What are the reasons to expect that gravity should be quantized?

Question

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?

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user MBN

Comments

@MBN: I think it's a good analogy. Once again, you know that 1+1 = 2 (in the ring of integers). But you are still asking why. This is what I don't get. Either you understand integers and then the statement is dead obvious. Or you don't understand them but then you should ask about integers not about why 1+1 = 2. Or in your case, why our world is inherently quantum because this basic fact makes it clear that gravity, much like any other phenomenon must behave according to rules of quantum theory.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user Marek

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@Marek: I am not asking why, I am asking if there are other known reasons. If noone knows any other, that's fine. I was simply curious. If you know another tell me, if you don't fine, but what is the purpose if this endless discusion?!

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user MBN

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@MBN: the purpose of this discussion is to determine the value of your question, among other things. Which is directly related to your inquiry about the reason for downvote and ways in which it could be improved ;)

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user Marek

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Duplicates: physics.stackexchange.com/questions/52211/…, physics.stackexchange.com/questions/10088/…

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user Dimensio1n0

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Measurement Analysis and Quantum Gravity by Mark Albers, Claus Kiefer, Marcel Reginatto (2008) was often cited recently. According to the authors, quantizing gravity is not necessary. "We have considered the argument made (...) that the quantum theory must
be extended to all physical systems, and have shown that this conclusion is not justified.".

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I can see that the question has a vote to close. Can anyone explain why? And is there anything that can be modified so that it becomes better?

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user MBN

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@MBN: I didn't vote to close but seeing the answers, I probably should have. This question (and answers too) doesn't bring any value, just controversy. One way in which this question could be improved is if you told us why you think gravity shouldn't be quantized as it is pretty much obvious to everyone that it should (or rather, must) be. Or back to your analogy, why do you think you are not working in the ring of integers (and to what ring did you move?) and 1+1=2 should stop to hold? ;)

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user Marek

Answer 1

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.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user Luboš Motl

Comments

@Marek: I said something to that extent a couple of times. For example, in my fist comment here to Lubos, I said that this is the obvious answer and I know, so I am looking for something else. Anyway, it seems that these are all the answers I will get.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user MBN

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@MBN: yeah, but you didn't really say why. Sorry but I really didn't get you and judging by the answers and comments, I am not the only one. In other words, your question doesn't say "I want a different proof of this" but rather it seems to say "Why on Earth should this hold?"

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user Marek

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Yes, it is probably not clear enough, but you can ask in the comments after the question for me to explain. I don't know why everyone (most) is jumping to conclusions. What I asked was not "Why on earth should that hold?" it was "What are the reasons for that to hold?" Anyway if I have written it badly I don;t get good answers, so I know for next time.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user MBN

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Could I extend this argument/question to the possibility of inserting any classical field (not just gravity) into a quantum theory? Presumably, by the above arguments, that must also be disallowed?

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user James

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Magistral as usual... Just smiling; locality is always violated, at least, as it is teached nowadays to undergraduates in most universities. (I don't talk of 2-laymen QM lectures which are nearer to showbiz spectacles than to sciences). Thus, how could it be an argument?

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@MBN: what other reasons? There is only one reason and it makes the answer obvious: our world behaves according to quantum mechanics, a fact that has been tested beyond any doubt. You don't need anything else (and there can't actually be anything else) to answer your question but you still prohibit this answer. That's what I don't get.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user Marek

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@Marek: think about it this way. I know one proof of a theorem and I want to know if there are other known proves. Note that I know that the theorem is true, I don't need a proof because I have one. I am just curious to if there are others. Why is that so hard to get!!!

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user MBN

Answer 2

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)

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This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user user346

Comments

@Deepak: I am afraid I don't understand your argument. Collapse is unphysical and so can't really be a base for any contradiction.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user Marek

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@MBN: experimental physicists... yeah :)

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user Marek

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Collapse is unphysical - right. And what should replace it then? I agree that one can have stable quantum states and superpositions of macroscopic objects. The reason I cite Penrose's argument is because I don't think that we will observe the sort of gravitationally-induced decoherence he predicts. But neither will we observe conventional quantum behavior in such systems. After all, there is no reason to believe that many-body quantum systems should obey the same rules that qubits do as regards to superposition, etc. I think we will find something more subtle than these either/or options.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user user346

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@Deepak: nothing replaces it, it just isn't there. In any sensible interpretation you can explain what was the effect that appeared as a collapse in Copenhagen interpretation.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user Marek

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@Deepak +1. The invocation of the Jacobson approach leaves us still with a statistical theory, and hence in the absence of another mathematics in a Hilbert space formalism, but Jacobson's argument only establishes the significance of the Planck length in the absence of any other detailed dynamics (however I have not followed the Jacobson, Padmanabhan, Verlinde literature in detail). Thanks for the Bredberg, Keeler, Lysov and Strominger reference.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user Peter Morgan

