Cthugha said:
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.
Cthugha said:
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.
Cthugha said:
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..
Cthugha said:
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.
Cthugha said:
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.