Antony Valentini has argued that the Born-Feynman probability rule (i.e, to take the modulus square of complex number path amplitudes ~ exp[i(classical action)/hbar] and to add the amplitudes coherently before squaring when the outcomes cannot be distinguished, but to square first before adding when they can, is not a fundamental law of nature, but is an accident corresponding to what he calls "sub-quantum equilibrium." What I am calling "Post-Quantum Mechanics" (PQM) corresponds to Valentini's "sub-quantum non-equilibrium" in which what he calls entanglement "nonlocal signaling" happens.
Subquantum Information and Computation
Antony Valentini
"It is argued that immense physical resources - for nonlocal communication, espionage, and exponentially-fast computation - are hidden from us by quantum noise, and that this noise is not fundamental but merely a property of an equilibrium state in which the universe happens to be at the present time. It is suggested that 'non-quantum' or nonequilibrium matter might exist today in the form of relic particles from the early universe. We describe how such matter could be detected and put to practical use. Nonequilibrium matter could be used to send instantaneous signals, to violate the uncertainty principle, to distinguish non-orthogonal quantum states without disturbing them, to eavesdrop on quantum key distribution, and to outpace quantum computation (solving NP-complete problems in polynomial time)"
https://arxiv.org/abs/quant-ph/0203049
Valentini wrote the above in 2002 before Huw Price, Ken Wharton, Rod Sutherland convincingly explained, in my opinion, that spacelike nonlocality is not a good way to think of quantum entanglement. The alternative "Costa de Beauregard zig-zag" used implicitly at least by Yakir Aharonov and John Cramer in their respective interpretations of quantum theory, is preferable because it is consistent with the symmetries of Einstein's classical theories of relativity if we allow "weak measurement" future causes of present effects as well as the usual past causes of present effects of orthodox von-Neumann "strong measurement" interpretations. Indeed, the observed violation of Bell's inequality can be most simply and elegantly understood as the effects of future causes (strong measurements) of past effects (at the moment of emission of a pair). From this point of view it is obvious why the space-time separations between strong measurements of the localized parts of the entangled whole do not matter. Those separations can be spacelike, timelike or lightlike even in curved classical spacetime where one can try to connect them with corresponding geodesics. Huw Price has also pointed out that John Bell was confused on the difference between "super-determinism" and "local retrocausality." This confusion caused him to erroneously think that local retro-causality conflicted with "free will." All of this presupposes that we live in a "block universe" one physicist in particular thinks that this means there is no dynamics. This not the place to argue this, although, I mention it in passing, since it was discussed in this workshop. Suffice it to say, that the Lagrangian form of dynamics only makes sense in the block universe picture in which we take the global 4D spacetime view. The "dynamical" view is that of the Hamiltonian formulation (3D + 1). One beautiful result of Sutherland's fully relativistic Lagrangian for Bohm's pilot-wave particle theory is that because of the Costa de Beauregard "zig-zag" and the use of Yakir Aharonov's advanced "destiny" and retarded "history" waves in the "weak measurements" of the particle motions between strong measurements, is that we no longer need higher-dimensional configuration space in the description of many-particle entanglement. Indeed, Sutherland has applied this notion to the problem of quantum gravity.
From the structure of Sutherland's Lagrangian, which has classical particle parts independent of h as well as quantum parts dependent on h, it became clear to me that Valentini need not use the word "sub-quantum." The "beables" are not at some hidden level at all. They are at the classical physics level. Furthermore, Valentini thinks that "non-equilibrium matter" is only found around the time of the Big Bang. On the contrary, I propose that all living matter is "non-equilibrium matter" in the sense of locally-decodable key-less entanglement signaling that is strictly forbidden in the limit of orthodox quantum theory. Indeed, I propose that Sutherland's weak measurement action-reaction piece of his Lagrangian corresponds to what Valentini called "sub-quantum non-equilibrium." Furthermore, when one reads Roger Penrose's books, e.g. Emperor's New Mind, Shadows of the Mind, Fashion, Faith and Fantasy etc. one sees mention of the possible importance of Herbert Frohlich's macro-quantum coherence in pumped open non-equilibrium dissipative structures. This leads me to further conjecture that any such open macro-quantum coherent pilot wave, but classically thermodynamically non-equilibrium system will be post-quantum with Sutherland's action-reaction not equal to zero. Indeed, I conjecture that the PQM action-reaction term will be proportional to the amount of external pump stress-energy current densities above Frohlich's critical threshold. The mathematical model here is formally similar to that of a coherent laser beam above threshold rather than in the thermodynamic equilibrium of a conventional Bose-Einstein condensate. Now it turns out that Sutherland's PQM action-reaction is proportional to a factor, which when set equal to zero in the limiting case PQM 竊' QM is exactly de Broglie's guidance equation that the particle world lines coincide with pilot wave "fluid" stream lines (gradients of the phase of the pilot waves). This explains why, in a beautiful way, we can dispense with the particles entirely in the orthodox quantum limit and pretend they are not there. Of course, doing that leads to bending over backwards with contortions like "wave function collapse", "problem of the classical limit" etc. - all non-problems in the Bohmian 1952 picture not to be confused with his later less intuitive "implicate/explicate order" speculations. I have no need of that hypothesis here. Finally, it needs to be pointed out that the basic Sutherland Lagrangian theory is non-statistical "God does not play dice" (Einstein) it is nonlinear and non-unitary. The statistical linear unitary QM limit comes from doing several things:
1) setting the wave action-particle reaction term to zero
2) integrating over the future destiny causes of past effects with the ad_hoc Born rule weighting factor ||^2.
As an example the Aharonov weak measurements at x are of the form for a local operator J
< J(x)>w = J/
Therefore, the integral over all possible = J
And it appears as if time only flows one-way from past to future in accord with the Arrow of Time of the Second Law of Thermodynamics as in Henry Stapp's talk at this conference for example.
