Harvey R. Brown

Philosophical foundations of quantum field theory

Rom Harre & Harvey Brown both of the University of Oxford: Introduction I. QUANTUM FIELD THEORY AS AN OBJECT OF PHILOSOPHICAL STUDY: TWO VIEWS: Michael Redhead, University of Cambridge: A philosopher looks at quantum field theory James T. Cushing, University of Notre Dame: Foundational problems in and methodological lessons from quantum field theory II. THE PROBLEMS OF VIRTUAL PARTICLES AND RENORMALIZATION: Robert Weingard, Rutgers University: Virtual particles and the interpretation of quantum field theory Rom Harre: Parsing the amplitudes Paul Teller, University of Illinois: Three problems of renormalization III. COVARIANCE PRINCIPLES IN QUANTUM FIELD THEORY: Gordon N. Fleming, Pennsylvania State University: Hyperplane-dependent quantized fields and Lorentz invariance Tian-yu Cao, Trinity College, Cambridge: Gauge theory and the geometrization of fundamental physics IV. MATHEMATICAL FOUNDATIONS OF QUANTUM FIELD THEORY: Ray F. Streater, Kings College, London: Why should anyone want to axiomatize quantum field theory? Simon Saunders, Wolfson College, Oxford: The algebraic notation of quantum field theory.

Solving the measurement problem: de Broglie-Bohm loses out to Everett

Abstract The quantum theory of de Broglie and Bohm solves the measurement problem, but the hypothetical corpuscles play no role in the argument. The solution finds a more natural home in the Everett interpretation.

The Origins of Time-Asymmetry in Thermodynamics: The Minus First Law

This paper investigates what the source of time-asymmetry is in thermodynamics, and comments on the question whether a time-symmetric formulation of the Second Law is possible.

Symmetries and Noether's theorems

Introduction Emmy Noethers greatest contributions to science were in algebra, but for physicists her name will always be remembered for her paper of 1918 on an invariance problem in the calculus of variations. The most celebrated part of this work, associated with her ‘first theorem’, has to do with the connection between continuous (global) symmetries in Lagrangian dynamics and conservation principles, though the main focus of the paper was the relationship between this and the second part of her paper, where she gives a systematic treatment of the more subtle and general case of continuous local symmetries (symmetries depending on arbitrary functions of the spacetime coordinates). The connection between global or ‘rigid’ symmetries and conservation principles in classical mechanics was hardly news in 1918. As Kastrup (1987) discusses in his historical review, it had been appreciated in the previous century by Lagrange, Hamilton, Jacobi, and Poincare, and an anticipation of Noethers first theorem in the special cases of the 10-parameter Lorentz and Galilean groups had been given by Herglotz in 1911 and Engel in 1916, respectively. Noethers own contribution is often praised for its degree of generality, and not without reason. But interestingly it does not cover the cases in which the symmetry transformation preserves the Lagrangian or Lagrangian density only up to a divergence term. It does not therefore cover such cases as the boost symmetry in classical pre-relativistic dynamics, although modern treatments of Noethers first theorem commonly rectify this defect.

Bohm particles and their detection in the light of neutron interferometry

Properties sometimes attributed to the “particle” aspect of a neutron, e.g., mass and magnetic moment, cannot straightforwardly be regarded in the Bohm interpretation of quantum mechanics as localized at the hypothetical position of the particle. This is shown by examining a series of effects in neutron interferometry. A related thought-experiment also provides a variation of a recent demonstration that which-way detectors can appear to behave anomolously in the Bohm theory.

On the reality of space-time geometry and the wavefunction

The action-reaction principle (AR) is examined in three contexts: (1) the inertial-gravitational interaction between a particle and space-time geometry, (2) protective observation of an extended wave function of a single particle, and (3) the causal-stochastic or Bohm interpretation of quantum mechanics. A new criterion of reality is formulated using the AR principle. This criterion implies that the wave function of a single particle is real and justifies in the Bohm interpretation the dual ontology of the particle and its associated wave function. But it is concluded that the Bohm theory is not dynamically complete because the particle and its associated wave function do not satisfy the AR principle.

Nonlocality and Gleason's lemma. Part I. Deterministic theories

J. S. Bells classic 1966 review paper on the foundations of quantum mechanics led directly to the Bell nonlocality theorem. It is not widely appreciated that the review paper contained the basic ingredients needed for a nonlocality result which holds in certain situations where the Bell inequality is not violated. We present in this paper a systematic formulation and evaluation of an argument due to Stairs in 1983, which establishes a nonlocality result based on the Bell-Kochen-Specker “paradox” in quantum mechanics.

The Insolubility Proof of the Quantum Measurement Problem

Modern insolubility proofs of the measurement problem in quantum mechanics not only differ in their complexity and degree of generality, but also reveal a lack of agreement concerning the fundamental question of what constitutes such a proof. A systematic reworking of the (incomplete) 1970 Fine theorem is presented, which is intended to go some way toward clarifying the issue.

The Galilean covariance of quantum mechanics in the case of external fields

Textbook treatments of the Galilean covariance of the time-dependent Schrodinger equation for a spinless particle seem invariably to cover the case of a free particle or one in the presence of a scalar potential. The principal objective of this paper is to examine the situation in the case of arbitrary forces, including the velocity-dependent variety resulting from a vector potential. To this end, we revisit the 1964 theorem of Jauch which purports to determine the most general form of the Hamiltonian consistent with “Galilean-invariance,” and argue that the proof is less than compelling. We then show systematically that the Schrodinger equation in the case of a Jauch-type Hamiltonian is Galilean covariant, so long as the vector and scalar potentials transform in a certain way. These transformations, which to our knowledge have appeared very rarely in the literature on quantum mechanics, correspond in the case of electrodynamical forces to the “magnetic” nonrelativistic limit of Maxwell’s equations in the...

Why special relativity should not be a template for a fundamental reformulation of quantum mechanics

In a comparison of the principles of special relativity and of quantum mechanics, the former theory is marked by its relative economy and apparent explanatory simplicity. A number of theorists have thus been led to search for a small number of postulates - essentially information theoretic in nature - that would play the role in quantum mechanics that the relativity principle and the light postulate jointly play in Einsteins 1905 special relativity theory. The purpose of the present paper is to resist this idea, at least in so far as it is supposed to reveal the fundamental form of the theory. It is argued that the methodology of Einsteins 1905 theory represents a victory of pragmatism over explanatory depth; and that its adoption only made sense in the context of the chaotic state state of physics at the start of the 20th century - as Einstein well knew.