Antony Valentini

Dynamical origin of quantum probabilities

We study the origin of the Born probability rule ρ = |ψ|2 in the de Broglie–Bohm pilot–wave formulation of quantum theory. It is argued that quantum probabilities arise dynamically, and have a status similar to thermal probabilities in ordinary statistical mechanics. This is illustrated by numerical simulations for a two–dimensional system. We show that a simple initial ensemble, with a non–standard distribution ρ ≠ |ψ|2 of particle positions, evolves towards the quantum distribution to high accuracy. The relaxation process ρ→|ψ|2 is quantified in terms of a coarse–grained H–function (equal to minus the relative entropy of ρ with respect to |ψ|2), which is found to decrease approximately exponentially over time, with a time constant that accords with a simple theoretical estimate.

Subquantum information and computation

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).

Beyond the Quantum

At the 1927 Solvay conference, three different theories of quantum mechanics were presented; however, the physicists present failed to reach a consensus. Today, many fundamental questions about quantum physics remain unanswered. One of the theories presented at the conference was Louis de Broglies pilot-wave dynamics. This work was subsequently neglected in historical accounts; however, recent studies of de Broglies original idea have rediscovered a powerful and original theory. In de Broglies theory, quantum theory emerges as a special subset of a wider physics, which allows non-local signals and violation of the uncertainty principle. Experimental evidence for this new physics might be found in the cosmological-microwave-background anisotropies and with the detection of relic particles with exotic new properties predicted by the theory.

On Galilean and Lorentz invariance in pilot-wave dynamics

Abstract It is argued that the natural kinematics of the pilot-wave theory is Aristotelian. Despite appearances, Galilean invariance is not a fundamental symmetry of the low-energy theory. Instead, it is a fictitious symmetry that has been artificially imposed. It is concluded that the search for a Lorentz-invariant extension is physically misguided.

Time scales for dynamical relaxation to the Born rule

We illustrate through explicit numerical calculations how the Born rule probability densities of non-relativistic quantum mechanics emerge naturally from the particle dynamics of de Broglie–Bohm pilot-wave theory. The time evolution of a particle distribution initially not equal to the absolute square of the wave function is calculated for a particle in a two-dimensional infinite potential square well. Under the de Broglie–Bohm ontology, the box contains an objectively existing ‘pilot wave’ which guides the electron trajectory, and this is represented mathematically by a Schrödinger wave function composed of a finite out-of-phase superposition of M energy eigenstates (with M ranging from 4 to 64). The electron density distributions are found to evolve naturally into the Born rule ones and stay there; in analogy with the classical case this represents a decay to ‘quantum equilibrium’. The proximity to equilibrium is characterized by the coarse-grained subquantum H-function which is found to decrease roughly exponentially towards zero over the course of time. The time scale τ for this relaxation is calculated for various values of M and the coarse-graining length ϵ. Its dependence on M is found to disagree with an earlier theoretical prediction. A power law, τ∝M−1, is found to be fairly robust for all coarse-graining lengths and, although a weak dependence of τ on ϵ is observed, it does not appear to follow any straightforward scaling. A theoretical analysis is presented to explain these results. This improvement in our understanding of time scales for relaxation to quantum equilibrium is likely to be of use in the development of models of relaxation in the early Universe, with a view to constraining possible violations of the Born rule in inflationary cosmology.

Astrophysical and cosmological tests of quantum theory

We discuss several proposals for astrophysical and cosmological tests of quantum theory. The tests are motivated by deterministic hidden-variables theories, and in particular by the view that quantum physics is merely an effective theory of an equilibrium state. The proposed tests involve searching for nonequilibrium violations of quantum theory in: primordial inflaton fluctuations imprinted on the cosmic microwave background, relic cosmological particles, Hawking radiation, photons with entangled partners inside black holes, neutrino oscillations and particles from very distant sources.

Pilot-Wave Theory of Fields, Gravitation and Cosmology

Our universe is characterised by: (i) The absence of practical instantaneous signals (signal-locality), and (ii) An all-pervading statistical ‘noise’ (uncertainty principle). Now, as Bell deduced, there is a fundamental nonlocality hidden behind quantum statistics. Relativity is not overtly violated, however. There seems to be a ‘conspiracy’ between relativity and quantum theory, whereby uncertainty noise prevents one from using subquantum nonlocality for practical signalling. Why should the nonlocality be hidden in this way? A physics whose coherence rests on such a peculiar conspiracy can hardly be regarded as fundamental.

Hidden Variables, Statistical Mechanics and the Early Universe

One of the central mysteries of quantum theory is that it seems to be fundamentally nonlocal—and yet the nonlocality cannot be used for practical signalling at a distance. The consistency of modern physics seems to depend on a ‘conspiracy’, in which nonlocality is hidden by quantum equilibrium noise. It is as if there is an underlying nonlocality which we are unable to control because of the statistical character of quantum events. I explore the possibility of quantum nonequilibrium for Hidden Variables Theories like the pilot-wave theory of de Broglie and Bohm in the context of nonlocality.

de Broglie–Bohm guidance equations for arbitrary Hamiltonians

In a pilot-wave theory, an individual closed system is described by a wavefunction ψ(q) and configuration q. The evolution of the wavefunction and configuration are respectively determined by the Schrodinger and guidance equations. The guidance equation states that the velocity field for the configuration is given by the quantum current divided by the density |ψ(q)|2. We present the currents and associated guidance equations for any Hamiltonian given by a differential operator. These are derived directly from the Schrodinger equation, and also as Noether currents arising from a global phase symmetry associated with the wavefunction in configuration space.

Non-local correlations in quantum electrodynamics

Abstract It is shown that a pair of initially uncorrelated bare atoms, separated by a distance R, develop non-local statistical correlations in a time t