Is quantum theory really necessary?

[DaveLush]

I have received a warning about the above links, that only peer-reviewed published papers are allowed. Two out of three of the immediately above papers have been published in peer-reviewed journals, so I will provide the references here.

There were two papers by C. K. Raju, one from 2004 Foundations of Physics, The title of this one is "The electrodynamic 2-body problem and the origin of quantum mechanics ", and was published in Found. Phys. 34 (2004) 937--62.

The second C. K. Raju paper with a second Raju who is at Harvard (maybe his son?) is newly posted on the archive although claimed submitted to Phys. Rev. E. I will consider it withdrawn from this discussion until it actually sees print.

The Hestenes paper, "Spin and Uncertainty in the Interpretation of Quantum Theory", was published in Am. J. Phys., 47(5), May 1979, 399-415.

In an earlier post I linked to a Hestenes page that links to the above paper and various others. I won't provide the actual references here but on that site there are 9 papers, Six of them provide citations to American Institute of Physics journals (either Am. J. Phys or J. Math. Phys). Of the others, one in Annales de la Louis de Broglie, another in a symposium proceedings, another newly posted to the pre-print archive.

As far as the rules are concerned, I read them prior to joining, but I am not too clear from the private message on whether the links to other than journal sites are permissible, provided that one is fastidious about providing the journal source data. Seems to me it is a great convenience for many people who don't have institutional license access to be able to access the pre-print archive and other author sites such as Hestenes', where many papers that have seen peer-reviewed publication may be found. In the future I will be happy to be more fastidious about providing the journal reference along with the link. I had been relying on that it is usually clear in the links I've provided, once you open it, that it is a peer reviewed paper (with exceptions as noted) but I will be happy to make it explicit. If that is not adequate I hope someone will let me know short of banning me. Later on I will re-read the rules but I don't recall them being so precise here about what is allowable.

I would mention also that I am being quizzed hard here by people and I want to show that I am not just making all this stuff up, because it seems to be completely new to everyone I guess. Some of the ideas have been around a very long time but one of the potentially most important, due to Christian, is new and unpublished. Well I guess I just want to point out, it seems the deck is somewhat stacked against me if I can't cite an Oxford professor's latest work, at least as something to think about, or as a basis for how I could consider such things while plausibly not being totally crazy. I do also understand though the motivation for the rules and as I've mentioned elsewhere I've seen how things can degenerate in the absense of any policy.

Finally I want to cite what I consider a very remarkable peer-reviewed journal-published paper by an author that I have mentioned already in this thread, Jayme De Luca's "Stiff three-frequency orbit of the hydrogen atom", Phys Rev E. 73 026221 (2006). This paper can be considered an alternative to the newer Raju paper that has not yet seen journal print. I didn't provide it initially because I feel it is larger in scope and harder to follow, but it did see peer-reviewed print. Also it has many excellent historical references like the 1938 Dirac classical electron theory and Eliezer and others. It can also be found on the Cornell pre-print archive but you have to search the full "Jayme De Luca" as there are many other De Lucas.

 

[DaveLush]

Post #35 I said:

"Yes, genuine geometric charged point particles and Maxwellian fields, and E + v x B forces, but the forces per the Lienard-Wiechert fields that have denominators that blow up relativistically."

I should have said

"... but the forces per the Lienard-Wiechert fields that have denominators that go to zero relativistically so they blow up."

 

[vanesch]

About Bohmian mechanics, the claim of non-locality is not mine.

I'm not disputing that Bohmian mechanics is non-local (on the contrary). But being non-local doesn't stop a theory from being classical - that was my point. Newtonian mechanics is also non-local (and for sure, it is classical, right). Bohmian mechanics comes close to a pre-relativistic classical theory (up to one nasty detail of course: the fact that there must be a second ontology in which the wavefunction lives...), and it finds its agreement with relativity in the same way as with an ether theory.

All this to me is "classical" (pre-relativistic).

