No. We do not have even a consistent theory for quantum gravity(and it seems probable that Einstein's theory cannot be quantized at all)

No. The disparity between the two theories is the reason that "quantum gravity" is one of the major unsolved problems in modern physics.

Several facts lead me to think of GR not as the classical limit of the expected quantum gravity but rather as the MACROSCOPIC limit thereof.

First of all, GR (and its Newtonian limit) is only observationally verified between sub-millimeter  scale to solar system scale. Direct application of GR to larger scales such as in cosmology has led to controversies, e.g. need the unknown dark energy to supplement GR. Note that the scale between sub-millimeter scale to solar system scale is where both classical physics and macroscopic physics should apply.

Next, the Einstein equation can be rewritten as $\Nabla_\mu G^{\mu\nu} = \nabla_\mu T^{\mu\nu}=0$, with the sacrifice of implicitly allowing the existence of a cosmological constant term on either sides. However, the second equality, $\nabla_\mu T^{\mu\nu}=0$, can be regarded as the relativistic fluid equation. So, the equation of motion for gravity in GR is identical to that of a fluid, which is a macroscopic concept.

Moreover,  attempts in getting a quantum theory of gravity with GR as its classical limit are either failed or still encountering serious problems with no hints of a clue on how to overcome them.  This makes me to think the problem from a different point of view: should one expect to establish the quantum theory of molecules by quantizing fluid mechanics?

Thanks for the reply, Prof. Liu Zhao.

Has it been possible to explain GR completely, as a Macroscopic limit of Quantum Gravity?

Not really.

That I think GR as a macroscopic theory because it bears many resemblance to the usual macroscopic theories like fluid system and/or thermodynamic systems. These resemblances are not only observed on the level of equations of motion, but also from other aspects of the theory. For instances,

1) When a static or stationary solution to GR is considered, it is usually equipped with equilibrium thermodynamic properties like e.g. temperature, entropy etc. Also, the analogues of the classic laws of thermodynamics can be realized in gravity in such situations.

2) When one considers fluctuations around a static gravity solution, another level of fluid dynamics can be realized as the holographic dual of the gravity system. 

3) More classic phenomena such as phase transitions are expected to arise either directly from gravity solutions or from the holographic perspectives.

I think all these are clues to understand GR as a macroscopic theory. That said, however, we still cannot expect to get GR from a limiting process  starting from quantum gravity, simply because we do not have such a quantum theory yet. On the other hand, even if we do have a model of quantum gravity, it is still not obvious on how to take its macroscopic limit. The barrier in between is something like a quantum statistical mechanics for gravity. Consider ordinary quantum gas, for instance. One cannot get the properties of a quantum gas by knowing quantum mechanics alone. Some knowledge about quantum statistical mechanics is a must. 

Dear Rifat,

YES, when we have one. They have to be special cases otherwise Quantum Gravity itself would be invalidated in these limits where these two theories have been tested to be valid.

Regards,

Rajat

There are two apsects of general relativity which are inconsistent with the reality. One is the linear definition of time and second is the geometrical description. Quantum gravity operates on a totally different energy scale which is outside the range of weak field approximation. And Quantum mechanics has to do with attraction between electrical charges and has nothing to do with gravity. So general relativity and quantum mechanics are fragmented theories. They cannot be special cases of the theory of Quantum Gravity.

Mr Vikram Zaveri, you have told that 

"There are two apsects of general relativity which are inconsistent with the reality. One is the linear definition of time and second is the geometrical description."

Would you please mention references for these?

Mr. Rifat Zaman.

Following article and the references therein gives further details on my earlier comments.

http://ptep-online.com/index_files/2015/PP-40-11.PDF

Yes.

QG in different limits goes to QM, GTR, etc. The following work on QG shows  exactly the big picture that you are asking for.

Effective Theory of Quantum Gravity : Soluble Sector,  S. Mishra  and J. Christian , Abramis Academic, UK, 2011.

Quantum gravity would be, if the name is justified, simply a particular example of a quantum theory.  The point is that "quantum theory" is not a single theory, but a class of theories, contain, say, quantum electrodynamics, Schrödinger theory, chromodynamics, and so on, and quantum gravity would be simply a member of this class of quantum theories. 

