Pauli exclusion principle: a Force or not?

[alxm]

The degenerate pressure is “the same” : as you compress a fermionic gas, the position of the individual particles becomes more and more sharp. Hence, according to HUP, their velocities becomes more and more broad. Hence the pressure…

Actually that's not quite right. That holds true for both bosons and fermions; particle-in-a-box, shrink the box size and the K.E. goes up, true. It is an example of a boundary condition acting as 'pressure' though. (shall we call it "box pressure"?) But the bosons can exist in the same, lowest-energy state whereas the fermions are "pushed" into higher energy states, since the Pauli principle 'stops' them from being in the same state. So in addition to your "box pressure" you have the "degeneracy pressure".

On a sidenote, I've always found it a bit fascinating that astrophysics and chemical physics overlap a bit here. If you treat electrons in an atom as a homogenous gas (e.g. Thomas-Fermi model), which neglects exchange antisymmetry/Pauli principle, then you get analogous expressions for degeneracy pressure coming back as a correction.

 

[tom.stoer]

As I think Zenith and I have already pointed out (and which you seem to have oddly ignored), your idea is just wrong, since there is already a completely mathematically well-defined quantum mechanical definition of force that explains the PEP.

Calm down!

I do not oddly ignore the pilot wave theory. I just want to clarify what I already said in post #21: You try to lead us to believe in this pilot wave theory as an approach that is well established in quantum mechanics. This is simply wrong! It is not helpful to present this idea as the holy grail of quantum mechanics.

Please have a look at the title of the thread: Pauli exclusion principle: a Force or not? I just explained that the Pauli principle has nothing to do with forces (or interactions) as known from ordinary quantum field theory. Whereas numerous interactions can be constructed on top of the mathematical framework of (relativistic) quantum field theory the Pauli principle is itself part of this mathematical framework. Force, pressure etc. are secondary effects arising from a fundamental framework.

 

[Maaneli]

You try to lead us to believe in this pilot wave theory as an approach that is well established in quantum mechanics. This is simply wrong!

No, it is not wrong. The deBB theory is well established (particularly in foundations of QM, quantum chemistry, and AMO physics circles) as an empirically valid approach to QM. It is true that it it is not widely used or widely understood in the broader physics community; but the reasons for that have nothing to do with the empirical validity of the deBB theory. I suggest you do a little more research about deBB theory before making judgments about its current status in the physics community.

It is not helpful to present this idea as the holy grail of quantum mechanics.

I am not presenting it as the 'holy grail' of QM. That's your projection. I have simply pointed out that deBB provides the quantum force explanation of the PEP which Zarqon seeks. And this is something which you cannot get out of the textbook accounts of the PEP.

 

[Maaneli]

I just explained that the Pauli principle has nothing to do with forces (or interactions) as known from ordinary quantum field theory.

But this has already been explained multiple times by other people on this thread. So why repeat it?

Whereas numerous interactions can be constructed on top of the mathematical framework of (relativistic) quantum field theory the Pauli principle is itself part of this mathematical framework. Force, pressure etc. are secondary effects arising from a fundamental framework.

Yes, but now we can go beyond the ordinary framework of relativistic QFT, and get an account of the PEP in terms of a quantum force which is (arguably) fundamental.

Please have a read through the link to Towler's talk which Zenith8 posted.

 

[tom.stoer]

I still doubt your "werll established"; but let's forget about that.

... but now we can go beyond the ordinary framework of relativistic QFT, and get an account of the PEP in terms of a quantum force which is (arguably) fundamental.

Please have a read through the link to Towler's talk which Zenith8 posted.

I checked some of your references but I haven't found anything that is quantum field theory. Can one do S-matrix-, renromalization-group-, lattice-gauge-calculations etc.?

 

[Maaneli]

I still doubt your "werll established"; but let's forget about that.I checked some of your references but I haven't found anything that is quantum field theory. Can one do S-matrix-, renromalization-group-, lattice-gauge-calculations etc.?

You'll have to be more specific about which references you are referring to. But if you are referring to the pilot-wave field theory papers, and saying that you "haven't found anything that is 'quantum field theory'" in them, then I seriously question your base level knowledge and understanding of QFT (assuming you have in fact checked some of the references).