 

[DaveLush]

vanesch, you should check out Hestenes' reformulation of the Dirac quantum theory of the electron. He shows it's isomorphic to a simpler Clifford algebra-based theory where the wavefunction is real. This has been published in Am. J. Phys in 2002 and 2003. He has reprints here:

http://modelingnts.la.asu.edu/html/overview.html

Hestenes says that his interpretation fits in with Bohm's. Plausibly he would consider the latter the Galilean limit of the former. In general though I think he believes that any place there's an imaginary value in QM it's due to a misunderstanding of the role of spin. I am not putting it well so you should check it out for yourself.

The "Spin and Uncertainty" paper I cited and linked further above covers how the proper non-relativistic version of the Dirac theory is the Pauli theory, not the Schroedinger theory. This is a potentially important difference for me and my hobby project. He says, the Schroedinger theory is not QM with no spin, but rather QM for a system in a spin eigenstate.

 

[akhmeteli]

vanesch, you should check out Hestenes' reformulation of the Dirac quantum theory of the electron. He shows it's isomorphic to a simpler Clifford algebra-based theory where the wavefunction is real.

This statement seems somewhat misleading, as the wavefunction in Hestenes' theory has eight real components, and it is easy to replace the four complex components in the wavefunction of the Dirac equation with eight real components. I am not trying to say that Hestenes' theory has no strong points, but this is not one of them.

 

[DaveLush]

ZapperZ, here is a cite directly addressing how a spin due to zitterbewegung can give rise to tunneling behavior. It's Rivas, "Is there a classical spin contribution to the tunnel effect?", Phy.Lett. A 248 (1998) 279-284.

 

[DaveLush]

This statement seems somewhat misleading, as the wavefunction in Hestenes' theory has eight real components, and it is easy to replace the four complex components in the wavefunction of the Dirac equation with eight real components. I am not trying to say that Hestenes' theory has no strong points, but this is not one of them.

akhmeteli, I don't think it is fair to say my statement is misleading. I did not say it was a scalar formulation. I will take your meaning to be more precisely though that my statement is one of little significance. I think it is fair to ask why a real formulation would be significant and it is not that easy for me to answer, I am discovering. I am still thinking about it. What comes to mind immediately is that Hestenes claims (in various peer-reviewed journal articles) to have geometrical or direct physical interpretations of all but one of compenents. That is, they don't require a complex space which must then be interpreted and typically as leading to a wavefunction that has a probabilitistic meaning. I think it is a benefit to have quantities that may be more directly interpreted as time or ensemble averages.

I will continue to think about this and look in Hestenes' journal-published work for a concise statement about why it is important. I'm confident such a statement can be found in his work and I'm certain it will be much more effectively put than I can do it.

 

[ZapperZ]

ZapperZ, here is a cite directly addressing how a spin due to zitterbewegung can give rise to tunneling behavior. It's Rivas, "Is there a classical spin contribution to the tunnel effect?", Phy.Lett. A 248 (1998) 279-284.

"can give rise to tunneling behavior" appears to mean "it can tunnel". It doesn't say it explains ALL tunneling phenomena. Just because there are classical components to tunneling (which is still dubious in itself) doesn't mean that that is the sole description of tunneling. So it is highly misleading to use this source as "proof" that there's a classical description of all tunneling phenomena.

I'd love to see how he plans to explain the Josephson tunneling using such a thing.

BTW, he seems to be the only one who is citing his paper (all 6 citations). That should tell you something.

Zz.

 

[akhmeteli]

akhmeteli, I don't think it is fair to say my statement is misleading. I did not say it was a scalar formulation.

If you had said that it was a scalar formulation, it would have been downright incorrect, and I did not say your statement was incorrect, I said that it SEEMED misleading, for the simple reason that it misled me :-). Moreover, it misled me so terribly that I had to look through Hestenes' article to find out what he actually did :-).

I will take your meaning to be more precisely though that my statement is one of little significance. I think it is fair to ask why a real formulation would be significant and it is not that easy for me to answer, I am discovering. I am still thinking about it.

