Introduction: space–time and the wave function

Vitaly Kuyukov

Wave function the space-time

Vitaly Kuyukov

Space-time and universal wave function

Eliade N. Stefanescu

We consider the two basic theories of the standard physics: (1) the theory of relativity, as a four-dimensional time-space description of our universe, with the invariance of the time-space interval which leads to the Lorentz transformation, and (2) quantum mechanics, based on the Schrödinger equation, with a solution called wave function. However, we find that this equation is very unsatisfactory, describing fully unlocalized free particles, any initially localized particle rapidly spreading in space, in disagreement with the fundamental Hamilton equations. In agreement with the Hamilton equations, we describe a quantum particle by propagation wave functions in the coordinate and momentum spaces, with the Lagrangian in the time dependent phase instead of the Hamiltonian coming from the Schrödinger equation. With the relativistic Lagrangian, we obtain wave functions describing invariant distributions propagating in space.

Detlef Dürr, Sheldon Goldstein, Travis Norsen +2 more

In relativistic space-time, Bohmian theories can be formulated by introducing a privileged foliation of space-time. The introduction of such a foliation-as extra absolute space-time structure-would seem to imply a clear violation of Lorentz invariance, and thus a conflict with fundamental relativity. Here, we consider the possibility that, instead of positing it as extra structure, the required foliation could be covariantly determined by the wave function. We argue that this allows for the formulation of Bohmian theories that seem to qualify as fundamentally Lorentz invariant. We conclude with some discussion of whether or not they might also qualify as fundamentally relativistic.

Alexander Macfarlane

Alyssa Ney, David Z. Albert

This is a new volume of original essays on the metaphysics of quantum mechanics. The essays address questions such as: What fundamental metaphysics is best motivated by quantum mechanics? What is the ontological status of the wave function? Does quantum mechanics support the existence of any other fundamental entities, e.g. particles? What is the nature of the fundamental space (or space-time manifold) of quantum mechanics? What is the relationship between the fundamental ontology of quantum mechanics and ordinary, macroscopic objects like tables, chairs, and persons? This collection includes a comprehensive introduction with a history of quantum mechanics and the debate over its metaphysical interpretation focusing especially on the main realist alternatives.