As for whether one can do S-matrix, renormalization group, and lattice-gauge calculations, the answers are yes, yes, and in-principle yes. I say 'in-principle' with regard to the last, because while there is no explicit pilot-wave formulation of lattice-gauge QCD, there do exists pilot-wave QFT models on a lattice, which reproduce the standard QFT predictions:

Bohmian Mechanics and Quantum Field Theory
Authors: Detlef Duerr, Sheldon Goldstein, Roderich Tumulka, Nino Zanghi
Journal reference: Phys.Rev.Lett. 93 (2004) 090402
http://arxiv.org/abs/quant-ph/0303156

Bell-Type Quantum Field Theories
Authors: Detlef Duerr, Sheldon Goldstein, Roderich Tumulka, Nino Zanghi
Journal reference: J.Phys. A38 (2005) R1
http://arxiv.org/abs/quant-ph/0407116

The continuum limit of the Bell model
Authors: Samuel Colin
http://arxiv.org/abs/quant-ph/0301119

A deterministic Bell model
Authors: Samuel Colin
Journal reference: Phys. Lett. A317 (2003), 349-358
http://arxiv.org/abs/quant-ph/0310055

Beables for Quantum Electrodynamics
Authors: Samuel Colin
To appear in the proceedings of the Peyresq conference on electromagnetism (September 2002). Annales de la Fondation de Broglie
http://arxiv.org/abs/quant-ph/0310056

Also, there is just no reason to think that there is any fundamental obstacle against specifically formulating a pilot-wave version of lattice-gauge theory.

 

[tom.stoer]

My impression is that these are still first attempts towards some toy models for QFT. So there is certainly not a fully developed Bohmian QFT available (but I admit that is to be expected as not so many people are working on Bohmian mechanics).

In addition it seems to me that one abandons determinism and introduces stochastic behaviour. I do not disagree that this may be the correct way to do it, but I question the whole approach towards a realistic, deterministic interpretation if one has to give up determinism even within Bohmian mechanics; what is the benefit of the whole approach then?

Last but not least I still do not see how the interpretation Pauli principle is affected. Even in these QFT-like papers one uses Grassman variables to deal with fermions. But in doing so one introduces the Pauli principe as a building principle into the theory w/o any explicit relation to "force" or "interaction".

So my claim from post #32 is still valid: the Pauli principle is itself part of this mathematical framework. Force, pressure etc. are secondary effects arising from it. Whereas numerous interactions can be given (not just the ones we observe in nature: electromagnetic force, strong force, ...), the Pauli principle is rooted in the structure of spacetime symmetry and has nothing to do with interactions constructed on top of it.

 

[Maaneli]

My impression is that these are still first attempts towards some toy models for QFT. So there is certainly not a fully developed Bohmian QFT available (but I admit that is to be expected as not so many people are working on Bohmian mechanics).

The one's by Duerr, Goldstein, Zanghi, and Tumulka (DGZT) fit that description. However, the models by Colin, Westman, and Struyve reproduces the full range of predictions of 'standard' abelian QFTs (though I'm not sure about the model by Nikolic). Although, I agree that they still seem to have somewhat of a 'cooked up' feel to them.

In addition it seems to me that one abandons determinism and introduces stochastic behaviour. I do not disagree that this may be the correct way to do it, but I question the whole approach towards a realistic, deterministic interpretation if one has to give up determinism even within Bohmian mechanics; what is the benefit of the whole approach then?

The use of stochastic behavior is only true of the DGZT Bell-type models. As Colin showed in his papers, one can take a continuum limit of those models, and get a fully deterministic fermionic pilot-wave QFT model. And as you can also see in Colin papers, he has generalized these deterministic models to reproduce the standard abelian QFT predictions. Also, the pilot-wave QFT models of Westman and Struyve are also deterministic. But it should be emphasized that the main goal of these pilot-wave QFT models is not just to restore determinism - rather, it is to supply QFT with a precise ontology, to solve the measurement problem while getting rid of the ad-hoc measurement postulates, and to even make testable new predictions for the case of quantum nonequilibrium in extreme astrophysical and cosmological situations:

Inflationary Cosmology as a Probe of Primordial Quantum Mechanics
Authors: Antony Valentini
http://arxiv.org/abs/0805.0163

De Broglie-Bohm Prediction of Quantum Violations for Cosmological Super-Hubble Modes
Authors: Antony Valentini
http://arxiv.org/abs/0804.4656

Black Holes, Information Loss, and Hidden Variables
Authors: Antony Valentini
http://arxiv.org/abs/hep-th/0407032

There are probably other good reasons for pursuing this pilot-wave approach to QFT, but the ones I cited are the most notables reasons, IMO.