Because there is a wide-spread opinion that complex wavefunctions (or couples of real wavefunctions, which is pretty much the same) are necessary to describe charged particles. Shroedinger considered a system of the Maxwell electromagnetic field interacting with a charged Klein-Gordon field (you may find the reference in some of my previous posts) and concluded, using the unitary gauge, that the above opinion is wrong, at least for that system. By the way, that system is relevant to your question: "Is quantum theory really necessary?", as the wavefunction (the charged Klein-Gordon field) can be algebraically eliminated from the equations of motion for that system (this is trivial), and, as I found out, the resulting equations of motion describe independent evolution of the electromagnetic field. Thus, it looks like a classical system can be equivalent to a quantum system. It is more difficult to say if a similar result can be achieved for the Dirac-Maxwell system. So you'll appreciate that when I read your statement I was intrigued and, as it turned out, misled :-).

What comes to mind immediately is that Hestenes claims (in various peer-reviewed journal articles) to have geometrical or direct physical interpretations of all but one of compenents. That is, they don't require a complex space which must then be interpreted and typically as leading to a wavefunction that has a probabilitistic meaning. I think it is a benefit to have quantities that may be more directly interpreted as time or ensemble averages.

I will continue to think about this and look in Hestenes' journal-published work for a concise statement about why it is important. I'm confident such a statement can be found in his work and I'm certain it will be much more effectively put than I can do it.

Certainly, there can well be other reasons (besides those I gave) why having real wavefunctions, rather than complex ones, is significant (it is typically much easier to work with complex numbers than with real ones, but this is a different question). It is important to understand though whether such replacement is more meaningful than a trivial replacement of a complex number with a couple of real ones. I like some aspects of Hestenes work, but I find it difficult to decide how important his work is.

 

[Maaneli]

Dear David Lush and ZapperZ,

There is in fact a classical account of tunneling within the framework of Stochastic Electrodynamics:

Tunneling as a classical escape rate induced by the vacuum zero-point radiation
Authors: A.J. Faria, H.M. Franca, R.C. Sponchiado
To be published in "Quanta, Relativity and Electromagnetism: The Search for Unity in Physics", Proceedings of a Symposium in Honor of Jean-Pierre Vigier (Paris, September, 2003). Kluwer Academic Publishers
http://arxiv.org/abs/quant-ph/0409119

 

[ZapperZ]

Dear David Lush and ZapperZ,

There is in fact a classical account of tunneling within the framework of Stochastic Electrodynamics:

Tunneling as a classical escape rate induced by the vacuum zero-point radiation
Authors: A.J. Faria, H.M. Franca, R.C. Sponchiado
To be published in "Quanta, Relativity and Electromagnetism: The Search for Unity in Physics", Proceedings of a Symposium in Honor of Jean-Pierre Vigier (Paris, September, 2003). Kluwer Academic Publishers
http://arxiv.org/abs/quant-ph/0409119

No, I don't actually buy that, because I've seen that already.

Stochastic electrodynamics have been used to give the "classical" description of the photoelectric effect as well. The PROBLEM with this description is that it can only go so far, i.e. explain the ROUGH, naive phenomenon, but never, ever, the details. I've mentioned this already that while the photoelectric effect can be explained by it, a more intricate phenomenon such as angle-resolved photoemission, resonant photoemission, and multiphoton photoemission have never been described using stochastic electrodynamics. No attempt has even been made to use that formulation to describe those phenomena. So given that fact, which one would you prefer to use - the one that can only explain the simplest version of the family of phenomena, or the one that can explain all of them without exception?

The same can be said with tunneling. Would you like to see if stochastic electrodynamics can actually get the density of states of the single-particle spectrum of a superconductor, or the phonon modes from the second derivative of the I-V curve?

Zz.

 

[malawi_glenn]

Stochastic Electrodynamics seems to be too much Ad-Hoc for me..

 

[Zacku]

I often encounter statements to the effect that classical physics cannot describe processes at the atomic and subatomic level. I also understand fully well that no one ever has to date successfully described these quantum processes, even the most basic ones, using classical physics. But that something has never been done is not a proof of impossibility, obviously. So, what are the best arguments for the universe being essentially non-classical? I would like to find out if there are some I don't know, and whether I can sustain an argument that the position that quantum theory is unique and essential is no more than an observation that there is no classical description that works.

