Pauli exclusion principle: a Force or not?

[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.