Editing De Broglie–Bohm theory (section)

=== Exploiting nonlocality ===
{{Main|Quantum non-equilibrium}}
[[File:Quantum Theory is a special case of a wider physics.svg|thumb|286x286px|right|Diagram made by [[Antony Valentini]] in a lecture about the De Broglie–Bohm theory. Valentini argues quantum theory is a special equilibrium case of a wider physics and that it may be possible to observe and exploit [[quantum non-equilibrium]]<ref>{{cite web|last1=Valentini|first1=Antony|title=Hidden Variables in Modern Cosmology|url=https://www.youtube.com/watch?v=XYZV9crCZM8| archive-url=https://ghostarchive.org/varchive/youtube/20211211/XYZV9crCZM8| archive-date=2021-12-11 | url-status=live|via=YouTube|publisher=Philosophy of Cosmology|access-date=23 December 2016|date=2013}}{{cbignore}}</ref>]]
[[Louis de Broglie|De Broglie]] and Bohm's causal interpretation of quantum mechanics was later extended by Bohm, Vigier, Hiley, Valentini and others to include stochastic properties. Bohm and other physicists, including Valentini, view the Born rule linking <math>R</math> to the [[probability density function]] <math>\rho = R^2</math> as representing not a basic law, but a result of a system having reached ''quantum equilibrium'' during the course of the time development under the [[Schrödinger equation]]. It can be shown that, once an equilibrium has been reached, the system remains in such equilibrium over the course of its further evolution: this follows from the [[Continuity equation#Quantum mechanics|continuity equation]] associated with the Schrödinger evolution of <math>\psi</math>.<ref>See for ex. Detlef Dürr, Sheldon Goldstein, Nino Zanghí: ''Bohmian mechanics and quantum equilibrium'', Stochastic Processes, Physics and Geometry II. World Scientific, 1995 [http://www.ge.infn.it/~zanghi/BMQE.pdf#page=5 page 5]</ref> It is less straightforward to demonstrate whether and how such an equilibrium is reached in the first place.

[[Antony Valentini]]<ref>{{cite journal | last1 = Valentini | first1 = A | year = 1991 | title = Signal-Locality, Uncertainty and the Subquantum H-Theorem. II | journal = Physics Letters A | volume = 158 | issue = 1–2| pages = 1–8 | doi=10.1016/0375-9601(91)90330-b|bibcode = 1991PhLA..158....1V }}</ref> has extended de Broglie–Bohm theory to include signal nonlocality that would allow entanglement to be used as a stand-alone communication channel without a secondary classical "key" signal to "unlock" the message encoded in the entanglement. This violates orthodox quantum theory but has the virtue of making the parallel universes of the [[chaotic inflation theory]] observable in principle.

Unlike de Broglie–Bohm theory, Valentini's theory the wavefunction evolution also depends on the ontological variables. This introduces an instability, a feedback loop that pushes the hidden variables out of "sub-quantal heat death". The resulting theory becomes nonlinear and non-unitary. Valentini argues that the laws of quantum mechanics are [[Emergence|emergent]] and form a "quantum equilibrium" that is analogous to thermal equilibrium in classical dynamics, such that other "[[quantum non-equilibrium]]" distributions may in principle be observed and exploited, for which the statistical predictions of quantum theory are violated. It is controversially argued that quantum theory is merely a special case of a much wider nonlinear physics, a physics in which non-local ([[Faster-than-light|superluminal]]) signalling is possible, and in which the uncertainty principle can be violated.<ref name="Valentini2009">{{cite journal|last1=Valentini|first1=Antony|title=Beyond the quantum|journal=Physics World|volume=22|issue=11|year=2009|pages=32–37|issn=0953-8585|doi=10.1088/2058-7058/22/11/36|arxiv=1001.2758|bibcode=2009PhyW...22k..32V|s2cid=86861670}}</ref><ref>{{cite web|last1=Musser|first1=George|title=Cosmological Data Hint at a Level of Physics Underlying Quantum Mechanics|url=https://blogs.scientificamerican.com/critical-opalescence/cosmological-data-hint-at-a-level-of-physics-underlying-quantum-mechanics-guest-post/|website=blogs.scientificamerican.com|publisher=Scientific American|access-date=5 December 2016|date=18 November 2013}}</ref>