The Interpretation of Non-Relativistic Quantum 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.

Kai S Lam

Ruth E. Kastner

This paper presents key aspects of the quantum relativistic direct-action theory that underlies the Relativistic Transactional Interpretation. It notes some crucial ways in which traditional interpretations of the direct-action theory have impeded progress in developing its quantum counterpart. Specifically, (1) the so-called 'light tight box' condition is re-examined and it is shown that the quantum version of this condition is much less restrictive than has long been assumed; and (2) the notion of a 'real photon' is disambiguated and revised to take into account that real (on-shell) photons are indeed both emitted and absorbed and therefore have finite lifetimes. Also discussed is the manner in which real, physical non-unitarity naturally arises in the quantum direct-action theory of fields, such that the measurement transition can be clearly defined from within the theory, without reference to external observers and without any need to modify quantum theory itself. It is shown that field quantization arises from the non-unitary interaction.

Iwo Białynicki‐Birula, Zofia Białynicka-Birula

R.E. Moss

José Orlando Rodrigues da Cunha Filho, Lucas de Castro Rodrigues Barros

This is a review article that investigates the three approaches to Rutherford Scattering Theory - Classical Mechanics, Non-Relativistic Quantum Mechanics, and Quantum Field Theory - and their distinctions. In the first sections, the mathematical models are demonstrated and a qualitative analysis of the main differences in each interpretation of the phenomenon is performed. Next, numerical simulations show the effects of dealing with relativistic or non-relativistic limits. The results make it clear that no theory is essentially wrong, but the newer ones are just more complete and consider more relevant parameters.