Last but not least I still do not see how the interpretation Pauli principle is affected. Even in these QFT-like papers one uses Grassman variables to deal with fermions. But in doing so one introduces the Pauli principe as a building principle into the theory w/o any explicit relation to "force" or "interaction".

As Struyve points out in his paper 'Field Beables for Quantum Field Theory', one cannot use Grassman fields to make a pilot-wave QFT, since the Grassman fields do not seem to give a consistent probability interpretation. However, as Colin and Struyve show in their co-authored paper, using a Dirac sea pilot-wave model works just fine for fermions.

But no, one does not have to introduce the PEP as an additional, ad-hoc principle in these QFT models. If you write the wavefunctional in these pilot-wave QFT models in polar form, and separate the real and imaginary parts of its corresponding Schroedinger equation, you would get a QFT generalization of the quantum potential, and the corresponding quantum force. You can then explain the PEP in terms of the quantum force (particles get repelled away from nodes in the amplitude of the wavefunctional), just as you can with the quantum force in the first-quantized pilot-wave theories. So all of Towler's discussion (the talk that Zenith8 posted) of how to treat the PEP and symmetries of the fermionic wavefunction in first-quantized pilot-wave theory, can also be generalized to the pilot-wave QFT models of Colin, Westman, and Struyve.

So my claim from post #32 is still valid: the Pauli principle is itself part of this mathematical framework. Force, pressure etc. are secondary effects arising from it. Whereas numerous interactions can be given (not just the ones we observe in nature: electromagnetic force, strong force, ...), the Pauli principle is rooted in the structure of spacetime symmetry and has nothing to do with interactions constructed on top of it.

So no, your claim is not still valid.

 

[GeorgCantor]

You can then explain the PEP in terms of the quantum force (particles get repelled away from nodes in the amplitude of the wavefunctional), just as you can with the quantum force in the first-quantized pilot-wave theories.

Why doesn't this nodal repulsion force work in quantum tunneling?

 

[tom.stoer]

As Struyve points out in his paper 'Field Beables for Quantum Field Theory', one cannot use Grassman fields to make a pilot-wave QFT, since the Grassman fields do not seem to give a consistent probability interpretation. However, as Colin and Struyve show in their co-authored paper, using a Dirac sea pilot-wave model works just fine for fermions.

I do not see this "Colin-Struyve paper" in you last list. Can you add a reference?
And what is the conclusion for fermions, then?

But no, one does not have to introduce the PEP as an additional, ad-hoc principle in these QFT models.

It's not ad hoc. Asap you use Grassmann variables / anti-communiting field operators according to the spin statistics theorem it's natural.

If you write the wavefunctional in these pilot-wave QFT models in polar form, and separate the real and imaginary parts of its corresponding Schroedinger equation, you would get a QFT generalization of the quantum potential, and the corresponding quantum force. You can then explain the PEP in terms of the quantum force (particles get repelled away from nodes in the amplitude of the wavefunctional), just as you can with the quantum force in the first-quantized pilot-wave theories.

This sounds interesting in this context; to which paper are you referring to?

 

[peteratcam]

So my claim from post #32 is still valid: the Pauli principle is itself part of this mathematical framework. Force, pressure etc. are secondary effects arising from it. Whereas numerous interactions can be given (not just the ones we observe in nature: electromagnetic force, strong force, ...), the Pauli principle is rooted in the structure of spacetime symmetry and has nothing to do with interactions constructed on top of it.

So no, your claim is not still valid.

I have to weigh in on tom.stoer's side here. The pressure of a gas is a thermodynamic variable. To get the thermodynamics, you first do the statistical mechanics by doing a weighted sum over the allowed states of the degrees of freedom involved. The Pauli exclusion principle tells you what states to include in the sum (not how to weight them!), and then you derive the pressure from that. Discussing a mysterious "quantum force" is not relevant to the thermodynamic generalised forces like pressure.

