Quantum non-equilibrium

Rather, in this theory the link between the probability density and the wave function has the status of a hypothesis, called the quantum equilibrium hypothesis, which is additional to the basic principles governing the wave function, the dynamics of the quantum particles and the Schrödinger equation.

Accordingly, quantum non-equilibrium describes a state of affairs where the Born rule is not fulfilled; that is, the probability to find the particle in the differential volume

Recent advances in investigations into properties of quantum non-equilibrium states have been performed mainly by theoretical physicist Antony Valentini, and earlier steps in this direction were undertaken by David Bohm, Jean-Pierre Vigier, Basil Hiley and Peter R. Holland.

The relevance of quantum non-equilibrium states to physics lies in the fact that they can lead to different predictions for results of experiments, depending on whether the De Broglie–Bohm theory in its stochastic form or the Copenhagen interpretation is assumed to describe reality.

(The Copenhagen interpretation, which stipulates the Born rule a priori, does not foresee the existence of quantum non-equilibrium states at all.)

That is, properties of quantum non-equilibrium can make certain classes of Bohmian theories falsifiable according to the criterion of Karl Popper.

In practice, when performing Bohmian mechanics computations in quantum chemistry, the quantum equilibrium hypothesis is simply considered to be fulfilled, in order to predict system behaviour and the outcome of measurements.

The causal interpretation of quantum mechanics has been set up by de Broglie and Bohm as a causal, deterministic model, and it was extended later by Bohm, Vigier, Hiley, Valentini and others to include stochastic properties.

Bohm and other physicists, including Valentini, view the Born rule linking

as representing not a basic law, but rather as constituting a result of a system having reached quantum equilibrium during the course of the time development under the Schrödinger equation.

In 1991, Valentini provided indications for deriving the quantum equilibrium hypothesis which states that

[5] Numerical simulations demonstrate a tendency for Born rule distributions to arise spontaneously at short time scales.

[6] Valentini showed that his expansion of the De Broglie–Bohm theory would allow “signal nonlocality” for non-equilibrium cases in which

Valentini furthermore showed that an ensemble of particles with known wave function and known nonequilibrium distribution could be used to perform, on another system, measurements that violate the uncertainty principle.

As it is unknown whether or how quantum non-equilibrium states can be produced, it is difficult or impossible to perform such experiments.