The only scientific sense that i can find to your question is to know which theory is the most fundamental one between classical mechanics and quantum mechanics (your examples made me think that QM could be an effective theory of CM).
-I, however, understand that it can be quite embarrassing arguing that a phenomenon can only be described in QM and then learn that a classical explanation does exist finally-

QM allows one to retrieve CM (via quasi-classical states, Herenfest theorem or the saddle point method applied to the path integral formulation of QM when $$\hbar \rightarrow 0$$) and to go explicitely beyond CM predictions through the Gutzwiller trace formula for example (whose corrections to saddle point approximation match well observations).
It is thus important to note that while a modified CM allows us to retrieve some qualitative results from QM, QM allows us to retrieve the whole CM theory.
That is, CM is included in QM. The only issue that may be a problem, then, is to know if it's finally the same theory written differently. But it can't actually be the case because they are not based on the same paradigm (for example in QM we can't measure exactly, in principle, the x-projection of the position and of the momentum of the same particule while there is absolutely no problem in CM, application of this "principle" can be seen with Bose-Einstein condensate for example).

 

[Andy Resnick]

I take issue with the claim that QM somehow includes CM. Perhaps that is true- certainly, QM is a theory of atoms and molecules, and so it is likely that macroscopic materials are described by QM.

That said, I have never seen a full formal QM treatment of continuous matter like a (classical) liquid or an elastomer. Or a non-crystalline solid. QM does not retrieve the "whole CM theory".

QM is great at describing weakly-interacting particles. QM is highly useful for many, many phenomena: lasers and transistors are two. But it is clearly not a complete theory. The velocity of a particle is not well-defined.

Newtonian CM is clearly flawed from the beginning: it claims to be a macroscopic theory, yet it is constructed by using infinitesimal mass-points and forces acting on infinitesimal points.

"Classical" QM is flawed because it requires a coordinate system; there is no background-independent formulation of QM, AFAIK.

 

[Zacku]

That said, I have never seen a full formal QM treatment of continuous matter like a (classical) liquid or an elastomer. Or a non-crystalline solid. QM does not retrieve the "whole CM theory".

I don't know either if the different topics you mentioned are really only based on CM. For this kind of subject one can often forget physics at the microscopic scale and only rely on symmetries of the system to get the correct free energy at equilibrium (there might be use of tools from coarse graining theory and renormalisation group behind these results that have to stay somewhere in mind anyway).
Formally you could have say that classical liquids involve CM via exact hierarchy equations such as the BBGKY one but there exist the same kind of exact equations in a quantum formulation that leads to the same transport equation for example (see Roger Balian about transport equations and thermodynamics).

The velocity of a particle is not well-defined.

that's probably right in practice but in principle, since QM formalism comes from Hamiltonian formulation of CM, there is no big problem to define the velocity, is there ?

 

[Andy Resnick]

I'm not sure what you mean by "Formally you could have say that classical liquids involve CM via exact hierarchy equations such as the BBGKY one...".

Continuum mechanics essentially begins with Cauchy's laws, along with the specification of jump conditions on boundaries. The origin of viscosity (or any constitutive relation, for that matter) is an open part of continuum mechanics, but if a constitutive relationship is given, mechanical behavior is completely specified by the governing equations.

My comment regarding velocity in QM comes from Page 4 of Landau/Lif****z, vol. 3. My goal is simply to illustrate that while some results are better explained via QM, some concepts are more straightforward in CM.

Or am I misunderstanding your point?

 

[Maaneli]

No, I don't actually buy that, because I've seen that already.

You've seen this paper already? What exactly do you object to about the claims of that paper? Are you denying now that even the simple barrier tunneling phenomena can be obtained in SED?

Stochastic electrodynamics have been used to give the "classical" description of the photoelectric effect as well.

I don't think that's true. You're probably thinking of the Lamb/Scully paper in which they derive the photoelectric effect for classical EM plane waves impinging on quantized matter. That's different from SED. The latter treats the entire system in a classical stochastic way.

The PROBLEM with this description is that it can only go so far, i.e. explain the ROUGH, naive phenomenon, but never, ever, the details. I've mentioned this already that while the photoelectric effect can be explained by it, a more intricate phenomenon such as angle-resolved photoemission, resonant photoemission, and multiphoton photoemission have never been described using stochastic electrodynamics. No attempt has even been made to use that formulation to describe those phenomena. So given that fact, which one would you prefer to use - the one that can only explain the simplest version of the family of phenomena, or the one that can explain all of them without exception?