As an aside, do the dBB crowd believe in eigenstates? Does quantum statistical mechanics work in the same way? I like magnets, and care less about particles - how should I think of the dBB theory of the hamiltonian H = J\mathbf S_1\cdot\mathbf S_2 ? I'm also a bit suspicious of the particle-centric dBB attempts at QFT. Surely it misses the point about a field theory

 

[Maaneli]

Why doesn't this nodal repulsion force work in quantum tunneling?

Why do you assume that it doesn't?

 

[Maaneli]

I have to weigh in on tom.stoer's side here. The pressure of a gas is a thermodynamic variable. To get the thermodynamics, you first do the statistical mechanics by doing a weighted sum over the allowed states of the degrees of freedom involved. The Pauli exclusion principle tells you what states to include in the sum (not how to weight them!), and then you derive the pressure from that. Discussing a mysterious "quantum force" is not relevant to the thermodynamic generalised forces like pressure.

First of all, the quantum force is not something 'mysterious'. Second of all, since the deBB theory gives you the dynamical equations for the trajectories of each particle (expressed in terms of the quantum force) in the gas, it can certainly give you the thermodynamic pressure as well. The claim here is not that the standard QM approach of using the PEP doesn't work - rather, the claim is that the standard QM approach has to take the PEP as a separate axiom of the theory with no further justification other than that it works, whereas the deBB approach to QM gives you a dynamical-causal explanation for the PEP.

As an aside, do the dBB crowd believe in eigenstates?

What do you mean by 'believe' in eigenstates? The wavefunction must certainly be regarded as an ontic field in deBB, if that's what you are asking about.

Does quantum statistical mechanics work in the same way?

Well no, not in the 'same way'. Because you have a law of motion for the particles, in addition to the Schroedinger evolution, the law of motion for the particles must also get modified for QSM. See for example:

Quantum dissipation in unbounded systems
Jeremy B. Maddox and Eric R. Bittner
Phys. Rev. E 65, 026143 (2002)
http://docs.google.com/viewer?a=v&q...c5x8M7&sig=AHIEtbQTvyTRy3ft07uVys5EfGnVGCqwmg

I like magnets, and care less about particles - how should I think of the dBB theory of the hamiltonian H = J\mathbf S_1\cdot\mathbf S_2 ?

In deBB theory, even your magnets are made up of particles. That Hamiltonian presumably has some corresponding wavefunction, in which case, there will necessarily be a corresponding continuity equation, and thus a corresponding guiding equation for the particles composing the magnets.

I'm also a bit suspicious of the particle-centric dBB attempts at QFT. Surely it misses the point about a field theory

First of all, there is nothing that a priori necessitates the deBB QFTs to be just like standard QFT. And in any case, those stochastic particle-centric deBB QFT's of DGZT do in fact reproduce the standard QFT predictions (for abelian gauge theories like QED and electroweak theory), as does the deterministic Dirac-sea pilot-wave QFT model of Colin and Struyve.

But if you want to insist on a pilot-wave theory in terms of field configurations only, you can have that too, as shown in the papers I referenced by Struyve and Westman.

 

[Maaneli]

I do not see this "Colin-Struyve paper" in you last list. Can you add a reference?
And what is the conclusion for fermions, then?

I referenced it in post #22. Here is the abstract:

"We present a pilot-wave model for quantum field theory in which the Dirac sea is taken seriously. The model ascribes particle trajectories to all the fermions, including the fermions filling the Dirac sea. The model is deterministic and applies to the regime in which fermion number is superselected. This work is a further elaboration of work by Colin, in which a Dirac sea pilot-wave model is presented for quantum electrodynamics. We extend his work to non-electromagnetic interactions, we discuss a cut-off regularization of the pilot-wave model and study how it reproduces the standard quantum predictions. The Dirac sea pilot-wave model can be seen as a possible continuum generalization of a lattice model by Bell. It can also be seen as a development and generalization of the ideas by Bohm, Hiley and Kaloyerou, who also suggested the use of the Dirac sea for the development of a pilot-wave model for quantum electrodynamics."
http://arxiv.org/abs/quant-ph/0701085

It's not ad hoc. Asap you use Grassmann variables / anti-communiting field operators according to the spin statistics theorem it's natural.

