Pauli exclusion principle: a Force or not?

[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.

 

[Zarqon]

Even though the dBB talk is slightly offtopic at times, I've still found it interesting overall to see a different kind of explanation. The main problem with dBB here is that it doesn't only give an interpretation on this particular issue but also comes with a baggage of giving an interpretation of everything else in QM, which I may not agree with (for example I'm still undecided on the determinism vs. true randomness).With regards to the standard explanation given here, by e.g. peteratcam and tom.stoer, I appreciate your answers, and I do get the point your trying to make about how it comes in in a different way, i.e. as the selection of what states to include.
However, for some reason I just have a problem to fully think of this as the solution.

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.

Perhaps this is why I have a problem. Being an experimentalist I'm used to thinking from the point of view of what I can see in the lab and what happens in "reality". When you say that it can't be backtracked, it feels to me like the "solution" is just some constructed formalism. What you see in neutorn stars/white dwarves is really something that looks like a force/potential curve (becuase it really plays on equal footing with gravity), and it then feels very dissatisfying say that the reason it's not a force is because of the particular structure of our invented formalism.

Note for clarity: I am of course aware of the success of the QM formalism, but that still doesn't mean that there isn't a more intuitive way of thinking about certain things.

 

[nismaratwork]

The success of formalism is everything, the utility of it is everything, just ask Dirac. :) Why not stick withe the formalism that produces results, knowing that we are approximating nature, than fooling yourself with the notion that slapping classical elements into the mix somehow makes it a completely descriptive theory? Silly.

 

[Maaneli]

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.

Well you're being a little sneaky by slipping in the word 'satisfying' as if there is some objective criterion for it. In any case, for all practical purposes, you are wrong. The Struyve Westman pilot-wave model of QED works just find in reproducing the standard QED predictions, by introducing beables only for the quantized EM field:

A minimalist pilot-wave model for quantum electrodynamics
W. Struyve and H. Westman
Journal-ref. Proc. R. Soc. A 463, 3115-3129 (2007)
>> We present a way to construct a pilot-wave model for quantum electrodynamics. The idea is to introduce beables corresponding only to the bosonic degrees of freedom and not to the fermionic degrees of freedom of the quantum state. We show that this is sufficient to reproduce the quantum predictions. The beables will be field beables corresponding to the electromagnetic field and they will be introduced in a similar way to that of Bohm's model for the free electromagnetic field. Our approach is analogous to the situation in non-relativistic quantum theory, where Bell treated spin not as a beable but only as a property of the wavefunction. After presenting this model we also discuss a simple way for introducing additional beables that represent the fermionic degrees of freedom. <<
http://eprintweb.org/S/article/arxiv/0707.3487

You did not get my point.

You were making a couple of different points, and I responded to the one that was the most obviously misguided.

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.

For all practical purposes, there is no problem for, say, the minimalist pilot-wave theory of Struyve and Westman for modeling photon bunching in terms of a quantum force. And you need to be more specific about what you think would count as 'convincing reasons' and why you don't think empirical equivalence is enough for you to concede that pilot-wave QFT models work adequately in describing the PEP for both fermions and bosons.

 

[Maaneli]

Even though the dBB talk is slightly offtopic at times, I've still found it interesting overall to see a different kind of explanation. The main problem with dBB here is that it doesn't only give an interpretation on this particular issue but also comes with a baggage of giving an interpretation of everything else in QM, which I may not agree with (for example I'm still undecided on the determinism vs. true randomness).

Thanks for your comments. I would only like to emphasize that interpretation is ultimately unavoidable in any mathematical formulation of QM, especially when you ask the question of what happens during a measurement. Also, the deBB theory need not be fundamentally deterministic. There are stochastic variants as well.

 

[Cthugha]

Well you're being a little sneaky by slipping in the word 'satisfying' as if there is some objective criterion for it. In any case, for all practical purposes, you are wrong. The Struyve Westman pilot-wave model of QED works just find in reproducing the standard QED predictions, by introducing beables only for the quantized EM field:
[...]
For all practical purposes, there is no problem for, say, the minimalist pilot-wave theory of Struyve and Westman for modeling photon bunching in terms of a quantum force. And you need to be more specific about what you think would count as 'convincing reasons' and why you don't think empirical equivalence is enough for you to concede that pilot-wave QFT models work adequately in describing the PEP for both fermions and bosons.

