My Discussions of Quantum Foundations with John Stewart Bell

Sheldon Goldstein

Stephen L. Adler

I briefly recall intersections of my research interests with those of John Bell. I then argue that the noise needed in theories of objective state vector reduction most likely comes from a fluctuating complex part in the classical spacetime metric; that is, state vector reduction is driven by complex-number-valued “ space–time foam.” Introduction My research interests have intersected those of John Bell three times. The first was when I found the forward lepton theorem for high-energy neutrino reactions, showing that for forward lepton kinematics, a conserved vector current (CVC) and a partially conserved axial vector current (PCAC) imply that the neutrino cross section can be related to a pion scattering cross section [1]. This led to an exchange of letters and discussions with Bell during 1964–5, which are described in the Commentaries for my selected papers [2]. The second was in the course of my work on the axial-vector anomaly [3], when I had further correspondence with John Bell, as described both in the Commentaries [4] and in the volume of essays on Yang–Mills theories assembled by 't Hooft [5]. The third time was a few years after Bell's death in 1990, when I became interested in the foundations of quantum theory and the quantum measurement problem, in the course of writing my book on quaternionic quantum mechanics [6]. Foundational issues in standard, complex quantum theory had preoccupied Bell for much of his career and led to his best known work. However, my correspondence with Bell in the 1960s never touched on quantum foundations, and I only read his seminal writings on the subject much later on. In this article I focus on this third area of shared interests. Objective Reduction Models There is now a well-defined phenomenology of state vector reduction, pioneered by the work of Ghirardi, Rimini, andWeber (GRW) and of Philip Pearle, and worked on by many others. John Bell was interested in this program from the outset.

Peter Sidajaya

Reinhold A. Bertlmann

I present my encounter with John Bell at CERN, our collaboration and joint work in particle physics. I also will recall our quantum debates and give my personal view on Bell's fundamental work on quantum theory, in particular, on contextuality and nonlocality of quantum physics. Some mathematical and geometric aspects of entanglement are discussed as influence of Bell's Theorem. Finally, I make some historical comments on the experimental side of Bell inequalities.

Martin Ringbauer