The ‘beables’ of relativistic pilot-wave theory

Ward Struyve

In this thesis we study the de Broglie-Bohm pilot-wave interpretation of quantum theory. We consider the domain of non-relativistic quantum theory, relativistic quantum theory and quantum field theory, and in each domain we consider the possibility of formulating a pilot-wave interpretation. For non-relativistic quantum theory a pilot-wave interpretation in terms of particle beables can readily be formulated. But this interpretation can in general not straightforwardly be generalized to relativistic wave equations. The problems which prevent us from devising a pilot-wave interpretation for relativistic wave equations also plague the standard quantum mechanical interpretation, where these problems led to the conception of quantum field theory. Therefore most of our attention is focussed on the construction of a pilot-wave interpretation for quantum field theory. We thereby favour the field beable approach, developed amongst others by Bohm, Hiley, Holland, Kaloyerou and Valentini. Although the field beable approach can be successfully applied to bosonic quantum field theory, it seems not straightforward to do so for fermionic quantum field theory.

Ward Struyve

We present a way to construct a pilot‐wave model for quantum field theory. 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 provide an illustration and a justification of this idea in the context of quantum electrodynamics. The beables are fields and correspond to the degrees of freedom of the electromagnetic field. The field beables are 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.

Sacha Greenfield

Ward Struyve, H Westman

We present a way to construct a pilot-wave model for quantum electrodynamics. The idea is to introduce beables corresponding only to the bosonic 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 will be introduced in a way similar 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 wave function. After presenting this model, we also discuss a simple way for introducing additional beables that represent the fermionic degrees of freedom.

Valia Allori