Oh, it seems that I did not make myself clear. I do not doubt the validity of pilot-wave approaches or that it is possible to model these effects in a pilot-wave framework. We are discussing empirically equivalent interpretations of QM, so all it boils down to a questions of style, elegance and clarity. And just as the relatively many people around here advocating pilot-wave theories by mentioning points where they think pilot-wave theories are more clear, stylish and elegant - like the exclusion principle in this thread - I think it should also be mentioned that there are a lot of cases where orthodox QM is more clear. As I am doing experimental optics ( with - as you might have guessed - a special interest in photon bunching) I consider the close connection between photon bunching and the PEP which can be very nicely seen in the framework of probability amplitudes as used in the quantum optical theory of coherence developed by Glauber as best described in orthodox QM. All that changes in switching from bosons to fermions is one sign in an interference term and you are able to treat the basic effects leading to phenomena as different as the exclusion principle (degeneracy pressure), photon bunching and BEC on equal footing and using exactly the same math (besides that one changing sign) in terms of interfering probability amplitudes, regardless of details like mass. All you need to know is whether particles are indistinguishable or not, whether they are bosons or fermions and in case of bosons you maybe need to know whether they are in a thermal, coherent, Fock or whatever state.

If you choose to describe this class of behaviors using a quantum force, you get an additional potential term
$$Q=-\frac{\hbar^2}{2m}\frac{\nabla^2 \sqrt{\rho}}{\rho}$$
and the quantum force
$$-\nabla Q$$
or something like that. You will have to cope with the mass term and modify more than just one sign to account for differences between massive and massless particles. You will also need to change more than just one sign to distinguish between thermal states and coherent states. Maybe you need also to change more than one sign to distinguish between fermions and bosons - I do not know. Generally, in the realm of optics pilot-wave approaches often seem somewhat constructed and unnecessarily complicated. Not wrong, but as I said before, not as satisfying or clear as orthodox QM.

So going full circle and getting fully back to the topic and the initial question, loosely speaking you can compare the situation of how orthodox QM handles the exclusion principle in a similar manner as thermodynamics treats absolute zero. Strictly speaking orthodox QM does not really forbid that several indistinguishable fermions ARE in the same state. However, all probability amplitudes leading to this state vanish, so for indistinguishable fermions it is forbidden to GET to the same state. This is similar to classical thermodynamics where it is in principle not forbidden for a system to BE at absolute zero, but to REACH absolute zero.

This treatment is at fist sight counterintuitive as commonly one is used to treat many particle systems like a neutron star by setting up forces and finding out the equilibrium position instead of applying destructive interference of probability amplitudes. However, there are in fact not that many situations where you have lots of indistinguishable fermions inside such a small volume that these effects become important so one should not be too puzzled by this situation.

To summarize, the ordinary QM approach and the pilot-wave approach both seem strange under certain circumstances. The orthodox approach uses probability amplitudes for indistinguishable particles which is well-known and established when dealing with bosons and waves like in the double slit experiment or in optics, but looks somehow weird (but nevertheless correct) when you try to apply it to indistinguishable fermions because there are not that many fermionic systems which require this treatment. The pilot-wave approach defines a quantum-force acting on particles which seems somehow natural and familiar when applied to fermionic systems like a neutron star, but looks somehow weirs (but nevertheless correct) when you try to apply it to massless bosons as you have forces moving massless particles around. Your choice.

 

[Maaneli]

Oh, it seems that I did not make myself clear. I do not doubt the validity of pilot-wave approaches or that it is possible to model these effects in a pilot-wave framework. We are discussing empirically equivalent interpretations of QM, so all it boils down to a questions of style, elegance and clarity.

Thanks for the clarification.

And just as the relatively many people around here advocating pilot-wave theories by mentioning points where they think pilot-wave theories are more clear, stylish and elegant - like the exclusion principle in this thread - I think it should also be mentioned that there are a lot of cases where orthodox QM is more clear. As I am doing experimental optics ( with - as you might have guessed - a special interest in photon bunching) I consider the close connection between photon bunching and the PEP which can be very nicely seen in the framework of probability amplitudes as used in the quantum optical theory of coherence developed by Glauber as best described in orthodox QM.