Yes, the spin-statistics theorem is ad-hoc. It merely postulates that fermionic wavefunctions are anti-symmetric under exchange of particle positions, and that bosonic wavefunctions are symmetric under exchange. Towler also explains this in his talk.

By contrast, in deBB, you can actually *derive* these postulates from the particle dynamics. A rigorous proof of this was given by Guido Bacciagaluppi in the context of the first-quantized deBB theory:

Derivation of the Symmetry Postulates for Identical Particles from Pilot-Wave Theories
Authors: Guido Bacciagaluppi
http://arxiv.org/abs/quant-ph/0302099

Remarks on identical particles in de Broglie-Bohm theory
Authors: Harvey R. Brown (Oxford), Erik Sjoeqvist (Uppsala), Guido Bacciagaluppi (Oxford)
Journal reference: Phys. Lett. A251 (1999) 229-235
http://arxiv.org/abs/quant-ph/9811054

This sounds interesting in this context; to which paper are you referring to?

This polar decomposition of the Schroedinger wavefunctional was primarily used by Bohm, Kaloyeraou, and Holland in their approaches to field theory. Struyve makes brief reference to it in his 'Field Beables' paper, but does not explicitly make use of it because he prefers the simpler first-order pilot-wave dynamics approach. Nevertheless, it is trivial to show that it is always possible to write the Schroedinger (or Klein-Gordon or Dirac) equation for the wavefunctional into a Madelung form with a quantum potential. Try it yourself! But if you would also like to see a concrete example of this being done (for the nonrelativistic Schroedinger case), have a look at page 519, section 12.4 "QFT in the Schroedinger picture and its interpretation" of Holland's book, The Quantum Theory of Motion:

http://books.google.com/books?id=Bs...AEwAw#v=onepage&q=schrodinger picture&f=false

 

[tom.stoer]

Yes, the spin-statistics theorem is ad-hoc. It merely postulates that fermionic wavefunctions are anti-symmetric under exchange of particle positions, and that bosonic wavefunctions are symmetric under exchange.

Let's look at Wikipedia http://en.wikipedia.org/wiki/Spin-statistics_theorem which I cite because I have no access to the original papers

The theorem states that:

• the wave function of a system of identical integer-spin particles has the same value when the positions of any two particles are swapped. Particles with wavefunctions symmetric under exchange are called bosons;
• the wave function of a system of identical half-integer spin particles changes sign when two particles are swapped. Particles with wavefunctions anti-symmetric under exchange are called fermions.

In other words, the spin-statistics theorem states that integer spin particles are bosons, while half-integer spin particles are fermions.

The spin-statistics relation was first formulated in 1939 by Markus Fierz,[1] and was rederived in a more systematic way by Wolfgang Pauli.[2] Fierz and Pauli argued by enumerating all free field theories, requiring that there should be quadratic forms for locally commuting observables including a positive definite energy density. A more conceptual argument was provided by Julian Schwinger in 1950. Richard Feynman gave a demonstration by demanding unitarity for scattering as an external potential is varied,[3] which when translated to field language is a condition on the quadratic operator that couples to the potential.[4]

Any proof of the theorem requires relativity, since the nonrelativistic Schrodinger field can be consistently formulated with any spin and either statistics.

I don't think that it's ad-hoc. It's not a postulate but a theorem.

 

[Maaneli]

Let's look at Wikipedia http://en.wikipedia.org/wiki/Spin-statistics_theorem which I cite because I have no access to the original papers



I don't think that it's ad-hoc. It's not a postulate but a theorem.

I did not say that the spin-statistics theorem is a postulate, I said the spin-statistics theorem postulates said symmetries of the wavefunction. In other words, those symmetries are merely taken as axioms of the theorem. And the theorem's 'proof' from relativistic invariance merely shows that these axioms are consistent with relativistic invariance. Towler also argues this:

"Often claimed antisymmetric form of fermionic Ψ arises from relativistic invariance requirement, i.e. it is conclusively established by the spin-statistics theorem of quantum field theory (Fierz 1939, Pauli 1940). Not so - relativistic invariance merely consistent with antisymmetric wave functions. Consider:

Postulate 1: Every type of particle is such that its aggregates can take only symmetric states (boson) or antisymmetric states (fermion).