Hmm you seem to be conflating a number of different issues. Also, I'm not sure what you mean that SED can only give the "ROUGH", "naive" phenomenon. Do you consider the following to be "rough", "naive" phenomena?:

Empirical agreements with predictions between SED versus QM and QED for linear systems such as for (1) calculations of ensemble averages of free electromagnetic fields, (2) systems of electric dipole simple harmonic oscillators (SHO), including the complicated situation of van der Waals at any distance, (3) all experimentally known Casimir/van der Waals type situations, (4) diamagnetism, (5) the retarded van der Waals forces between electric dipole oscillators at temperatures T = 0, (6) the repulsive Casimir-type force prediction between a perfectly conducting plate and an infinitely permeable plate, (7) the Unruh-Davies effect, and perhaps even more such phenomena?

Now, it is true that SED has not been applied to the more complicated condensed matter phenomena; and since that is the case, in fairness we simply cannot say for sure if it will work or not. No question it would be a very difficult (perhaps impossibly difficult), nonlinear problem though. Indeed I think that is why it has not been applied to these various emission processes - because at the moment it can only give the QM ground state for hydrogen, in lengthy numerical simulations! Don't bother to jump on this point though, as I never claimed that it can or should be able to do the things you suggest.

What could very well work for all those emission phenomena, is a semiclassical theory in which the classical ZPF of SED is used to replaced the second quantized ZPF of QED, or even replace the classical self-field effects of charged matter that is first or second quantized. The reasons to expect this is plausible is that the SED ZPF shares all the same statistical properties (N-point correlation functions) as the QED ZPF, when the latter is obtained from symmetric ordering of field operators in the Heisenberg operator equations of motion. Indeed Marshall and Franca have already shown that the classical ZPF gives the correct excited state decay rates for quantized matter. Also, Barut has shown that the classical self-fields of charged first or second quantized matter can also be used to replace the QED ZPF, and still account for all known QED effects in low orders of perturbations, including the photoelectric effect. So, given the fluctuation-dissipation theorem that applies to dissipative forces and stochastic noise, I would expect that replacing the classical self-fields with the classical SED ZPF, but keeping the matter first or second quantized, should be sufficient to explain the condensed matter phenomena you propose as a challenge. Though to my knowledge, no one has done much with this.

The same can be said with tunneling. Would you like to see if stochastic electrodynamics can actually get the density of states of the single-particle spectrum of a superconductor, or the phonon modes from the second derivative of the I-V curve?

As a matter of principle, it would be interesting to see how far this classical ZPF induced tunneling effect can be taken, even if it is a mathematically difficult problem. After all, I bet at one time no one thought that SED could correctly derive any of the phenomena on the list above that I presented.

 

[ZapperZ]

You've seen this paper already? What exactly do you object to about the claims of that paper? Are you denying now that even the simple barrier tunneling phenomena can be obtained in SED?

No, I have seen the argument being given that SED seems to be able to describe quantum tunneling.

I don't think that's true. You're probably thinking of the Lamb/Scully paper in which they derive the photoelectric effect for classical EM plane waves impinging on quantized matter. That's different from SED. The latter treats the entire system in a classical stochastic way.

Only if there's something different between that and "Stochastic Optics" the way Marshall and Santos did it. If they are different, then I meant the latter.

Hmm you seem to be conflating a number of different issues. Also, I'm not sure what you mean that SED can only give the "ROUGH", "naive" phenomenon. Do you consider the following to be "rough", "naive" phenomena?:

I am characterizing "photoelectric effect" as the "rough, naive phenomenon". It is "rough and naive" because

(i) it ignores the band structure effects of the material
(ii) it simplifies any matrix element effects of the coupling of the photons to the initial and final state of the photoemission process
(iii) it ignores the details of the energy and momentum spread of the emitted photoelectrons.

