacetime effects it might be more in the way of quantum corrections to fluctuations with some underlying quantum field. Currently there are models which give quantum gravity up to 7 loop corrections, or 8 orders of quantization. Of course the tree level of quantum gravity is formally the same as classical gravity.

This is suggested not as some theory I am offering up, but as a possible way to think about things.

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This is interesting. –  MBN Mar 16 '11 at 16:16
    
+1 for this connection to QCD –  lurscher Mar 16 '11 at 16:58

I have seen two converging paths as compelling reasons for quantizing gravity, both dependent on experimental observations.

One is the success of gauge theories in particle physics the past decades, theories that organized knowledge mathematically economically and elegantly. Gravitational equations are very tempting since they look like a gauge theory.

The other is the Big Bang theory of the beginning of the universe that perforce has to evolve the generation of particles and interactions from a unified model, as the microseconds grow. It is attractive and elegant that the whole is unified in a quantum theory that evolves into all the known interactions, including gravity.

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The question didn't talk about unification of forces. Just about quantization of gravity. Whereas your answer doesn't... –  Marek Mar 15 '11 at 22:26
    
@Marek I would think it obvious that one cannot unify a quantum theory with a non quantum one using the same mathematical descriptions . –  anna v Mar 16 '11 at 4:53
    
@anna: so what? You are talking about unification again. The question doesn't... –  Marek Mar 16 '11 at 7:28
    
I think @anna is trying to say that the expectation (or requirement) is that the four forces unify at some scale, along with the fact that (at least) three of these are QFTs. So the unified theory would also, presumably, be a QFT. And the logic of grand unification then implies that gravity, which is one sector of this big theory, should also have a quantum description. –  user346 Mar 16 '11 at 11:54
    
@Deepak Vaid. Yes. My use of the english language must be at fault. @Marek the question up top asked for "specific examples/reasons why gravity should be quantized", and I gave two of them, imo. –  anna v Mar 16 '11 at 14:36

I will take a very simplistic view here. This is a good question and was carefully phrased: «gravity ... be quantised ... ». Unification is not quite an answer to this particular question. If GenRel produces singularities, as it does, then one can wonder if those singularities can really be the exact truth. Since singularities have been smoothed over by QM in some other contexts, this is a motivation for doing that to GenREl which was done to classical mechanics and E&M. But not necessarily for « quantising gravity ». According to GenRel, gravity is not a force. It is simply the effect of the curvature of space-time... In classical mechanics, the Coulomb force was a real force... So if we are going to be motivated to do to GenRel that which was done to classical mechanics, it would not be natural to quantise gravity, but rather to formulate QM in a curved space-time (with the appropriate back-reaction---and that, of course, is the killer since probably some totally new and original idea is necessary here, so that the result will be essentially quantum enough to be a unification). MBN has explicitly contrasted these two different options: quantising gravity versus doing QM or QFT in curved space-time. Either approach addresses pretty much every issue raised here: either would provide unification. Both would offer hopes of smoothing out the singularities.

So, to sum up the answer

IMHO there is no compelling reason to prefer quantising gravity over developing QFT in curved space-time, but neither is easy and the Physics community is not yet convinced by any of the proposals.

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-1: QM in curved space doesn't work, because quantum stuff is not just responding to gravity, it is also creating gravity. So if you make a superposition of masses, you need a superpostion of gravity fields. Further semiclassical gravity suffers from the same consistency problems that plague semiclassical electromagnetic interactions--- this is the BKS theory which fails to conserve energy. When you don't have gravitons, a gravitational wave cannot interact with matter in a way that conserves energy graviton by graviton, because a single graviton gravity wave can only excite one position. –  Ron Maimon Dec 15 '11 at 10:02
    
>it is also creating gravity.## ## I think that that is what I was referring to by the appropriate back reaction being needed.## ## >When you don't have gravitons, a gravitational wave cannot interact with matter in a way that conserves energy## ##@Ron I would appreciate a reference for this –  joseph f. johnson Dec 15 '11 at 14:43
    
So if you have a particle which is in a superposition with probability 1/2 to be here and 1/2 to be there, where does it's gravitational field come from? From here? From there? From half way in between? It's clear that the field is superposed. There is no way to treat matter as quantum and a field as classical. It is impossible, it is discredited, it's BKS. –  Ron Maimon Dec 15 '11 at 18:58
    
For things way beyond the standard model, you are making too many assumptions to really rule out what you want to rule out. The notions of 'particle' and superposition may need adjustments, so that something which seems impossible could be managed. All you've done is pointed to an obstacle, and it would be helpful to me to have a precise reference to a published argument that without gravitons, conservation of energy fail. After all, quantum fields are still plagued with difficulties too, one should not spend the entire stock of one's indulgence on only one side! –  joseph f. johnson Dec 15 '11 at 21:33
    
I am sympathetic to the idea that quantum mechanics might not be exact, I often toss and turn at night over this question. But a semiclassical gravity field interacting with quantum matter is certainly not the answer. The arguments for energy nonconservation are in BKS paper, where they analyze semiclassical EM field interacting with a quantum atom (before full QM, but the arguments are the same). The later Bohr Rosenfeld analysis is a famous argument that field quantization is required, and it applies mutatis mutandis to gravity. –  Ron Maimon Dec 16 '11 at 1:38

There are two questions here. The first is not so much whether we expect a unifying theory to be "quantum" as much as whether we expect a unifying theory to be probabilistic/statistical. I suppose that at or within 5 or 10 orders of magnitude of the Planck scale we can expect that we will still have to work with a statistical theory. Insofar as Hilbert space methods are the simplest effective mathematics for generating probability measures that can then be compared with the statistics of measurements, it's likely we will keep using this mathematics until some sort of no-go theorem proves that we have to use more sophisticated and harder to use mathematical tools (non-associative algebras of observables, etc., etc., etc., none of which most of us will choose to use unless we really have to).