All known particles are bosons or fermions. All known bosons have integer spin and all known fermions have half-integer spin. So there must be - and there is - a connection between statistics (i.e. symmetry of states) and spin. But what does Pauli’s proof actually establish?

• Non-integer-spin particles (fermions) cannot consistently be quantized with symmetrical states (i.e. field operators cannot obey boson commutation relationship)
• Integer-spin particles (bosons) cannot be quantized with antisymmetrical states (i.e. field operators cannot obey fermion commutation relationship).

Logically, this does not lead to Postulate 1 (even in relativistic QM). If particles with integer spin cannot be fermions, it does not follow that they are bosons, i.e. it does not follow that symmetrical/antisymmetrical states are the only possible ones (see e.g. ‘parastatistics’). Pauli’s result shows that if only symmetrical and antisymmetrical states possible, then non-integer-spin particles should be fermions and integer-spin particles bosons. But point at issue is whether the existence of only symmetrical and antisymmetrical states can be derived from some deeper principle.

Actually, fact that fermionic wave function is antisymmetric - rather than symmetric or some other symmetry or no symmetry at all - has not been satisfactorily explained. Additional postulate of orthodox QM. Furthermore, antisymmetry cannot be given physical explanation as wave function only considered to be an abstract entity that does not represent anything physically real."

Even Pauli himself recognized the ad hocness of his EP:

“..[the Exclusion Principle] remains an independent principle which excludes a class of mathematically possible solutions of the wave equation. .. the history of the Exclusion Principle is thus already an old one, but its conclusion has not yet been written. .. it is not possible to say beforehand where and when one can expect the further development..” [Pauli, 1946]

“ I was unable to give a logical reason for the Exclusion Principle or to deduce it from more general assumptions. .. in the beginning I hoped that the new quantum mechanics [would] also rigorously deduce the Exclusion Principle.” [Pauli, 1947]

http://www.tcm.phy.cam.ac.uk/~mdt26/PWT/lectures/towler_pauli.pdf

By comparison, I am saying that the deBB theory allows one to *derive* these axioms from the deBB particle dynamics.

 

[GeorgCantor]

Why do you assume that it doesn't?

Does the wavefunction of the deBB live on configuration space or in real space? The 'imaginary' and 'real' parts of the wavefunction you mentioned earlier in the thread would in this case be the ones that tunneled through a classically forbidden barrier and the ones that didn't, right?

 

[Cthugha]

I am not presenting it as the 'holy grail' of QM. That's your projection. I have simply pointed out that deBB provides the quantum force explanation of the PEP which Zarqon seeks. And this is something which you cannot get out of the textbook accounts of the PEP.

Funny, I always considered the possibility to express the PEP in terms of a quantum force in deBB as an argument against deBB. Common QM treats bosons and fermions on equal footing. Probability amplitudes leading to indistinguishable bosons/fermions ending up in the same state interfere constructively/destructively. The difference between PEP and - for example - photon bunching is just one sign in the interference term.

In common QM you see the tendency for photons to bunch also getting stronger with the factorial of particles involved. Accordingly also the number of (in principle possible) states not available due to destructive interference increases in the same manner, thus explaining the "quantum force" as a change in the ground state of n indistinguishable fermionic particles as opposed to n independent particles.

In the first round of deBB, photons were not supposed to be particles, so this close analogy does not arise there. Even though more modern approaches to deBB also give rise to the possibility of treating photons as particles, it is still not possible to treat the PEP and its sister effect photon bunching on a similar ground: While attributing the PEP to a quantum force works, assuming a force pushing massless particles around does not make too much sense. You need to treat these cases on unequal footing.

 

[nismaratwork]

How did this turn into a dBB for sale thread?! dBB seems to just keep up with QM, and its best feature is not being annihilated by Bell, and little else. The whole notion of a pilot wave raises issues such as the one GeorgCantor asks in #47. If anything here is ad hoc, it's dBB with pilot waves guiding Schrodinger trajectories.

 

[Count Iblis]

The pilot wave guides PF posters to talk about dBB on QM threads.