None of these things are in the standard photoelectric effect experiment. Yet, they are part of the detailed treatment of the photoemission phenomenon. That is why I characterized the standard photoelectric effect as "rough and naive". It is similar to estimating a cow to be a sphere. From very far, you can do many different types of approximation and arrive at almost the same answer. It is only when you get very close and look at the details that you can distinguish which is the more accurate description of it. I would think that, after so many years of proclaiming that there is another "alternative" to describing the photoelectric effect, they would have proceeded to the next step and gone beyond doing the spherical cow approximation and try to match the details already.

And that's also something I would expect out of any alternative tunneling description. Can it be used to derive, let's say, the Fowler-Nordheim model?

Zz.

 

[Maaneli]

Though I should add that I would expect significant modifications to SED to be made, if it is ever capable of handling condensed matter physics, let alone energy quantization in general.

 

[Maaneli]

I would think that, after so many years of proclaiming that there is another "alternative" to describing the photoelectric effect, they would have proceeded to the next step and gone beyond doing the spherical cow approximation and try to match the details already. And that's also something I would expect out of any alternative tunneling description.

Zz.

This is a fair point. But please keep in mind the technical difficulty of taking these logical next steps, and the time and man power devoted to advancing these alternative models is quite small, and so it is not too surprising that it has not been done yet!

 

[ZapperZ]

This is a fair point. But please keep in mind the technical difficulty of taking these logical next steps, and the time and man power devoted to advancing these alternative models is quite small, and so it is not too surprising that it has not been done yet!

Fair enough. However, because of that incompleteness, it cannot be considered as an "alternative". The Bohr model is not an "alternative" to the full QM treatment of an atom just because it has managed to match the most naive model of an atom but not the more complete, non-simplified observations, i.e. the details. That is the main point of my argument that I'm trying to get across.

Zz.

 

[Maaneli]

Fair enough. However, because of that incompleteness, it cannot be considered as an "alternative". The Bohr model is not an "alternative" to the full QM treatment of an atom just because it has managed to match the most naive model of an atom but not the more complete, non-simplified observations, i.e. the details. That is the main point of my argument that I'm trying to get across.

Zz.

I agree with you here. But I didn't claim it was a true alternative to the full QM treatment of an atom. That was David Lush's claim, I think.

 

[DaveLush]

I have to say, I regret naming this thread as I did. I only meant to start a discussion about whether QM is certainly a fundamental theory, or not.

I can only agree that currently and for the foreseeable future there is no alternative to QM in many regimes, essentially all regimes where it applies.

Personally I do hope to see quantum theory put on a firmer basis than the Heisenberg uncertainty principle. Seems to me it's a leap of faith to go from saying that one can't measure the position and velocity of a particle simultaneously to saying that they cannot even be simultaneously defined. I view the HUP as a contrived justification for how matrix mechanics is structured. Historically, the HUP was developed (published in 1927) after matrix mechanics (published in 1925), which is consistent with it being a justification of matrix mechanics after the fact. Matrix mechanics is a nice theory that explains a lot of things, and it is inherent in it that position and velocity are not simultaneously defined with arbitrary position. So fine, but that is no justification for claiming that there is a universal fact that they don't simultaneously exist.

If there is a more prosaic reason why quantum mechanics is true, I would like to know it.

 

[ZapperZ]

I have to say, I regret naming this thread as I did. I only meant to start a discussion about whether QM is certainly a fundamental theory, or not.

I can only agree that currently and for the foreseeable future there is no alternative to QM in many regimes, essentially all regimes where it applies.

Personally I do hope to see quantum theory put on a firmer basis than the Heisenberg uncertainty principle. Seems to me it's a leap of faith to go from saying that one can't measure the position and velocity of a particle simultaneously to saying that they cannot even be simultaneously defined. I view the HUP as a contrived justification for how matrix mechanics is structured. Historically, the HUP was developed (published in 1927) after matrix mechanics (published in 1925), which is consistent with it being a justification of matrix mechanics after the fact. Matrix mechanics is a nice theory that explains a lot of things, and it is inherent in it that position and velocity are not simultaneously defined with arbitrary position. So fine, but that is no justification for claiming that there is a universal fact that they don't simultaneously exist.