The arguably more characteristic feature of quantum theory is a scale of action, Planck's constant, which determines, inter alia, the scale of quantum fluctuations and the minimal incompatibilities of idealized measurements. From this we have the Planck length scale, given the other fundamental constants, the speed of light and the gravitational constant. From this point of view, to say that we wish to "quantize" gravity is to assume that the Planck scale is not superseded in dynamical significance at very small scales by some other length scale.

The lack of detailed experimental data and an analysis that adequately indicates a natural form for an ansatz for which we would fit parameters to the experimental data is problematic for QG. There is also a larger problem, unification of the standard model with gravity, not just the quantization of gravity, which introduces other questions. In this wider context, we can construct any length scale we like by multiplying the Planck length by arbitrary powers of the fine structure constant, any of which might be natural given whatever we use to model the dynamics effectively. The natural length for electro-geometrodynamics might be $\ell_P\alpha^{-20.172}$ (or whatever, $\ell_P e^{\alpha^{-1}}$ isn't natural in current mathematics, but something as remarkable might be in the future), depending on the effective dynamics, and presumably we should also consider the length scales of QCD.

Notwithstanding all this, it is reasonable to extrapolate the current mathematics and effective dynamics to discover what signatures we should expect on that basis. We have reason to think that determining and studying in detail how experimental data is different from the expected signatures will ultimately suggest to someone an ansatz that fits the experimental data well with relatively few parameters. Presumably it will be conic sections instead of circles.

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Well, i was not asking about unification and related matters. –  MBN Mar 16 '11 at 15:11
    
@MBN Unification in some form or another is at least part of the pressure to quantize gravity, so that gravity could then be unified with the standard model of particle physics. I think this isn't a strong argument that quantization is necessary, but it isn't a bad reason for trying. I'd take this to underlie Luboš' Answer, insofar as he effectively worries about contradictions in the wider context that includes gravity and quantum theory. –  Peter Morgan Mar 16 '11 at 15:36
    
That's true. (two more characters) –  MBN Mar 16 '11 at 15:56

I will answer recasting the question as a thought experiment, based on the example proposed by Lubos;

1) a quantum object A in a superposition of two states separated by a distance $X$ somewhere in empty space

2) A has an associated gravity, with associated space-time curvature

3) now system B, will approach the region where A is found, and measure space-time curvature, but will not interact directly with A or its non-gravitational fields

4) now the system M (aka Measuring Apparatus) approaches the region where both A and B are found, and it will try to measure state correlation between A and B states

"gravity is quantum" potential outcome:

A and B are statistically correlated (entangled), supporting that B coupled with a linear superposition of gravitational fields

"gravity is classical" potential outcome:

A and B are uncorrelated quantum mechanically (a direct product of both densities), supporting that any substantial gravity field will collapse (this is basically what Penrose proposes as a mechanism for measurement collapse)

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+1 for mentioning Penrose and the fact that this is (originally) his argument! –  user346 Mar 16 '11 at 0:40
    
So you (that is Penrose) are proposing a way to test if gravity needs to be quantized or not? That's nice but until it is performed we will not know. –  MBN Mar 16 '11 at 4:02
    
Dear Deepak, this is an extremely, extremely lousy reason for giving an answer thumbs up. And by the way, this sequence of thoughts denies not only that gravity is quantum but that anything in the world is quantum. It's OK for a schoolkid from an elementary school but I don't think that it's appropriate for SE. –  Luboš Motl Mar 16 '11 at 7:07
    
@Lubos I have discovered your weakness! Now if I want you to proofread one my answers I just have to sneak in Penrose's name into it :p All kidding aside. You have your reasons for voting as you do. I have mine. Let's just leave it that. As for the quantum nature of reality, of course, nature is quantum. That is not the issue. The question is whether gravity - as encoded in Einstein's equations - is a fundamental microscopic interaction or if, instead, it is an effective interaction which emerges in some thermodynamic limit of the true microscopic d.o.f. –  user346 Mar 16 '11 at 7:37
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This also happens to be perfectly compatible with the existence of macroscopic quantum states. In fact, this approach would allow us greater control of the quantum properties of gravitationally non-negligible mass distributions. But if we don't understand what the true microscopic d.o.f are - strings, loops, etc. - and keep trying to "quantize" the Einstein-Hilbert action, it would be analogous to trying to understand what the microscopic d.o.f of an ideal gas as by quantizing the equation of state $ PV=nRT$! –  user346 Mar 16 '11 at 7:40

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