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The philosophical significance of the concept of superposition in quantum field theory

Douglas S. Earl

Published Sep 1, 2020• 0 citations
OpenAlex

Abstract

I analyse the applicability of the concept of superposition within quantum field theory (QFT) in order to consider the physical interpretation of a simple interacting theory. \nFirst, I consider the significance of ‘superposition’ in classical physics motivated by the philosophical framework developed by Wilson (2006; 2017), via the analyses of ‘superposition’ developed by Volkmann (1896; 1910) and Simons (1987) in addition to a historical survey of its application with special reference to Fourier techniques. The concept has a patchwork or façade structure, with application subject to ‘prolongation’ and ‘semantic mimicry’. Proper usage of ‘superposition’ is associated with identifying partial states and laws that provide a natural description of complicated phenomena supporting physically salient explanations, inductive inferences and counterfactual reasoning. \nSecondly, I demonstrate that application of ‘superposition’ in quantum physics is a prolongation of its classical usage involving new rules of application. \nThirdly, I analyse the historical origins of QFT and the mature theory to indicate where, and how, proper application of ‘superposition’ is made to free theories, whilst semantic mimicry is involved in the interpretation of interacting theories. Improper and often implicit appeals are made to ‘superposition’ to incorrectly claim physical interpretations of interacting theories. Two major related failures of ‘superposition’ are identified, associated with the initial postulation of putative fields and corresponding states associated with different particle types, and with the nonlinearity of the coupled field equations, so that natural descriptions of interacting states using familiar concepts are unavailable. Renormalization is interpreted as a symptom and pragmatic partial remedy for the failure of ‘superposition’ such that empirically successful calculations are supported using LSZ scattering theory and the Gell-Mann and Low theorem. \nFinally, I suggest that the interpretation of QFT is best approached within the context of an engineer’s perspective rather than a metaphysician’s, having implications for wider philosophical debates.

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It is very likely that most readers and authors of articles appearing in Classical and Quantum Gravity are interested in what might loosely be termed the philosophy of science. It is equally likely, with perhaps a few exceptions, that the research of these same readers and authors has not been influenced in the least by the work of professional philosophers of science. This is certainly the case for those of us who work in quantum field theory. One must therefore ask who the intended audience is for a book which purports to discuss the philosophical implications of quantum field theory. In the preface, the author states that there are two intended audiences for his book. The first is `other interested interpreters of physics' who wish to learn something about quantum field theory in as painless a way as possible. The second is for students of physics who are bogged down in the details of learning quantum field theory and cannot see the overall picture. I am not convinced that either audience will find this book to be of much use. There are two basic problems with this book. The first is that the quantum field theory in it is of the old-fashioned kind, and is not really representative of the way the subject is either taught or thought of today. The second is that there is not sufficient background material present to make this book suitable for a novice reader. For example, I wonder how much a reader who has not studied quantum mechanics in any depth will get out of a treatment which launches into Hilbert space and a discussion of states without much in the way of proper introduction. Any reader who is familiar with the workings of quantum field theory will find much to disagree with in this book. For example, the author tries to make a case that a Fock space description is better than talking about particle labels and restricting to symmetric or antisymmetric states. The reason claimed for this is that there are states in Fock space which are neither symmetric nor antisymmetric under particle interchange which must be discarded. (In the author's words, this introduces `surplus formal structure'.) However, in Fock space an equally arbitrary choice is made by focusing on relations among the creation and annihilation operators which involve only commutation or anticommutation relations. Although this is acknowledged by Teller, no satisfactory explanation is given as to why one procedure is any less arbitrary than the other. The book is incomplete in many ways, with many interesting points mentioned just in passing. For example, the discussion around the Newton--Wigner position operator would have been greatly enhanced by including more details, such as an explanation as to why quanta described by Newton--Wigner states seem to propagate at superluminal speeds. It is hard to believe that a reader who has not met the Rindler vacuum before would find Teller's discussion to be very informative. After being so critical of this book, I should mention a part which I did enjoy and would recommend to students of physics. This is the last chapter of the book which contains a discussion of renormalization theory. It is my experience that students often find renormalization theory confusing, and may find Teller's semiqualitative discussion illuminating.