If there is a more prosaic reason why quantum mechanics is true, I would like to know it.

I must say that I don't quite understand the logic of your objection. It seems to rest entirely on something that is not fundamental - the HUP. It may surprise you that the HUP is merely a consequence, not the cause. You may want to look, instead, to the basic postulates of QM and what is some time known as the "First Quantization" of QM. It deals with the commutating relations between two observables.

Secondly, and I believe I've mentioned this already (maybe not in this thread), there's nothing to prevent you from making a measurement the position, and a measurement of the momentum, of a single particle with arbitrary accuracy that is limited to the technology at hand. It is just that after you make that first measurement, how well you can predict the 2nd measurement depends on the accuracy of your first measurement. Refer to the example I gave for a single-slit diffraction. You can't say something to the effect that you don't like HUP, when the most blatant example of HUP at work is the single slit diffraction that is staring at you right in the face. Physics cannot be falsified based simply on a matter of tastes!

Zz.

 

[Zacku]

I'm not sure what you mean by "Formally you could have say that classical liquids involve CM via exact hierarchy equations such as the BBGKY one...".

Continuum mechanics essentially begins with Cauchy's laws, along with the specification of jump conditions on boundaries. The origin of viscosity (or any constitutive relation, for that matter) is an open part of continuum mechanics, but if a constitutive relationship is given, mechanical behavior is completely specified by the governing equations.

Actually I am a lot more used to statistical mechanics than continuum mechanics. And I have seen many derivations of continuum mechanics equations or principles from CM first principles using statistical mechanics, that's what I meant.
It is, for example, well known that Navier-Stockes equation in hydrodynamics is only an order one solution of the Boltzmann equation in the time relaxation approximation. And there exist many ways to derivate more or less rigorously this Boltzmann equation from CM (through the BBGKY hierarchy for example).
I was just saying that the same approaches exist in QM and give the same results in the classical limit.

My comment regarding velocity in QM comes from Page 4 of Landau/Lif****z, vol. 3.

I admit that I'm not very familiar with the concept of velocity in QM (except in solid physics) so I will trust you for this part.

My goal is simply to illustrate that while some results are better explained via QM, some concepts are more straightforward in CM.

I totally agree with that. But, according to me, there is a big difference between a better suited model and a wrong one.
I argue that the best classical model that you can do in CM will have the best form for the action (or lagrangian description) to describe the phenomenon you want to explain. As I remember, this Lagrangian approach is very used, even in continuum mechanics.
If you are not in the CM range of validity (comparison between $$\hbar$$ and the order of magnitude of the action,say) then, this best classical model is wrong and you have to add QM corrections that are, in principle, measurable.

Or am I misunderstanding your point?

I don't know...

P.S : excuse me for the english.

 

[Andy Resnick]

Actually I am a lot more used to statistical mechanics than continuum mechanics. And I have seen many derivations of continuum mechanics equations or principles from CM first principles using statistical mechanics, that's what I meant.
It is, for example, well known that Navier-Stockes equation in hydrodynamics is only an order one solution of the Boltzmann equation in the time relaxation approximation. And there exist many ways to derivate more or less rigorously this Boltzmann equation from CM (through the BBGKY hierarchy for example).
I was just saying that the same approaches exist in QM and give the same results in the classical limit.

I admit that I'm not very familiar with the concept of velocity in QM (except in solid physics) so I will trust you for this part.

I totally agree with that. But, according to me, there is a big difference between a better suited model and a wrong one.
I argue that the best classical model that you can do in CM will have the best form for the action (or lagrangian description) to describe the phenomenon you want to explain. As I remember, this Lagrangian approach is very used, even in continuum mechanics.
If you are not in the CM range of validity (comparison between $$\hbar$$ and the order of magnitude of the action,say) then, this best classical model is wrong and you have to add QM corrections that are, in principle, measurable.

I don't know...

P.S : excuse me for the english.

I think we are in agreement, for the most part. My quibble is your comment that "the best classical model that you can do in CM will have the best form for the action (or lagrangian description) to describe the phenomenon you want to explain". There are many phenomena for which there is no Lagrangian (or Hamiltonian), becasue of dissipative processes. Sure, certain terms can be put in by hand, but that's different from having a first-principles derivation.