Well I would disagree regarding clarity, especially since the orthodox QM description of photons still suffers from the measurement problem and the lack of any clear ontology. Also, as I have pointed out earlier, the PEP remains merely a separate axiom of the theory, with no deeper explanation (the spin-statistics theorem is not an explanation). But I would agree that it is probably more mathematically convenient to use the orthodox QM approach for making the kinds of statistical predictions that you care about in your experiments. So for all practical purposes, go ahead and use the orthodox QM approach, unless the pilot-wave approach turns out to have some novel computational advantages.

If you choose to describe this class of behaviors using a quantum force, you get an additional potential term
$$Q=-\frac{\hbar^2}{2m}\frac{\nabla^2 \sqrt{\rho}}{\rho}$$
and the quantum force
$$-\nabla Q$$
or something like that. You will have to cope with the mass term and modify more than just one sign to account for differences between massive and massless particles. You will also need to change more than just one sign to distinguish between thermal states and coherent states. Maybe you need also to change more than one sign to distinguish between fermions and bosons - I do not know. Generally, in the realm of optics pilot-wave approaches often seem somewhat constructed and unnecessarily complicated.

In the Struyve-Westman minimalist pilot-wave model for QED, there is only one wavefunctional encoding the properties of both bosons and fermions. And the quantum potential in this model is constructed out of the amplitude of this wavefunctional. So in this sense, the pilot-wave description of bosons and fermions is elegantly unified.

I'll also mention that for first-quantized photon wavefunctions such as the Riemann-Silberstein wavefunction, the corresponding wave equation is in fact a Schroedinger-like equation which can be polar decomposed into a hydrodynamical Madelung form with a mass-independent quantum potential. See for example page 33, section 10, equations 162-167, of this paper by Iwo Bialynicki-Birula:

Photon wave function, in Progress in Optics, Vol. 36, Ed. E. Wolf, Elsevier, Amsterdam 1996, p.245.
http://www.cft.edu.pl/~birula/publ/photon_wf.pdf

And, not surprisingly, one can easily make a pilot-wave theory of photons out of this Madelung form of the Riemann-Silberstein wavefunction and wave equation. Thus, there also exists an entirely first-quantized pilot-wave theory of photons which can be used in tandem with the usual first-quantized pilot-wave theory of electrons. And for both photons and electrons, there is a quantum potential and quantum force. So there you have another example of how you can treat bosons and fermions on essentially 'equal footing' in a pilot-wave theory.

Also, I think it should be appreciated that the goal of using a pilot-wave version of QED is to give a dynamical model of *individual photons* between measurement events, and not merely a calculus for computing the statistical distribution of photons in some particular ensemble of measurements. The latter is the goal of the orthodox formulation of QED. It should also be noted that the pilot-wave version of QED reproduces the statistical predictions of orthodox QED, and implies all of the mathematics of orthodox QED, whereas the reverse is not true. Interestingly, this relationship between pilot-wave QED and orthodox QED is also quite analogous to the relationship between classical statistical mechanics and classical thermodynamics. The former gives a dynamical description of the individual particles composing and producing the bulk thermodynamic properties (e.g. temperature and pressure) of matter distributions, while the latter only gives a statistical account of the bulk thermodynamic properties of matter distributions. And it is interesting to note that 150 years ago, when atoms were just considered as metaphysical fictions, these objections (about being unnecessarily complicated) that you raise against the pilot-wave theory could have been (and were in fact) used against the statistical mechanics of Bernoulli, Boltzmann, Gibbs, etc..

So going full circle and getting fully back to the topic and the initial question, loosely speaking you can compare the situation of how orthodox QM handles the exclusion principle in a similar manner as thermodynamics treats absolute zero. Strictly speaking orthodox QM does not really forbid that several indistinguishable fermions ARE in the same state. However, all probability amplitudes leading to this state vanish, so for indistinguishable fermions it is forbidden to GET to the same state. This is similar to classical thermodynamics where it is in principle not forbidden for a system to BE at absolute zero, but to REACH absolute zero.

Well from the point of view of pilot-wave QM, it is impossible for several indistinguishable fermions to both *be* and *get* in the same state.