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techniques cannot be extended to the non-perturbative regimes is that one does not have a formulation of quantum mechanics that also obeys the equivalence principle and allows one to consistently define superpositions of quantum states of the gravitational field.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user user346

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@Deepak, yes it would require a 'good' formulation of QFTonCS.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user MBN

Answer 3

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.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user user1355

Comments

@sb1 that is a very good point. +1.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user user346

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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.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user MBN

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@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.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user user1355

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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.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user MBN

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@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.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user user1355

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@sb1: I guess I don't understand you, but your answer still seems to me to be just very general remarks and nothing specific.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user MBN

Answer 4

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.

This post imported from StackExchange Physics at 2014-04-01 16:41 (UCT), posted by SE-user Lawrence B. Crowell

Comments

This is interesting.

This post imported from StackExchange Physics at 2014-04-01 16:41 (UCT), posted by SE-user MBN

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+1 for this connection to QCD

This post imported from StackExchange Physics at 2014-04-01 16:41 (UCT), posted by SE-user lurscher

Answer 5

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.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user anna v

Comments

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.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user user346

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@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.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user anna v

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@Deepak, I don't understand why the unified theory should be a QFT. Or even could be. There are known theorems on quantization of gravity that pretty much exclude this possibility. Also, quantization of gravity is implied by many simpler conceptual facts. The issue of unification is orthogonal and one can very well imagine a universe where gravity would be described differently (although still quantum) than rest of the forces.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user Marek

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There are known theorems on quantization of gravity that pretty much exclude this possibility, @Marek could you point me to some of these. I'm not sure what you're referring to.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user user346

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@Deepak: Weinberg-Witten theorem

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user Marek

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The question didn't talk about unification of forces. Just about quantization of gravity. Whereas your answer doesn't...

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user Marek

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@Marek I would think it obvious that one cannot unify a quantum theory with a non quantum one using the same mathematical descriptions .

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user anna v

Answer 6

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.

This post imported from StackExchange Physics at 2014-04-01 16:41 (UCT), posted by SE-user joseph f. johnson

Comments

-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.

This post imported from StackExchange Physics at 2014-04-01 16:41 (UCT), posted by SE-user Ron Maimon

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>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

This post imported from StackExchange Physics at 2014-04-01 16:41 (UCT), posted by SE-user joseph f. johnson

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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.

This post imported from StackExchange Physics at 2014-04-01 16:41 (UCT), posted by SE-user Ron Maimon

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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!

This post imported from StackExchange Physics at 2014-04-01 16:41 (UCT), posted by SE-user joseph f. johnson

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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.

This post imported from StackExchange Physics at 2014-04-01 16:41 (UCT), posted by SE-user Ron Maimon

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I don't think you have noticed that the axioms of QM could remain exactly true even if one adjusted notions of particle and superposition. The axioms say use a Hilbert space, they do not impose which one. They say use a Hamiltonian, they do not say which one. They do not tell you how to interpret superposition of states and do not tell you how Hamiltonians of measurement apparati are correlated with Quantum Observable. All of that is `adjustable'. Linearity, I suppose, is not.

This post imported from StackExchange Physics at 2014-04-01 16:41 (UCT), posted by SE-user joseph f. johnson

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@josephf.johnson : interesting point of view! There is a difference between Copenhagen's and realists's Hilbert spaces : to dot product, ie applied to compute correlations. Hilbert introduced his dot product in a 'natural way' into a not yet relativistic/causal theory. It is the unique source of the theoretical acausality. A free minded lab's data study would had shown interesting things.

Answer 7

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.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user Peter Morgan

Comments

Well, i was not asking about unification and related matters.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user MBN

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@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.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user Peter Morgan

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That's true. (two more characters)

This post imported from StackExchange Physics at 2014-04-01 16:41 (UCT), posted by SE-user MBN

Answer 8

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)

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user lurscher

Comments

+1 for mentioning Penrose and the fact that this is (originally) his argument!

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user user346

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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.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user MBN

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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.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user Luboš Motl

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@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.

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user user346

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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$!

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user user346

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@Lubos, it sounds like you have evidence that the above proposed experiment will have certain outcome rather than the other one. But the fact that "all the other things are quantum" does not per se prove that a certain outcome in the above experiment will be unavoidable. Both are logically possible, even if we all agree that it would be more aesthetically pleasing that gravity would be as quantum as "everything else"

This post imported from StackExchange Physics at 2014-04-01 16:40 (UCT), posted by SE-user lurscher

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Quantized or not, it does not matter for macroscopic observations of gravity effects.