Sure, CM has limited validity- as does QM. CM at least extends to general relativity.

 

[reilly]

Once again: QM is absolutely necessary, and will be until an alternative theory yields all QM results -- hydrogen to Higgs; crystal lattice structure to superconductivity; radioactive decay to transistors, and on and on. QM might be likened to a tapestry or mosaic; getting a few squares right amounts to a curiosity and nothing more. To compete with QM requires a huge number of results identical to QM, and, to date, there's no alternative theory that can even begin to compete.
Regards,
Reilly Atkinson

 

[Zacku]

I think we are in agreement, for the most part.

So do I.

My quibble is your comment that "the best classical model that you can do in CM will have the best form for the action (or lagrangian description) to describe the phenomenon you want to explain". There are many phenomena for which there is no Lagrangian (or Hamiltonian), becasue of dissipative processes. Sure, certain terms can be put in by hand, but that's different from having a first-principles derivation.

I thought you would say something like that, which is right but depends fundamentally of the scale of study.
Indeed, continuum mechanics is a coarse grained mechanics and you can't solve the problem at this scale with only CM first principles based on the long range (fundamental) interactions known in CM. You have to add effective interactions such as dissipation in the medium to match what is observed. These interactions, I agree, aren't well discribed in a variational approach and, practically, this is not the best way to treat a problem in continuum mechanics. BUT I think that we also agree about this point because, microscopically, these effective interactions come from an average of a more fundamental interparticle interactions that can be discribed by a variational approach.

That said, it is obvious that a lot of macroscopic phenomena only explained, for the moment, by QM theory can also be explained in CM by an appropriate effective modeling that will take into account, partly, quantum effects as one can see in the debate above about SED.
Nevetheless, I want to underline the fact that this "explanation" is on the one hand due to the QM (theory) whose effects are valid whatever the phenomenon under study and on the other hand due to an effective modeling that can only (a priori) handle the phenomenon for which it has be made and nothing else, which is a big difference, in my opinion.

CM at least extends to general relativity.

That's true but I hope it's only a matter of time...

 

[Andy Resnick]

<snip>

I thought you would say something like that, which is right but depends fundamentally of the scale of study.
Indeed, continuum mechanics is a coarse grained mechanics and you can't solve the problem at this scale with only CM first principles based on the long range (fundamental) interactions known in CM. You have to add effective interactions such as dissipation in the medium to match what is observed. These interactions, I agree, aren't well discribed in a variational approach and, practically, this is not the best way to treat a problem in continuum mechanics. BUT I think that we also agree about this point because, microscopically, these effective interactions come from an average of a more fundamental interparticle interactions that can be discribed by a variational approach.

<snip>

Can I just say it's a breath of fresh air to speak with someone else who understands a balanced approach to science?

Maybe it's becasue I just read Lee Smolin's "Trouble with Physics" book, but lately I have very little patience for scientists (not just physicists) who frenetically generate data and papers containing insipid results, all the while claiming (without presenting evidence) that longstanding unsolved problems have been trivially solved some time ago.

 

[Zacku]

Can I just say it's a breath of fresh air to speak with someone else who understands a balanced approach to science?

You're welcome .

Maybe it's becasue I just read Lee Smolin's "Trouble with Physics" book

I have to read this book too.

 

[reilly]

That said, it is obvious that a lot of macroscopic phenomena only explained, for the moment, by QM theory can also be explained in CM by an appropriate effective modeling that will take into account, partly, quantum effects as one can see in the debate above about SED.

Please show us "an appropriate effective model"

Regards,
Reilly Atkinson

 

[Zacku]

Please show us "an appropriate effective model"

Regards,
Reilly Atkinson

I haven't one and I'm not very interested in this kind of work actually.
I just wanted to point out the fact that it was not impossible, in principle (I somehow exaggerated with the word "obviously"), to make effective models that take into account quantum effects for specific cases.

However, the term "appropriate" is quite subjective, according to me, and even the Bohr model can be appropriate in some extent to explain hydrogen spectroscopy although it is fundamentally wrong in term of microscopic understanding.