If GR would become a limit of QG is another question.  I would say that there has to be a classical limit of QG, which has to be a classical theory of gravity which is in some domain indistinguishable from GR.  But, for example, GR allows solutions with nontrivial topology and with closed causal loops, as well as singularities.  The classical limit of QG is not obliged to have these properties. 

Good point Scmelzer.  Usually by QM we mean No-rel QM. You are including QFTs like QED, QCD etc. in the broader definition. Alright. In that sense what you say is OK. Even QG will be just another Quantum Theory.

Regarding the second point, the classical limit may contain the singularities and all that since the classical limit would be Newtonian Gravity since Point masses are singularities.

Regards,

Rajat

Rajat, of course the classical limit may contain all that, but it is not necessary. If it would give the Newtonian limit only for continuous mass distributions it would be fine and without singularties. Imagine a QG which has a critical distance (typical for effective theories) and no localization of masses below that critical length.  The theory itself would be without singularities, would give in the (classical non-relativistic) limit Newtonian theory with continuous mass distributions, and now one can obtain point masses and the related singularities already in the Newtonian theory itself. 

Thank you llja for the clarification. I fully agree with what you say. By the way the Quantum gravity that we are talking about would not be a final theory of everything. It would only explain physical phenomena in different low energy and large length scale limits

Regards,

Rajat

Yes, if one gives up the idea that GR is a fundamental theory about space and time, and accepts that it is only an effective theory about clocks and rulers, which breaks down below some unknown critical distance (which is in no way obliged to have a connection with the Planck length), then it may be quite easily quantized - people know already how to quantize effective theories - but it will be valid only for large (in comparison with the critical) distances and not be a final theory of everything.  

Thanks for your comments.

Then what do you think, will be the characteristics of a "theory of everything"? 

@Rajat Pradhan

@Ilja Schmelzer

My own proposal for a theory of everything you can find at http://arxiv.org/abs/0908.0591 See also my home page http://ilja-schmelzer.de/

So, it has to go beyond pure field theory, giving a unifying interpretation of the fields. But it can remain, yet, a continuous theory - with some model for what happens at the critical distance. 

Then it will be a simple standard quantum theory.  With a preferred background, which is necessary, my argument that there cannot be a background-free quantum gravity see http://arxiv.org/abs/0909.1408 A preferred frame is necessary because of the violation of Bell's inequality - to give up realism and causality would be the alternative, but this gives nothing in exchange. 

No, because  a quantum version of the Einstein covariant theory , which is the best classical theory of gravitation we have, does not exists

@ J. A. Souza

One can get the quantum theory of gravity, by first quantizing the Newton-Cartan  theory,and then relativizing it.  The following is the reference.

Effective Theory of Quantum Gravity : Soluble Sector,  S. Mishra  and J. Christian , Abramis Academic, UK, 2011.

"A preferred frame is necessary because of the violation of Bell's inequality - to give up realism and causality would be the alternative, but this gives nothing in exchange."

you mean something like CMBR frame??

Yes, the CMBR frame is clearly the natural candidate for this role.

I think that a working theory of quantum gravity will have to include QM as a subset, but might not include our current general theory as a classical limit.

I think it'll generate ==a== general theory of relativity, just not the version that we currently use. Parts of GR1916 seem quite bad, and it seems to include some arbitrary "manual overrides" where we suspend the theory's internal logic to allow agreement with empirical evidence. And then there's that issue of the theory's incorporation of SR, even through SR seemed to be in conflict with fundamental GR principles (inertia without gravitation). And then there's the suspension of some Mach-Einstein principles that happened in 1960 to prevent the theory crashing.

More fundamentally, though, general relativity's definitions and concepts of causality seem to be at odds with those of QM, and seem to lack a certain required sophistication.

GR1916's treatment of horizons sucks. Consider a cosmological horizon - since the local physics allows massenergy and information to pass in both directions, it fluctuates and radiates in response to events that occur behind it. Effectively, a cosmological horizon is an acoustic horizon, and the local physics therefore seems to be an acoustic metric, whose phenomenology seems to be a good match for quantum mechanics (the acoustic horizon radiation can be re-modelled statistically as Hawking radiation).