The pilot-wave approach defines a quantum-force acting on particles which seems somehow natural and familiar when applied to fermionic systems like a neutron star, but looks somehow weirs (but nevertheless correct) when you try to apply it to massless bosons as you have forces moving massless particles around. Your choice.

Again though, it only seems intuitively weird if you are thinking about forces and fields from the mind-set of classical mechanics and electrodynamics. But since pilot-wave theory is not classical physics, that should tell you that such a mind-set is not a fair perspective from which to judge the intuitiveness of the pilot-wave theory.

 

[Cthugha]

Well I would disagree regarding clarity, especially since the orthodox QM description of photons still suffers from the measurement problem and the lack of any clear ontology.

Maybe, but these are problems of philosophical and not of physical nature as long as there are no differing predictions to test experimentally. Accordingly I consider most pilot-wave advocates to be philosophers as most of them just recalculate known stuff according to a different interpretation. Maybe with the exception of Valentini who seems to be one of few still remembering what physics is about and making predictions - although they will unfortunately not be testable in the near future.
Before you answer: I know that you will disagree and consider it as physics. I just want to point out that I do not consider calling that topic philosophy a devaluating statement. It is fine discussing philosophy.

Also, as I have pointed out earlier, the PEP remains merely a separate axiom of the theory, with no deeper explanation (the spin-statistics theorem is not an explanation). But I would agree that it is probably more mathematically convenient to use the orthodox QM approach for making the kinds of statistical predictions that you care about in your experiments. So for all practical purposes, go ahead and use the orthodox QM approach, unless the pilot-wave approach turns out to have some novel computational advantages.

Yes, we can discuss this back and forth. But as this is slightly off-topic I would like to cut it short. All discussions about the required number of axioms in pilot-wave and orthodox QM approaches end up with the conclusion that for every axiom you do not need in pilot-wave theories you threw in another one not needed in orthodox QM. Usually you get the same number or "relative weight" of axioms in both.

In the Struyve-Westman minimalist pilot-wave model for QED, there is only one wavefunctional encoding the properties of both bosons and fermions. And the quantum potential in this model is constructed out of the amplitude of this wavefunctional. So in this sense, the pilot-wave description of bosons and fermions is elegantly unified.

Ok, so we have different ideas of what is elegant. That is okay.

Also, I think it should be appreciated that the goal of using a pilot-wave version of QED is to give a dynamical model of *individual photons* between measurement events, and not merely a calculus for computing the statistical distribution of photons in some particular ensemble of measurements.

Yes, I see the intention. I just do not see the necessity. Optics and especially the realm of coherence theory largely rely on collective and field effects in orthodox QM and photons do not show any signs of being particles at all besides quantized interaction. The basic premise is that there are no individual photons inside one coherence volume. In pilot-wave theory, you simply shift the uncertainty of the light field towards a non-accessible knowledge of initial conditions, so in terms of physics you gain very little from having a model for individual photons.

And it is interesting to note that 150 years ago, when atoms were just considered as metaphysical fictions, these objections (about being unnecessarily complicated) that you raise against the pilot-wave theory could have been (and were in fact) used against the statistical mechanics of Bernoulli, Boltzmann, Gibbs, etc..

Statistical mechanics led to new predictions and new physics in the regime away from the thermodynamic limit. I am not saying that they are nonsense, but pilot-wave theories still have to show that they are more than just interpretations if they are supposed to reach significance.

Again though, it only seems intuitively weird if you are thinking about forces and fields from the mind-set of classical mechanics and electrodynamics. But since pilot-wave theory is not classical physics, that should tell you that such a mind-set is not a fair perspective from which to judge the intuitiveness of the pilot-wave theory.

Oh, come on. Saying that pilot-wave theory seems counterintuitive when applied to photons while orthodox QM seems counterintuitive when applied to degeneracy pressure and such stuff was a fair statement. However, I think this discussion leads us too far from the original question. I do not want to hijack this thread. If you want to discuss anything further open a different thread.

 

[Maaneli]

I prefer not to start a new thread, mainly because I sense that we are nearing the end of this exchange. So I'll just make a few final follow up comments and then leave it there, unless you desire to continue discussing some of these issues, in which case, I'll create another thread as you suggest.

