The Philosophy of Fields and Particles in Classical and Quantum Mechanics, Including the Problem of Renormalisation.

Peter Gibbins

Quantum theory is our deepest theory of the nature of matter. It is a theory that, notoriously, produces results which challenge the laws of classical logic and suggests that the physical world is illogical. This book gives a critical review of work on the foundations of quantum mechanics at a level accessible to non-experts. Assuming his readers have some background in mathematics and physics, Peter Gibbins focuses on the questions of whether the results of quantum theory require us to abandon classical logic and whether quantum logic can resolve the paradoxes produced by quantum mechanics. He argues that quantum logic does not dispose of the problems faced by classical logic, that no reasonable interpretation of quantum mechanics in terms of 'hidden variables' can be found, and that after all these years quantum mechanics remains a mystery to us. Particles and Paradoxes provides a much-needed and valuable introduction to the philosophy of quantum mechanics and, at the same time, an example of just what it is to do the philosophy of physics.

Simon W. Saunders

Max Joseph Fahn, Kristina Giesel

Abstract We investigate the one-particle sector for the field-theoretical model of gravitationally induced decoherence for a scalar field in Fahn et al (2023 Class. Quantum Grav. 40 094002) with a special focus on the renormalisation of the one-particle master equation. In contrast to existing models in the literature, where the renormalisation is usually performed after the Markov and rotating wave approximation (RWA) and often only for certain limits such as the non- or ultra-relativistic limit, here we apply the renormalisation directly after the one-particle projection. With this strategy, we show that UV-divergent contributions in the one-particle master equation can be identified with the vacuum contributions in the self-energy of the scalar field in the effective quantum field theory and depending on the chosen one-particle projection method, its vacuum bubbles, while the additional thermal contributions in the self-energy are all UV-finite. To obtain the renormalised one-particle master equation, we use an on-shell renormalisation procedure of the underlying effective QFT. We then apply the Markov and RWA, specifying a condition under which the Markov approximation can be applied in the case of the ultra-relativistic limit. We compare our results with those available in the literature. This includes an analysis of two different kinds of one-particle projections, a comparison of the application and effects of renormalisation of quantum mechanical and field theoretical models, the non-relativistic and ultra-relativistic limits of the renormalised one-particle master equations, and a comparison with a quantum mechanical toy model for gravitationally induced decoherence in the context of neutrino oscillations.

Gino Tarozzi

Patrick Sibelius

Tadashi Nakajima

We analyze the measurement problem in quantum mechanics from two aspects of Wittgenstein’s philosophy. First, Wittgenstein emphasizes how the first false step can be voided so that a philosophical problem is dissolved, rather than solved. In the unsuccessful theories of the measurement problem, the postulate of classicality of apparatus (PCA) turned out to be the first false step implicitly adopted. By discarding the PCA and by adopting the microscopic quantum jump interpretation simultaneously, the measurement problem itself disappeared completely. Second, from Wittgenstein’s view of languages, the microscopic world is described by quantum mechanics, whose language is the Schrödinger equation, while the macroscopic world is described by classical physics, whose language is either calculus for Newtonian mechanics or vector analysis for electromagnetism. Both worlds are described by mathematical languages, but they are distinct. The measurement problem deals with the transition from microscopic to macroscopic. There is no single physical theory to explain this transition, and there is no corresponding mathematical language to describe it. This shows why the measurement problem must be described by an ordinary language in use. As concrete examples of the unsuccessful theories, we discuss the works of Niels Bohr and John von Neumann. This is a unique situation in which philosophy is used to assess the validity of physical theories. Finally, we show the classicality of a one-particle state with an extreme number of bosons. Therefore, there is no change in language in a macroscopic quantum jump.