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 nonstandard 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.

We provide a systematic and self-contained exposition of the subject of localized qubits in curved spacetimes. This research was motivated by a simple experimental question: if we move a spatially localized qubit, initially in a state |\psi_1>, along some spacetime path \Gamma from a spacetime point x_1 to another point x_2, what will the final quantum state |\psi_2> be at point x_2? This paper addresses this question for two physical realizations of the qubit: spin of a massive fermion and polarization of a photon. Our starting point is the Dirac and Maxwell equations that describe respectively the one-particle states of localized massive fermions and photons. In the WKB limit we show how one can isolate a two-dimensional quantum state which evolves unitarily along \Gamma. The quantum states for these two realizations are represented by a left-handed 2-spinor in the case of massive fermions and a four-component complex polarization vector in the case of photons. In addition we show how to obtain from this WKB approach a fully general relativistic description of gravitationally induced phases. We use this formalism to describe the gravitational shift in the COW 1975 experiment. In the non-relativistic weak field limit our result reduces to the standard formula in the original paper. We provide a concrete physical model for a Stern-Gerlach measurement of spin and obtain a unique spin operator which can be determined given the orientation and velocity of the Stern-Gerlach device and velocity of the massive fermion. Finally, we consider multipartite states and generalize the formalism to incorporate basic elements from quantum information theory such as quantum entanglement, quantum teleportation, and identical particles. The resulting formalism provides a basis for exploring precision quantum measurements of the gravitational field using techniques from quantum information theory.Comment: 53 pages, 7 figures; v2: published version with further corrections. v3: some references and equation typesetting fixe

In this work we develop a formalism for describing localised quanta for a real-valued Klein-Gordon field in a one-dimensional box [0, R]. We quantise the field using non-stationary local modes which, at some arbitrarily chosen initial time, are completely localised within the left or the right side of the box. In this concrete set-up we directly face the problems inherent to a notion of local field excitations, usually thought of as elementary particles. Specifically, by computing the Bogoliubov coefficients relating local and standard (global) quantizations, we show that the local quantisation yields a Fock space F L which is unitarily inequivalent to the standard one F G . In spite of this, we find that the local creators and annihilators remain well defined in the global Fock space F G , and so do the local number operators associated to the left and right partitions of the box. We end up with a useful mathematical toolbox to analyse and characterise local features of quantum states in F G . Specifically, an analysis of the global vacuum state |0 G ∈ F G in terms of local number operators shows, as expected, the existence of entanglement between the left and right regions of the box. The local vacuum |0 L ∈ F L , on the contrary, has a very different character. It is neither cyclic nor separating and displays no entanglement. Further analysis shows that the global vacuum also exhibits a distribution of local excitations reminiscent, in some respects, of a thermal bath. We discuss how the mathematical tools developed herein may open new ways for the analysis of fundamental problems in local quantum field theory.

We present a way to construct a pilot-wave model for quantum electrodynamics. The idea is to introduce beables corresponding only to the bosonic degrees of freedom and not to the fermionic degrees of freedom of the quantum state. We show that this is sufficient to reproduce the quantum predictions. The beables will be field beables corresponding to the electromagnetic field and they will be introduced in a similar way to that of Bohm's model for the free electromagnetic field. Our approach is analogous to the situation in non-relativistic quantum theory, where Bell treated spin not as a beable but only as a property of the wavefunction. After presenting this model we also discuss a simple way for introducing additional beables that represent the fermionic degrees of freedom.Comment: LaTex, 17 pages, no figures; v2 minor corrections, journal versio