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Essay Review: CPT Invariance and the Spin-Statistics Connection

Noel Swanson

Published Mar 2, 2018• 0 citations
OpenAlex

Abstract

Essay review of Jonathan Bain's book "CPT Invariance and the Spin-Statistics Connection," to appear in Philosophy of Science.

Related papers

CPT Invariance and the Spin-Statistics Connection

Jonathan Bain

This book seeks to answer the question "What explains CPT invariance and the spin-statistics connection?" These properties play foundational roles in relativistic quantum field theories (RQFTs), are supported by high-precision experiments, and figure into explanations of a wide range of phenomena, from antimatter, to the periodic table of the elements, to superconductors and superfluids. They can be derived in RQFTs by means of the famous CPT and Spin-Statistics theorems; but, the author argues, these theorems cannot be said to explain these properties, at least under standard philosophical accounts of scientific explanation. This is because there are multiple, in some cases incompatible, ways of deriving these theorems, and, secondly, because the theorems fail for the types of theories that underwrite the empirical evidence: non-relativistic quantum theories, and realistic interacting RQFTs. The goal of this book is to work towards an understanding of CPT invariance and the spin-statistics connection by first providing an analysis of the necessary and sufficient conditions for these properties, and second by advocating a particular account of explanation appropriate for this context.

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Non-RQFT Derivations of CPT Invariance and the Spin–Statistics Connection

Jonathan Bain

Chapter 4 evaluates attempts to derive CPT invariance and the spin–statistics connection (SSC) outside the framework of relativistic quantum theories. It first considers attempts at non-relativistic quantum mechanical derivations of the SSC. These attempts split into those that adopt the framework of finite-dimensional (i.e., non-field-theoretic) non-relativistic quantum mechanics, and fall under the general heading of “configuration space approaches,” and an approach that adopts the framework of non-relativistic quantum field theory. The chapter indicates how recent work in the philosophy of physics literature on the relation between permutation invariance and indistinguishability sheds light on the limitations of the former, while the discussion in Chapter 3 demonstrates where the latter fails. The chapter then considers attempts to derive CPT invariance in relativistic classical field theories from both a pragmatist (Lagrangian) and a purist (algebraic) perspective.

Oxford University Press eBooks•Apr 1, 2016•0 citations

CPT Invariance as Basic for Interpreting Quantum Mechanics

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Springer eBooks•Jan 1, 1983•1 citation

Spin, or actually: Spin and Quantum Statistics

Jürg Martin Fröhlich

The history of the discovery of electron spin and the Pauli principle and the mathematics of spin and quantum statistics are reviewed. Pauli’s theory of the spinning electron and some of its many applications in mathematics and physics are considered in more detail. The role of the fact that the tree-level gyromagnetic factor of the electron has the value g e = 2 in an analysis of stability (and instability) of matter in arbitrary external magnetic fields is highlighted. Radiative corrections and precision measurements of g e are reviewed. The general connection between spin and statistics, the CPT theorem and the theory of braid statistics, relevant in the theory of the quantum Hall effect, are described. “He who is deficient in the art of selection may, by showing nothing but the truth, produce all the effects of the grossest falsehoods. It perpetually happens that one writer tells less truth than another, merely because he tells more ‘truth’.” (T. Macauley, ‘History’, in Essays, Vol. 1, p 387, Sheldon, NY 1860) These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

arXiv:0801.2724•Birkhäuser Basel eBooks•Jan 1, 2009•4 citations

CPT invariance and interpretation of quantum mechanics

O. Costa de Beauregard

Foundations of Physics•Aug 1, 1980•15 citations
This book seeks to answer the question "What explains CPT invariance and the spin-statistics connection?" These properties play foundational roles in relativistic quantum field theories (RQFTs), are supported by high-precision experiments, and figure into explanations of a wide range of phenomena, from antimatter, to the periodic table of the elements, to superconductors and superfluids. They can be derived in RQFTs by means of the famous CPT and Spin-Statistics theorems; but, the author argues, these theorems cannot be said to explain these properties, at least under standard philosophical accounts of scientific explanation. This is because there are multiple, in some cases incompatible, ways of deriving these theorems, and, secondly, because the theorems fail for the types of theories that underwrite the empirical evidence: non-relativistic quantum theories, and realistic interacting RQFTs. The goal of this book is to work towards an understanding of CPT invariance and the spin-statistics connection by first providing an analysis of the necessary and sufficient conditions for these properties, and second by advocating a particular account of explanation appropriate for this context.
Chapter 4 evaluates attempts to derive CPT invariance and the spin–statistics connection (SSC) outside the framework of relativistic quantum theories. It first considers attempts at non-relativistic quantum mechanical derivations of the SSC. These attempts split into those that adopt the framework of finite-dimensional (i.e., non-field-theoretic) non-relativistic quantum mechanics, and fall under the general heading of “configuration space approaches,” and an approach that adopts the framework of non-relativistic quantum field theory. The chapter indicates how recent work in the philosophy of physics literature on the relation between permutation invariance and indistinguishability sheds light on the limitations of the former, while the discussion in Chapter 3 demonstrates where the latter fails. The chapter then considers attempts to derive CPT invariance in relativistic classical field theories from both a pragmatist (Lagrangian) and a purist (algebraic) perspective.
The history of the discovery of electron spin and the Pauli principle and the mathematics of spin and quantum statistics are reviewed. Pauli’s theory of the spinning electron and some of its many applications in mathematics and physics are considered in more detail. The role of the fact that the tree-level gyromagnetic factor of the electron has the value g e = 2 in an analysis of stability (and instability) of matter in arbitrary external magnetic fields is highlighted. Radiative corrections and precision measurements of g e are reviewed. The general connection between spin and statistics, the CPT theorem and the theory of braid statistics, relevant in the theory of the quantum Hall effect, are described. “He who is deficient in the art of selection may, by showing nothing but the truth, produce all the effects of the grossest falsehoods. It perpetually happens that one writer tells less truth than another, merely because he tells more ‘truth’.” (T. Macauley, ‘History’, in Essays, Vol. 1, p 387, Sheldon, NY 1860) These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.