© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Oxford University Press eBooks

CPT Invariance and the Spin-Statistics Connection

Jonathan Bain

Published Apr 1, 2016• 11 citations

Abstract

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.

DOI: 10.1093/acprof:oso/9780198728801.001.0001

Related papers

What Explains CPT Invariance and the Spin–Statistics Connection?

Jonathan Bain

Chapter 5 addresses the question, “What explains CPT invariance and the spin–statistics connection (SSC)?” It first considers why we should care about explaining CPT invariance and the SSC. It then argues that the CPT and spin–statistics theorems cannot be said to provide the sought after explanations. It offers instead an explanation of the SSC in interacting non-relativistic theories. This explanation explains by virtue of a derivation from non-fundamental principles in non-interacting relativistic quantum field theories (RQFTs), and an explication of intertheoretic relations between interacting RQFTs, non-interacting RQFTs, and interacting non-relativistic theories. The chapter ends by arguing that the presence of both the SSC and CPT invariance in realistic interacting RQFTs cannot be explained by even this type of explanation, and that currently, the existence problem precludes a full understanding of these properties in realistic interacting RQFTs.

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

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

Non-relativistic proofs of the spin-statistics connection

Anil Shaji, E. C. G. Sudarshan

A recent paper by Peshkin [1] has drawn attention again to the problem of understanding the spin statistics connection in non-relativistic quantum mechanics. Allen and Mondragon [2] has pointed out correctly some of the flaws in Peshkin's arguments which are based on the single valuedness under rotation of the wave functions of systems of identical particles. We examine carefully the claim that is made in the title of [2] that there can be ``no spin-statistics connection in non-relativistic quantum mechanics''. We show that we can derive the spin statistics connection for non-relativistic quantum field theories which have equations of motion of the Hamiltonian type based on SU(2) invariance of the Lagrangian. The formalism and machinary of non-relativistic quantum field theory as opposed to usual quantum mechanics is necessary for constructing our proof.

arXiv:quant-ph/0306033•Jun 4, 2003•7 citations

CPT Invariance, the Spin-Statistics Connection, and the Ontology of Relativistic Quantum Field Theories

Jonathan Bain

Erkenntnis•Oct 7, 2011•9 citations

Introduction

James Lindesay

This book examines the foundational consistency of quantum mechanics incorporated within relativistic frameworks. Quantum physics remains a perplexing formalism that, although very successful in explaining physical phenomena, poses many philosophical and interpretational questions. Several of the subtleties of quantum physics become more manifest when quantum processes are described using relativistic dynamics. For instance, the successful connection of spin to quantum statistics is a consequence of the consistent incorporation of special relativity into the quantum formalism. There should be similar profound explanations awaiting discovery as gravitating phenomena are successfully incorporated into quantum formulations. The common theme of this manuscript is the examination of the incorporation of relativistic behaviors upon the foundations of quantum physics. The approach is to keep all formulations as close to observed phenomena as possible, rather than to present a set of speculative models whose primary motivations are internal aesthetics. In the search for the most elegant models of physical phenomena, one must recognize that at its core, physics is an experimental science. The dimensional analysis of fundamental units, taught at the very beginning of introductory physics classes, demonstrates that phenomenology lies at the foundations of physics. Fundamental ideas such as correspondence, the principle of relativity, and complementarity provide direct contact with the physics used to guide this exploration. This manuscript is an elaboration and expansion on previously published work, but also contains some new material.

Cambridge University Press eBooks•May 16, 2013•0 citations

Critical Notice: "The Conceptual Development of 20th Century Field Theories", by Tian Yu Cao

Simon W. Saunders

Cao makes two claims of particular philosophical interest, in his book "The Conceptual Development of 20th Century Field Theories". (i) The history of these developments refutes Kuhn's relativistic epistemology, and (tacitly) (2) the question of realism in quantum field theory can be addressed independent of one's views on the probem of measurement. I argue that Cao is right on the first score, although for reasons different from the ones he cites, but wrong on the second. In support of the first of these claims, I review in detail the correspondence between the treatment of critical phenomena in condensed matter physics, and of scaling in the renormalization group of RQFT.

•Jun 1, 2001•0 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 5 addresses the question, “What explains CPT invariance and the spin–statistics connection (SSC)?” It first considers why we should care about explaining CPT invariance and the SSC. It then argues that the CPT and spin–statistics theorems cannot be said to provide the sought after explanations. It offers instead an explanation of the SSC in interacting non-relativistic theories. This explanation explains by virtue of a derivation from non-fundamental principles in non-interacting relativistic quantum field theories (RQFTs), and an explication of intertheoretic relations between interacting RQFTs, non-interacting RQFTs, and interacting non-relativistic theories. The chapter ends by arguing that the presence of both the SSC and CPT invariance in realistic interacting RQFTs cannot be explained by even this type of explanation, and that currently, the existence problem precludes a full understanding of these properties in realistic interacting RQFTs.

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.

A recent paper by Peshkin [1] has drawn attention again to the problem of understanding the spin statistics connection in non-relativistic quantum mechanics. Allen and Mondragon [2] has pointed out correctly some of the flaws in Peshkin's arguments which are based on the single valuedness under rotation of the wave functions of systems of identical particles. We examine carefully the claim that is made in the title of [2] that there can be ``no spin-statistics connection in non-relativistic quantum mechanics''. We show that we can derive the spin statistics connection for non-relativistic quantum field theories which have equations of motion of the Hamiltonian type based on SU(2) invariance of the Lagrangian. The formalism and machinary of non-relativistic quantum field theory as opposed to usual quantum mechanics is necessary for constructing our proof.

This book examines the foundational consistency of quantum mechanics incorporated within relativistic frameworks. Quantum physics remains a perplexing formalism that, although very successful in explaining physical phenomena, poses many philosophical and interpretational questions. Several of the subtleties of quantum physics become more manifest when quantum processes are described using relativistic dynamics. For instance, the successful connection of spin to quantum statistics is a consequence of the consistent incorporation of special relativity into the quantum formalism. There should be similar profound explanations awaiting discovery as gravitating phenomena are successfully incorporated into quantum formulations. The common theme of this manuscript is the examination of the incorporation of relativistic behaviors upon the foundations of quantum physics. The approach is to keep all formulations as close to observed phenomena as possible, rather than to present a set of speculative models whose primary motivations are internal aesthetics. In the search for the most elegant models of physical phenomena, one must recognize that at its core, physics is an experimental science. The dimensional analysis of fundamental units, taught at the very beginning of introductory physics classes, demonstrates that phenomenology lies at the foundations of physics. Fundamental ideas such as correspondence, the principle of relativity, and complementarity provide direct contact with the physics used to guide this exploration. This manuscript is an elaboration and expansion on previously published work, but also contains some new material.

Cao makes two claims of particular philosophical interest, in his book "The Conceptual Development of 20th Century Field Theories". (i) The history of these developments refutes Kuhn's relativistic epistemology, and (tacitly) (2) the question of realism in quantum field theory can be addressed independent of one's views on the probem of measurement. I argue that Cao is right on the first score, although for reasons different from the ones he cites, but wrong on the second. In support of the first of these claims, I review in detail the correspondence between the treatment of critical phenomena in condensed matter physics, and of scaling in the renormalization group of RQFT.