I believe that if we accept the fact that the WQPD [Wigner QuasiProbabilityDistribution] is in fact a regular probability distribution (so there is nothing "quasi" about it) despite not being globally non-negative, Bell's analysis falls apart (probabilities are not non-negative & measurements at distant points of entangled [correlated] particles are not independent) and we can reduce the results of the Aspect, &c., experiments to mere correlation, Bertlmann's socks. For instance, if the wave function is d(x2-x1) (d = Dirac Delta Function), the wave function of the original 1935 EPR thought experiment, the WQPD is d(x2-x1)d(p1+p2), which cannot be reduced to form p(x1,p1)p(x2,p2)--i.e., there is correlation/Bertlmann's socks). Naturally, one has to use the 2-particle WQPD. I believe that a similar circumstance would occur if one calculated the WQPD for spin/position as well as momentum/position. Whaddya think? As for negative probabilities: we simply have to redefine a "probability" as a tool for calculating mean values rather than the classical definition (# times something happened/# runs of experiment). Stuart Boehmer
As an aside, in quantum optics it is possible to construct alternatives to the Wigner distribution that are explicitly always positive (the Q- or Husimi distribution; or the positive-P distribution). The positive-P uses a phase space doubled in size, but in fact is able to have a direct (and not controversial or speculative) interpretation as a probablility distribution.
However, these are constructed for bosons, and rely on a basis of coherent states, so are not obviously relevant to socks :-)
Hi everyone!
The problem of wave function collapse is a mystery in the “wave function is fundamental” formulation but is a snap in the “Wigner Probability Distribution is fundamental” formulation.
If you make a measurement, this updates your state of knowledge & the probability P(p,q) changes instantly.
For instance, if initially P(p,q) = P’(p,q) & you measure p = p’ +/-dp at location q +/-dq (where in general dpdq > h, say, D) then P changes to 1/D*Hdp(p – p’)Hdq(q-q’) where Hdx(x) is the Heaviside function = 0 if x^2 > dx^2 and = 1 otherwise.
On this basis I have been claiming that QM is fully materialistic and P(p,q) is simply a matter of the state of knowledge of the observer/experimenter just as in classical statistical thermodynamics.
However, it is at least mildly disturbing that the laws of physics are couched in terms of the state of knowledge, P(p,q), and not in terms of the state of the world (p,q). I therefore now conclude that QM isn’t materialistic at all; rather, it is IDEALISTIC in the radical sense of Berkeley et al.—there is no underlying material reality, it’s all in the mind. In the words of Einstein…the world is merely an illusion albeit a very persistent one.
Reality is entirely subjective and the Post-Modernists are right: you’re free to come to any conclusion you like regarding what the “truth” is. In the words of Pontius Pilate…what IS truth?
This is a radical, disturbing and counterintuitive conclusion (perhaps it is not too original an interpretation of QM, but the significance of it really hits me in the eye now: it is new to me if no one else).
Namaste 🙏
Stuart Boehmer
Has anyone noticed that QM indistinguishable particles are just entangled distinguishable particles?
In that case, if I’m right that entanglement = correlation (I am 😊 ), we could study classical indistinguishable particles as a special case of correlation between them. We also could study classical EPR & Bell experiments & settle the matter (of whether entanglement = Bertlmann’s socks/correlation) once and for all……………
Namaste
Stuart Boehmer
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