Quantizing Fluid Mechanics & Gravity: A Debate

[Narasoma]

I ever read that there is no meaning for quantizing fluid mechanics. While left hand side of Einstein field equation used fluid-like approximation for matter (momentum-energy tensor). Therefore, if the first statement is correct then there is no meaning for quantizing gravity, right?

 

[Mihai_B]

"A complete field theory knows fields and not the concepts of particle and motion. For these must not exist independently of the field but are to be treated as part of it."
July 1935, A.Einstein, N.Rosen - The Particle Problem in the General Theory of Relativity

If we consider particles like "geometric" holes uniting different "sheets" and since this "holes" are to be treated as part of the field then we have a theory of fields and how fields interact with fields and we don't need the concept of particle.

The problem is with our way of using and/or understanding geometry, because a simple Euclidean geometry (or even a simple vector algebra) will not be enough for expressing and/or understanding how the real world behaves - which is beyond our comprehensionI. Physical Meaning of Geometrical Propositions
In your schooldays most of you who read this book made acquaintance with the noble building of Euclid's geometry and you remember - perhaps with more respect than love - the magnificent structure, on the lofty staircase of which you were chased about for uncounted hours by conscientious teachers. By reason of your past experience, you would certainly regard everyone with disdain who should pronounce even the most out-of-the-way proposition of this science to be untrue. But perhaps this feeling of proud certainty would leave you immediately if someone were to ask you: "What, then, do you mean by the assertion that these propositions are true?" Let us proceed to give this question a little consideration.
December 1916, A.Einstein, Relativity - The Special and the General Theory
[and then it talks about neighbouring points in Euclidean geometry and the defects that arise from this concept when it is applied to physical world]

But some physicists are kinda' more attracted to the "quanta" theory and so most studies and experiments regarding the quantum level (beyond 10^-15m) are treaded using quantum theory (QED, QFT, QCD, etc and all other SU and SUSY - I call it "Suzy" ) which "seems" to be (but not all the time) more concerned about averages, aberrations, probabilities, behavior over time... and tend to use words like "incertitude", "chaos", "random", "unrepeatable", "statistics", etc ... So what someone that prefers the relativistic view of things must do is to extrapolate from experiments and quantum theory results and use this data to complete "missing" pieces ...

While the two theories actually talk about same experiments but each of them uses it's own terminology. If one is to know which "terms" from one theory are their respective counterparts in the other theory, one could use results from the other theory without wasting time arguing about "incertitude" vs "determinism" - and concentrate on causality - why is this happening and how can I use this here and there.
"The question of the particular field law is secondary in the preceding general considerations.
At the present time, the main question is whether a field theory of the kind here contemplated can lead to the goal at all. By this is meant a theory which describes exhaustively physical reality, including four-dimensional space, by a field. The present-day generation of physicists is inclined to answer this question in the negative. In conformity with the present form of he quantum theory, it believes that the state of a system cannot be specified directly, but only in the indirect way by a statement of the statistics of the results of measurement attainable on the system.
The conviction prevails that the experimentally assured duality of nature (corpuscular and wave structure) can be realized only by such a weakening of the concept of reality.
I think that such a far-reaching theoretical renunciation is not for the present justified by our actual knowledge, and that one should not desist from pursuing to the end the path of the relativistic field theory."
Appendix V - Relativity and the Problem of Space, Generalized Theory of Gravitation, June 9th 1952.It's not really true that we don't have a theory of quantum gravity united with GR ... it's more like some people don't like or agree with such theories, they call such theories "not mainstream", "not validated", "unprovable", "not falsifiable", etc

For instance ER=EPR is a good start to learn about the links between gravity(geometry) and quantum mechanics

Juan Maldacena - Entanglement, gravity and tensor networks Strings


Leonard Susskind - Entanglement and Complexity: Gravity and Quantum Mechanics


PS: this is just a forum post not a "dogma" :) My apology for the missing/wrong stuff.

 

[PeterDonis]

I ever read that there is no meaning for quantizing fluid mechanics.

Where did you read that?

While left hand side of Einstein field equation used fluid-like approximation for matter (momentum-energy tensor).

It's the RHS, not the LHS, where the stress-energy tensor is usually written, and there is no requirement that that tensor has to take the form of a perfect fluid. That form is used as a good approximation for certain cases, but that's all.

if the first statement is correct then there is no meaning for quantizing gravity, right?

No, because the fluid model is just an approximation, and if you have trouble quantizing it, you can always just use a different model.

Also, "quantizing gravity" is usually taken to mean quantizing the metric, not the stress-energy tensor. The stress-energy tensor describes matter and energy, not gravity, and we already know how to quantize all the forms of matter and energy that we know of.

 

[vanhees71]

Well, formally one can "canonically quantize" ideal fluid mechanics:

https://arxiv.org/abs/1011.6396

From a fundamental point of view, this however doesn't make sense since we have already quantized the matter successfully, and fluid mechanics is just a coarse-grained description of the low-energy collective excitations of a strongly coupled many-body system (note that ideal hydrodynamics implies that your fluid is always strictly in local thermal equilibrium, i.e., the relaxation time to equilibrium (mean free path of particles making up the sluid) is vanishing). So it's the other way around: You use quantum many-body theory (many-body quantum field theory) to derive first course-grained equations of motion, which leads to a transport equation which with further approximations like the quasi-particle approximation leads to a Boltzmann-Uehling-Uhlenbeck transport equation, which then can be used to derive hydrodynamic equations for situations close to local equilibrium.