Classical and Quantum Gravity•Jul 1, 1996•11 citations
I analyse the applicability of the concept of superposition within quantum field theory (QFT) in order to consider the physical interpretation of a simple interacting theory. \nFirst, I consider the significance of ‘superposition’ in classical physics motivated by the philosophical framework developed by Wilson (2006; 2017), via the analyses of ‘superposition’ developed by Volkmann (1896; 1910) and Simons (1987) in addition to a historical survey of its application with special reference to Fourier techniques. The concept has a patchwork or façade structure, with application subject to ‘prolongation’ and ‘semantic mimicry’. Proper usage of ‘superposition’ is associated with identifying partial states and laws that provide a natural description of complicated phenomena supporting physically salient explanations, inductive inferences and counterfactual reasoning. \nSecondly, I demonstrate that application of ‘superposition’ in quantum physics is a prolongation of its classical usage involving new rules of application. \nThirdly, I analyse the historical origins of QFT and the mature theory to indicate where, and how, proper application of ‘superposition’ is made to free theories, whilst semantic mimicry is involved in the interpretation of interacting theories. Improper and often implicit appeals are made to ‘superposition’ to incorrectly claim physical interpretations of interacting theories. Two major related failures of ‘superposition’ are identified, associated with the initial postulation of putative fields and corresponding states associated with different particle types, and with the nonlinearity of the coupled field equations, so that natural descriptions of interacting states using familiar concepts are unavailable. Renormalization is interpreted as a symptom and pragmatic partial remedy for the failure of ‘superposition’ such that empirically successful calculations are supported using LSZ scattering theory and the Gell-Mann and Low theorem. \nFinally, I suggest that the interpretation of QFT is best approached within the context of an engineer’s perspective rather than a metaphysician’s, having implications for wider philosophical debates.
Abstract Much attention has been directed to the philosophical implications of quantum field theory (QFT) in recent years; this paper attempts a survey in low-technical terms. First the relations of QFT to other kinds of theory, classical and quantum, particle and field, are discussed. Then various formulations of QFT are introduced, along with related interpretations. Finally a review is made of some of the most interesting foundational problems. For our discussion of the foundations of quantum field theory (QFT) it will be useful to have a map showing where QFT stands in relation to other physical theories. Figure 1 locates theories as points of a three-dimensional lattice: describing particles or fields, formulated in different spacetimes and either classical or quantum. Consider the classical plane of Figure
Quantum field theory (QFT) can be analyzed in terms of its mathematical structure, its conceptual system for physical descriptions, or its basic ontology. The analysis can be done logically or historically. In this chapter, only the genesis of the conceptual foundations of QFT relevant to its basic ontology will be treated; no discussion of its mathematical structures or its epistemological underpinnings will be given. Some conceptual problems, such as those related to probability and measurement, will be discussed, but only because of their relevance to the basic ontology of QFT, rather than their intrinsic philosophical interest. Here, by basic ontology I mean the irreducible entities that QFT is invented to describe. The often mentioned candidates for the basic ontology of QFT, in fact of the physical world, are the discrete particle and the continuous field. Another possible candidate (the spacetime point) has also been suggested recently (Redhead, 1983). Since the aim of this chapter is to analyze the historical process in which the conceptual foundations of QFT were laid down, rather than the logical structure of QFT which philosophers of the present day treat, no discussion of the last possibility will be given. The content of this chapter involves the formation and interpretation, in a roughly chronological order, of the concepts of the wave function, quantization, quantization of the field, the vacuum, interactions between fields, and renormalization. The first two topics will be discussed in relation to the quantization of the field, with their role being taken as the starting point of the conceptual development of QFT.
