Alex Blum

This paper examines the development of causal perturbation theory, a reformulation of perturbative quantum theory (QFT) starting from a causality condition rather than a time-evolution equation. We situate this program alongside other causality-based reformulations of relativistic quantum theory which flourished in the post-war period, contrasting it in particular with axiomatic QFT. Whereas the axiomatic QFT tradition tried to move beyond the perturbative expansion, causal perturbation theory can be thought of as a foundational investigation of this approximation method itself. Our reconstruction of this forgotten research program offers new perspectives on contemporary debates about relativistic causality conditions and the problem of ultraviolet divergences.

In this section, I will discuss two key breakthroughs achieved by Heisenberg in the years 1957/58, which ultimately convinced him that he was on the right track, led him to present his theory in several overblown public presentations, and temporarily even convinced Pauli to join Heisenberg in his endeavor. The two breakthroughs concerned the possible mathematical consistency of the theory and its possible empirical adequacy in the face of the burgeoning number of new particles being discovered at high-energy accelerators. We will discuss these two breakthroughs in turn, beginning with the question of consistency.

This paper re-evaluates the formative year of quantum mechanics—from Heisenberg’s first paper on matrix mechanics to Schrödinger’s equivalence proof—by focusing on the role of radiation in the emerging theory. We argue that the radiation problem played a key role in early quantum mechanics, a role that has not been taken into account in the standard histories. Radiation was perceived by the main protagonists of matrix and wave mechanics as a central lacuna in these emerging theories and continued to contribute to the theoretical development and conceptual clarification of quantum mechanics. Studying the interplay between quantum mechanics and radiation, the paper provides an account of (a) how quantum mechanics was able to connect to its empirical basis in spectroscopy and (b) how Schrödinger’s equivalence proof emerged from his explorative calculations on the emission of radiation.

This paper studies the notion of virtuality in the Bohr-Kramers-Slater theory of 1924. We situate the virtual entities of BKS within the tradition of the correspondence principle and the radiation theory of the Bohr model. We show how, in this context, virtual oscillators emerged as classical substitute radiators and were used to describe the otherwise elusive quantum transitions. They played an effective role in the quantum theory of radiation while remaining categorically distinct and ontologically separated from the quantum world of the Bohr model. The notion of virtuality thus differs markedly from its counterpart in quantum mechanics or QFT.