Dirk-André Deckert

Quantum Dynamics with Bohmian Trajectories

We describe the advantages and disadvantages of numerical methods when Bohmian trajectory grids are used for numerical simulations of quantum dynamics. We focus on the crucial noncrossing property of Bohmian trajectories, which, numerically, must be given careful attention. Failure to do so causes instabilities or leads to false simulations.

On Irreversibility and Radiation in Classical Electrodynamics of Point Particles

The direct interaction theory of electromagnetism, also known as Wheeler-Feynman electrodynamics, is often misinterpreted and found unappealing because of its reference to the absorber and, more importantly, to the so-called absorber condition.Here we remark that the absorber condition is indeed questionable and presumably not relevant for the explanation of irreversible radiation phenomena in our universe. What is relevant and deserves further scrutiny is the emergent effective description of a source particle in an environment. We therefore rephrase what we consider the relevant calculation by Wheeler and Feynman and comment on the status of the theory.

Delay Equations of the Wheeler–Feynman Type

We present an approximate model of Wheeler–Feynman electrodynamics, for which uniqueness of solutions is proved. It is simple enough to be instructive but close enough to Wheeler–Feynman electrodynamics such that we can discuss its natural type of initial data, constants of motion, and stable orbits with regard to Wheeler–Feynman electrodynamics.

Time-evolution of the external field problem in Quantum Electrodynamics

We construct the time-evolution for the second quantized Dirac equation subject to a smooth, compactly supported, time dependent electromagnetic potential and identify the degrees of freedom involved. Earlier works on this (e.g. Ruijsenaars) observed the Shale-Stinespring condition and showed that the one-particle time-evolution can be lifted to Fock space if and only if the external field had zero magnetic components. We scrutinize the idea, observed earlier by Fierz and Scharf, that the time-evolution can be implemented between time varying Fock spaces. In order to define these Fock spaces we are led to consider classes of reference vacua and polarizations. We show that this implementation is up to a phase independent of the chosen reference vacuum or polarization and that all induced transition probabilities are well-defined and unique.

Breaking quantum linearity: Constraints from human perception and cosmological implications

Resolving the tension between quantum superpositions and the uniqueness of the classical world is a major open problem. One possibility, which is extensively explored both theoretically and experimentally, is that quantum linearity breaks above a given scale. Theoretically, this possibility is predicted by collapse models. They provide quantitative information on where violations of the superposition principle become manifest. Here we show that the lower bound on the collapse parameter λ, coming from the analysis of the human visual process, is ~7±2 orders of magnitude stronger than the original bound, in agreement with more recent analysis. This implies that the collapse becomes effective with systems containing ~104–105 nucleons, and thus falls within the range of testability with present-day technology. We also compare the spectrum of the collapsing field with those of known cosmological fields, showing that a typical cosmological random field can yield an efficient wave function collapse.

Maxwell-Lorentz Dynamics of Rigid Charges

We establish global existence and uniqueness of the dynamics of classical electromagnetism with extended, rigid charges and fields which need not to be square integrable. We also consider a modified theory of electromagnetism where no self-interaction occurs. That theory and our results are crucial for approaching the as yet unsolved problem of the general existence of dynamics of Wheeler-Feynman electromagnetism, which we shall address in the follow up paper. We conclude by discussing the energy conservation without self-interaction.

Consistency of multi-time Dirac equations with general interaction potentials

In 1932, Dirac proposed a formulation in terms of multi-time wave functions as candidate for relativistic many-particle quantum mechanics. A well-known consistency condition that is necessary for existence of solutions strongly restricts the possible interaction types between the particles. It was conjectured by Petrat and Tumulka that interactions described by multiplication operators are generally excluded by this condition, and they gave a proof of this claim for potentials without spin-coupling. Under suitable assumptions on the differentiability of possible solutions, we show that there are potentials which are admissible, give an explicit example, however, show that none of them fulfills the physically desirable Poincare invariance. We conclude that in this sense, Dirac’s multi-time formalism does not allow to model interaction by multiplication operators, and briefly point out several promising approaches to interacting models one can instead pursue.

From the Universe to Subsystems: Why Quantum Mechanics Appears More Stochastic than Classical Mechanics

By means of the examples of classical and Bohmian quantum mechanics, we illustrate the well-known ideas of Boltzmann as to how one gets from laws defined for the universe as a whole the dynamical relations describing the evolution of subsystems. We explain how probabilities enter into this process, what quantum and classical probabilities have in common and where exactly their difference lies.

Dirac equation with external potential and initial data on Cauchy surfaces

With this paper, we provide a mathematical review on the initial-value problem of the one-particle Dirac equation on space-like Cauchy hypersurfaces for compactly supported external potentials. We, first, discuss the physically relevant spaces of solutions and initial values in position and mass shell representation; second, review the action of the Poincare group as well as gauge transformations on those spaces; third, introduce generalized Fourier transforms between those spaces and prove convenient Paley-Wiener- and Sobolev-type estimates. These generalized Fourier transforms immediately allow the construction of a unitary evolution operator for the free Dirac equation between the Hilbert spaces of square-integrable wave functions of two respective Cauchy surfaces. With a Picard-Lindelof argument, this evolution map is generalized to the Dirac evolution including the external potential. For the latter, we introduce a convenient interaction picture on Cauchy surfaces. These tools immediately provide another proof of the well-known existence and uniqueness of classical solutions and their causal structure.

Relationalism about mechanics based on a minimalist ontology of matter

This paper elaborates on relationalism about space and time as motivated by a minimalist ontology of the physical world: there are only matter points that are individuated by the distance relations among them, with these relations changing. We assess two strategies to combine this ontology with physics, using classical mechanics as an example. The Humean strategy adopts the standard, non-relationalist physical theories as they stand and interprets their formal apparatus as the means of bookkeeping of the change of the distance relations instead of committing us to additional elements of the ontology. The alternative theoretical strategy seeks to combine the relationalist ontology with a relationalist physical theory that reproduces the predictions of the standard theory in the domain where these are empirically tested. We show that, as things stand, this strategy cannot be accomplished without compromising a minimalist relationalist ontology.