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical principles underlying the theory, we rigorously construct a discrete model of quantum mechanics. Kets are names, or labels which categorise states of matter but do not directly describe them. The principle of superposition is seen as a definitional truism in the categorisation of states. This resolves the measurement problem of quantum mechanics by attributing the collapse of the wave function to information. The probability interpretation has a natural meaning in which the configuration of interacting particles plays the role of a hidden variable. The model supports a form of relativistic quantum field theory which does not depend on quantisation or second quantisation from classical mechanics. Continuous laws of wave mechanics are found in a discrete metaphysic which does not involve waves. Classical law is the expected behaviour of many elementary particles. The constraints on the theory are sufficient to establish that particles are point-like entities with specific properties found in nature. Newton's first law and conservation of momentum are established from the principle of homogeneity. Maxwell's equations are derived from the simple interaction in which a Dirac particle emits or absorbs a photon. Feynman rules are calculated for the discrete theory and differ from the standard rules by the removal of the ultraviolet divergence and the use of proper loop integrals. They give finite and unambiguous results.
Abstract Quantum field theory (QFT) is the union of quantum mechanics and Einstein’ s special theory of relativity. QFT is the most fundamental physical theory and provides the answers to questions about the basic structure of the physical world. However, the way QFT describes the world is so different from the way our senses present it to us that it requires an overhaul of philosophic categories and arguments. How can we know the microscopic world without a satisfactory measurement theory? What are the general conditions of the world that make possible such knowledge? What are the presuppositions of physical theories? Dr.Auyang argues that the current relational substantial debate on space-time is inadequate and the observer-observed distinction in quantum interpretations illusory because they are hampered by philosophical constructs too narrow to accommodate the complicated structures of modern philosophical theories. Modern physical theories have incorporated many presuppositions of empirical knowledge, and consequently the theories inform us about the general nature of the world and out relation to it, in addition to information about elementary particles. The conceptual structure of QFT is extracted and articulated in commonsense terms, and used to answer many longstanding philosophical questions.
It is very likely that most readers and authors of articles appearing in Classical and Quantum Gravity are interested in what might loosely be termed the philosophy of science. It is equally likely, with perhaps a few exceptions, that the research of these same readers and authors has not been influenced in the least by the work of professional philosophers of science. This is certainly the case for those of us who work in quantum field theory. One must therefore ask who the intended audience is for a book which purports to discuss the philosophical implications of quantum field theory. In the preface, the author states that there are two intended audiences for his book. The first is `other interested interpreters of physics' who wish to learn something about quantum field theory in as painless a way as possible. The second is for students of physics who are bogged down in the details of learning quantum field theory and cannot see the overall picture. I am not convinced that either audience will find this book to be of much use. There are two basic problems with this book. The first is that the quantum field theory in it is of the old-fashioned kind, and is not really representative of the way the subject is either taught or thought of today. The second is that there is not sufficient background material present to make this book suitable for a novice reader. For example, I wonder how much a reader who has not studied quantum mechanics in any depth will get out of a treatment which launches into Hilbert space and a discussion of states without much in the way of proper introduction. Any reader who is familiar with the workings of quantum field theory will find much to disagree with in this book. For example, the author tries to make a case that a Fock space description is better than talking about particle labels and restricting to symmetric or antisymmetric states. The reason claimed for this is that there are states in Fock space which are neither symmetric nor antisymmetric under particle interchange which must be discarded. (In the author's words, this introduces `surplus formal structure'.) However, in Fock space an equally arbitrary choice is made by focusing on relations among the creation and annihilation operators which involve only commutation or anticommutation relations. Although this is acknowledged by Teller, no satisfactory explanation is given as to why one procedure is any less arbitrary than the other. The book is incomplete in many ways, with many interesting points mentioned just in passing. For example, the discussion around the Newton--Wigner position operator would have been greatly enhanced by including more details, such as an explanation as to why quanta described by Newton--Wigner states seem to propagate at superluminal speeds. It is hard to believe that a reader who has not met the Rindler vacuum before would find Teller's discussion to be very informative. After being so critical of this book, I should mention a part which I did enjoy and would recommend to students of physics. This is the last chapter of the book which contains a discussion of renormalization theory. It is my experience that students often find renormalization theory confusing, and may find Teller's semiqualitative discussion illuminating.