Maybe, but these are problems of philosophical and not of physical nature as long as there are no differing predictions to test experimentally. Accordingly I consider most pilot-wave advocates to be philosophers as most of them just recalculate known stuff according to a different interpretation. Maybe with the exception of Valentini who seems to be one of few still remembering what physics is about and making predictions - although they will unfortunately not be testable in the near future.

The measurement problem does actually have practical consequences, particularly for understanding how to define the quantum-classical limit (which is still an unsolved problem in physics, believe it or not). It also has significant consequences for how one develops a model of quantum cosmology, and models the transition of the universal wavefunction from a pure to mixed state.

Actually, Valentini's predictions have a fair chance of being tested with the CMB data being gathered by the current Planck satellite.

Before you answer: I know that you will disagree and consider it as physics. I just want to point out that I do not consider calling that topic philosophy a devaluating statement. It is fine discussing philosophy.

Cool, I respect that.

Yes, we can discuss this back and forth. But as this is slightly off-topic I would like to cut it short. All discussions about the required number of axioms in pilot-wave and orthodox QM approaches end up with the conclusion that for every axiom you do not need in pilot-wave theories you threw in another one not needed in orthodox QM. Usually you get the same number or "relative weight" of axioms in both.

Well let's see: All the required equations of motion of pilot-wave theory are encoded within the Schroedinger equation itself. The only modifications are that (1) the Schroedinger wavefunction is taken to be ontological, and (2) in addition to the Schroedinger wavefunction, there is an ontological configuration of point particles whose dynamics is related to the Schroedinger wavefunction by the guiding equation (equivalently, the current velocity in the usual quantum continuity equation). By contrast, orthodox QM requires in addition to the Schroedinger equation, (1) the Born rule axiom, (2) several axioms about the results of 'measurements', and (3) the PEP axiom. Seems to me like the number of axioms in orthodox QM is considerably greater!

Yes, I see the intention. I just do not see the necessity. Optics and especially the realm of coherence theory largely rely on collective and field effects in orthodox QM and photons do not show any signs of being particles at all besides quantized interaction. The basic premise is that there are no individual photons inside one coherence volume. In pilot-wave theory, you simply shift the uncertainty of the light field towards a non-accessible knowledge of initial conditions, so in terms of physics you gain very little from having a model for individual photons.

The 'necessity' depends on what you care about. If you just want a mathematically convenient way of calculating stuff for your experiments, then, in the case of optics, it's probably not necessary. But if you want a clear and logically self-consistent explanation of the quantum optical happenings between measurement events, then it is quite necessary.

Re your statement "in terms of physics", it sounds like you have a very operationalist and instrumentalist view of physics. But there's certainly nothing a priori that says or requires that the only correct view of physics is an operationalist and instrumentalist one.

Statistical mechanics led to new predictions and new physics in the regime away from the thermodynamic limit. I am not saying that they are nonsense, but pilot-wave theories still have to show that they are more than just interpretations if they are supposed to reach significance.

Ah, but keep in mind that it took over 120 years for the first new prediction (Einstein's Brownian motion) to be proposed and experimentally confirmed! In any case, pilot-wave theories have already shown the capacity to be, in principle, empirically discriminated from orthodox QM. The reason is that pilot-wave theories allow for (and give plausible statistical-mechanics-based reasons for) initial particle (or field) distributions in the early universe to deviate from the Born-rule distribution. And Valentini has already shown that in the context of cosmic inflation, a nonequilibrium initial distribution of fields would in fact lead to measurable inhomogeneities in the CMB spectrum. I am also currently developing extensions of pilot-wave theories to semiclassical gravity, which suggest the possibility of empirical discrimination from standard semiclassical gravity via matter-wave interferometry with macromolecules. So we already know that pilot-wave theories are more than just interpretations. They really are different theories of quantum physics.

Oh, come on. Saying that pilot-wave theory seems counterintuitive when applied to photons while orthodox QM seems counterintuitive when applied to degeneracy pressure and such stuff was a fair statement. However, I think this discussion leads us too far from the original question. I do not want to hijack this thread. If you want to discuss anything further open a different thread.

The issue with degeneracy pressure in orthodox QM is not that it's counterintuitive, but rather that it's introduced in the orthodox QM formalism merely by postulate, and has no causal explanation.