 

[DrChinese]

The pilot wave guides PF posters to talk about dBB on QM threads.

Actually, there are a lot of days I feel influenced by a pilot wave. It's what causes that drowning sensation...

 

[zenith8]

So you're just feeling a bit jealous that deBB - unlike SQM - can actually answer this question, and you're all trying to get over your insecurity through the use of weak humor or pretending that deBB has nothing to do with QM. Shrug. Perfectly understandable..

 

[Maaneli]

Does the wavefunction of the deBB live on configuration space or in real space? The 'imaginary' and 'real' parts of the wavefunction you mentioned earlier in the thread would in this case be the ones that tunneled through a classically forbidden barrier and the ones that didn't, right?

It's just the configuration space wavefunction of standard/textbook/orthodox/common QM. Yeah, the wavefunction (equivalently, it's real and imaginay parts) can have non-zero values inside the barrier. And the physical potential that the deBB particle sees not just V, but (V+Q), where Q is the quantum potential.

I'm curious, is there a point you're trying to make? Or just asking questions?

 

[Maaneli]

In the first round of deBB, photons were not supposed to be particles

Actually, one of the first (albeit primitive) pilot-wave theories was developed for photons by Slater in 1926 (or 1923, not sure). And Slater's theory treated photons as point particles.

While attributing the PEP to a quantum force works, assuming a force pushing massless particles around does not make too much sense.

If you're thinking of it from the point of view of classical mechanics and electrodynamics, I agree it does not make sense. But deBB is simply not classical physics. And understood on its own terms, it makes perfect sense.

 

[peteratcam]

Nevertheless: does anybody know about a reference explaining the calculation for the neutron star?

A comprehensive account for electron degeneracy pressure is given in K Huang, Statistical Mechanics, 2nd edition, Sec 11.2, pg 247: The Theory of White Dwarf Stars

I don't think you can calculate the neutron star - it's dense nuclear matter.

A much more readable account is in Chapter 36 of Blundell & Blundell, Concepts in Thermal Physics.
These references just happen to be the books in my office, so there will be plenty of others.

To [STRIKE]answer[/STRIKE] ramble about the force/not a force question again in a different way:
Quantum statistical mechanics tells us that all thermodynamic properties of anything are determined by its partition function:
Z[\beta,V] = {\rm Tr} e^{-\beta \hat H}
Anything which enters as a term in \hat H is either kinetic energy, or something you could call a force.
Things like the PEP are statements about the subspace of states which are Traced over, they are not forces, since they don't enter into the Hamiltonian.
But from the thermodynamic point of view, you can't work backwards from a partition function and decide whether the PEP is a strange type of repulsion, or a restriction on states. A classic example is the elastic band: from a thermodynamic point of view, it certainly produces a force under tension, and you wouldn't think it was so much different from a spring. But microscopically, the force of a spring is a real microscopic force* while the elastic band's force is all down to entropy, a feature of the space of states allowed to it. These entropic forces are fascinating and confusing, and I think there might be justification in calling the PEP repulsion an entropic force, but on a microscopic level you would never call PEP a force.

*I don't want to think about whether elastic solids deeply rely on the PEP to not fall apart.

 

[GeorgCantor]

It's just the configuration space wavefunction of standard/textbook/orthodox/common QM. Yeah, the wavefunction (equivalently, it's real and imaginay parts) can have non-zero values inside the barrier. And the physical potential that the deBB particle sees not just V, but (V+Q), where Q is the quantum potential.

So the 'real' particle is not really 'real' in the strictest sense during quantum tunneling and the deBB theory is only a classical-like theory at best. Then how do you determine which states are imaginary or real(if i understand correctly, the PEP is considered a repulsive force only in the case with the real parts of the wavefunction, whereas the the ones with a negligible potential are not subject to the PEP). And how do the real parts of the wavefunction traverse classically forbidden barriers? Or are they not 'real' until they have tunnelled?

DeBB proponents insist that there is a 'picture' behind this theory(as Einstein famously liked to say), so in principle it shouldn't involve adhoc, cooked up notions.

 

[tom.stoer]

Quantum statistical mechanics tells us that all thermodynamic properties of anything are determined by its partition function:

...