But if the cosmological horizon behaviour is general for curvature horizons, then we need black hole horizons to fluctuate and radiate according to internal events, too. QM agrees that this is what must happen. But under GR1916, this can't happen, partly because of the coordinate-system conventions and concepts of observability and causality that it inherited from Einstein's special theory. It seems that we can recreate similar QM-style behaviour in a gravitational horizon by swapping out the SR Minkowski metric with a more sophistiated relativistic acoustic metric and switching from SR-style causality to "acoustic metric"-style causality, but that requires a serious review and rewrite of GR, and it seems that until now, we've been holding off from doing this work in case "something comes up" to solve the problem for us, without requiring that rewrite.

Unfortunately, since Einstein pointed out the possible need for a major GR rewrite back in 1950, no alternative solution seems to have appeared, and we've instead rewritten the definitions of classical theory to make a 100% reduction to SR physics compulsory, and reassure ourselves that GR1916 can't be wrong, and to consolidate and entrench the position of GR1916 to make that rewrite project look impossible.

So ...  (IMO) there doesn't seem to be any obvious technical problem with producing an acoustic-metric-based theory of quantum gravity that reduces contains QM and ==a== general theory of relativity as subsets, but I don't think that that general theory will be the one that we currently use. I think that GR's current version is just too cobbled-together, and too structurally incompatible with proper real-world principles to work within a larger theory. We currently make GR1916 look good by fudging it and setting arbitrary limits and avoiding any arguments that are known to crash it. If the theory's being used in isolation then you an get away with stuff like that, but not if its forming part of a larger rigorously-constructed system that also incorporates QM.

Mohammad, the problem of quantization of gravity is only a problem of quantization of GR in its spacetime interpretation.  If one goes back to the Lorentz ether (which can be easily generalized to GR) then quantization is not a problem.  The problem appears if one wants to believe GR is about some fundamental "Spacetime", and not about the influence of gravity on clocks and rulers.

If GR would be only about clocks and rulers on some fixed background, it would be no more problematic to quantize GR than it is to quantize usual condensed matter theory. Simply, the usual condensed matter would have to be replaced by the "ether".  

Even the "problem of non-renormalizability" would disappear, because we know today very well than non-renormalizable theories may be effective theories - long distance limits of theories which become invalid below a critical distance.  For the Lorentz ether, there is such a natural "critical distance" - the atomic distance of the ether. 

See http://arxiv.org/abs/gr-qc/0205035 about the Lorentz ether.

Ilja: IMO, the problem with quantising GR to produce QM is that althrough it seems that we can try to reverse-engineer a classical field theory that could be thought of as underlying QM ("stochastic QM" arguments, Kh. Namsrai), that hypothetical underlying classical field theory doesn't seem to correspond to GR1916.

A hypothetical general theory that would seem to correspond to QM (after quantisation) would seem to have to include velocity-dependent distortion effects, since the uncertainty principle doesn't just smear a particle's mass into the surrounding region, but also its momentum.

We'd then have an underlying classical theory that includes velocity-dependent curvature, and since SR 's geometry assumes (for convenience)  the complete absence of velocity-dependent curvature effects, and GR1916 is designed (for convenience) to reduce exactly to SR physics, if "correct" classical theory was to be defined by compatibility with quantum mechanics, then neither SR or GR1916 would be correct classical theory.

Eric, add to GR1916 harmonic coordinates as preferred coordinates, and choose a time-like one of them as preferred time, and you have a classical interpretation of GR1916 with continuity and Euler equations.  Add another minor modification so that the harmonic condition becomes an Euler-Lagrange equation, which adds not more than for scalar massless dark matter fields, and you have a Lagrange formalism for this, with the harmonic conditions now as local Noether conservation laws, and a classical Hamilton formalism.  What else do you need?  A classical condensed matter theory on a fixed background. 

So, there is really nothing to object against the equations of GR1916, add four dark matter fields and all is completely fine. 

Given that the velocity of this Lorentz ether is v^i = g^0i/g^00, the expression for curvature depends on this velocity too, so your point of "velocity-dependent curvature" is not an objection.