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NavierStokes from Quantum Mechanics? 
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#1
Nov1013, 06:09 PM

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In Victor Stenger's book, "Quantum Gods" he states:
Edit: If you have references that back up your responce, please provide. Thank you! 


#2
Nov1013, 06:20 PM

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If you come up with the proper limits, which usually involve taking some statistical averages, then yes I think that's correct.
If we really believe quantum mechanics is correct, and we have a set of classical equations which work beautifully at a certain scale, then I think it's quite intuitive that one should be a limiting case of the other  with some additional assumptions in place. 


#3
Nov1013, 06:48 PM

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#4
Nov1113, 06:40 AM

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NavierStokes from Quantum Mechanics?
Hi AlephZero. Thanks for the responce. Looking at the reference, it seems to be geared toward predicting molecular properties from quantum mechanics as opposed to NS equations.
I think you're right in that fluids can be approximated as a continuum from point particles for a gas at least. As I recall, that is done using van Der Waals forces and adding in conservation of energy and momentum. For a liquid, I would think one needs to consider molecules with a finite volume. I would think the derivation must have been done many times. I really don't doubt the derivation is possible, I just wonder what the best reference might be. Someone must have done this many years ago. In fact, doing a Google search seems to bring up lots of hits, but I'd be curious to see where it started and how it's best explained. Consider that if the statement is true, there should be a reference to the appropriate individual's work on this topic and not just a statement provided as a suggestion. 


#5
Nov1113, 07:49 AM

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To be fair, there is some work applying the fluctuationdissipation theorem to hydrodynamics a good summary is in Chapter 8 of Chaikin and Lubensky's "Principles of condensed matter physics". Dattagupta and Puri "Dissipative phenomena in condensed matter" also has a good summary of current research in quantum dissipative systems. 


#6
Nov1113, 07:56 AM

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Victor Stenger makes a completely nonsensical claim.
As AndyResnick says, constitutive relations are critical features in the modelling leading up to NS, and generally none of them has been justified "ab initio". They are, essentially, (at most!) empirically justified, which is quite a different beast, showing Stenger doesn't know what he talks about. But, even the empirical justification is not really that well founded; rather, the standard NS equations are the SIMPLEST modelling, in a mathematical sense to work with. 


#7
Nov1113, 07:57 PM

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Andy and arildno, thank you for your explanations. I’d like to understand this a bit better though. Perhaps you can shed a bit more light on this?
I was watching a YouTube video the other day with Steven Weinberg who suggested that the “laws of thermodynamics are entailed by elementary particle physics”. By extension, Steven seemed to infer that classical laws such as described by the NS equations were entailed by elementary particle physics therefore, I assume, they are entailed by quantum mechanics. Arlindo has pointed out that “proving compatibility of NS with QM is NOT the same as deriving NS from QM.” Perhaps Victor’s statement that NS are deducible from QM steps over the line, making the statement false? Just to clear up one lingering doubt about what is meant here, I take it that constitutive relations are (in general) not derivable from quantum mechanics? That surprises me. I would have thought simple things like stress/strain in a solid for example, simply follow from forces between atoms and how those forces vary depending on distance. Similarly, I would have thought that forces between fluid molecules (or atoms) could be described using QM equations such that in principal at least, one might in some way derive NS equations from QM equations. The section of Victor Stenger’s book that discusses this regards “bottomsup” emergence. At the beginning of this section he says: Thanks again. 


#8
Nov1113, 10:24 PM

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I don't see why what he says is so wrong  starting from the quantum mechanics formalism, and then applying the tools of statistical physics to deal with many particles, you should be able to arrive at the NS equations just fine...
Things like dissipation and entropy will come when you make use of the statistical formalism. Unless, you're arguing that you should be able to derive things like the NS equations purely from the Schrödinger equation, without introducing any other assumptions or tool. 


#9
Nov1213, 08:32 AM

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The real question is perhaps "why do we not yet have a microscopic theory of dissipation?" I have my opinions and this is an active area of research, but the fact remains that we don't. Similarly, while we can restrict constitutive equations based on firstprinciples logic (frame indifference, local action, etc), specific constitutive relations (and material parameters that occur within them) are empirical. I also agree it's important to be clear continuum mechanics (of which thermodynamics and the NS equations are subsets) doesn't violate "the laws of physics", but neither is it completely derivable from first principles. Whether this is a bug or a feature is userdefined..... 


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