Things like the PEP are statements about the subspace of states which are Traced over, they are not forces, since they don't enter into the Hamiltonian.

That's exactly my point of view.

K Huang, Statistical Mechanics, 2nd edition, Sec 11.2, pg 247: The Theory of White Dwarf Stars

I nearly forgot that I have it here :-)

 

[Maaneli]

So the 'real' particle is not really 'real' in the strictest sense during quantum tunneling

Huh? How did you leap to concluding that the particle is not really 'real'? I don't follow the logic.

Then how do you determine which states are imaginary or real(if i understand correctly, the PEP is considered a repulsive force only in the case with the real parts of the wavefunction, whereas the the ones with a negligible potential are not subject to the PEP).

It sounds like you're just confused about the polar decomposition of the Schroedinger equation, not necessarily the deBB theory itself.

When you separate the imaginary parts of the SE, you just get the usual quantum continuity equation with the current velocity given by grad S/m, and the probability density given by R^2. This is a real-valued equation. When you separate the real parts of the SE, you just get a modified Hamilton-Jacobi equation with the quantum potential defined in terms of R, and the kinetic energy defined in terms of grad S. This is also a real-valued equation. The two equations are then coupled via the phase, S, and the amplitude, R.

The PEP is a repulsive quantum force that occurs near the nodes (where the amplitude of the wavefunction is equal to zero) produced by two overlapping, antisymmetric, fermionic wavefunctions with the same spin. For a mathematical description of this, see page 19 of this talk:

http://www.tcm.phy.cam.ac.uk/~mdt26/PWT/lectures/towler_pauli.pdf

And how do the real parts of the wavefunction traverse classically forbidden barriers? Or are they not 'real' until they have tunnelled?

I think it would be best for you to just study a concrete example:

(Should link you to 5.3 - Tunneling through a square barrier)
http://books.google.com/books?id=Bs...&resnum=1&ved=0CBIQ6AEwAA#v=onepage&q&f=false

Also have a look at this:

Bohmian Mechanics with Complex Action: A New Trajectory-Based Formulation of Quantum Mechanics
Authors: Yair Goldfarb, Ilan Degani, David J. Tannor
http://arxiv.org/abs/quant-ph/0604150

 

[Maaneli]

So the 'real' particle is not really 'real' in the strictest sense during quantum tunneling and the deBB theory is only a classical-like theory at best. Then how do you determine which states are imaginary or real(if i understand correctly, the PEP is considered a repulsive force only in the case with the real parts of the wavefunction, whereas the the ones with a negligible potential are not subject to the PEP). And how do the real parts of the wavefunction traverse classically forbidden barriers? Or are they not 'real' until they have tunnelled?

DeBB proponents insist that there is a 'picture' behind this theory(as Einstein famously liked to say), so in principle it shouldn't involve adhoc, cooked up notions.

There's another nice example of tunneling in deBB on pages 26-28 of these lecture slides:

http://www.tcm.phy.cam.ac.uk/~mdt26/PWT/lectures/bohm3.pdf

 

[Cthugha]

Actually, one of the first (albeit primitive) pilot-wave theories was developed for photons by Slater in 1926 (or 1923, not sure). And Slater's theory treated photons as point particles.

I was talking about "the first round of deBB" which certainly does not include stuff like Slater's (which was wrong in several aspects btw.) as this was way before the second B in deBB. ;)
Bohm and Hiley considered fermions to be particles, but bosons as fields. Although there are more modern approaches, the issue of how to treat photons correctly in some pilot-wave-like theory is far from being solved in a satisfying manner.

If you're thinking of it from the point of view of classical mechanics and electrodynamics, I agree it does not make sense. But deBB is simply not classical physics. And understood on its own terms, it makes perfect sense.

You did not get my point. The reversed effect of the PEP for bosons, photon bunching, is easily explained in exactly the same framework as the PEP in orthodox QM. If you insist on explaining the PEP as a quantum force in a pilot-wave theory, you should either be equally able to describe photon bunching (or maybe start with the easier case of Hong-Ou-Mandel interference) as the effect of some quantum force also or you should have a very convincing reason why massive fermions and massless photons need to be treated differently in your theory in contrast to orthodox QM.

Maybe one of these points applies, but I am aware of neither.