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Are Rindler quanta real? Inequivalent particle concepts in quantum field theory

Rob Clifton

Published Sep 23, 2009• 1 citation
Publisher

Abstract

Abstract Sagredo: Do we not see here another example of that all­pervading principle of complementarity which excludes the simultaneous applicability of concepts to the real objects of our world? Is it not so that, rather than being frustrated by this limitation of our conceptual grasp of the reality, we see in this unification of opposites the deepest and most satisfactory result of the dialectical process in our struggle for understanding? ­ Josef Jauch, Are Quanta Real? A Galilean Dialogue (1973) We are extremely grateful to John Earman and Laura Ruetsche for many stimulating discussions which provided the impetus for writing this paper, and to Aristidis Arageorgis for writing a provocative and inspiring dissertation. We would also like to thank Klaas Landsman and Rainer Verch for help with the proof of Proposition 6.

DOI
10.1093/oso/9780199270156.003.0009

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Abstract Sagredo: Do we not see here another example of that all­pervading principle of complementarity which excludes the simultaneous applicability of concepts to the real objects of our world? Is it not so that, rather than being frustrated by this limitation of our conceptual grasp of the reality, we see in this unification of opposites the deepest and most satisfactory result of the dialectical process in our struggle for understanding? ­ Josef Jauch, Are Quanta Real? A Galilean Dialogue (1973) We are extremely grateful to John Earman and Laura Ruetsche for many stimulating discussions which provided the impetus for writing this paper, and to Aristidis Arageorgis for writing a provocative and inspiring dissertation. We would also like to thank Klaas Landsman and Rainer Verch for help with the proof of Proposition 6.
Philosophical reflection on quantum field theory has tended to focus on how it revises our conception of what a particle is. However, there has been relatively little discussion of the threat to the ‘reality’ of particles posed by the possibility of inequivalent quantizations of a classical field theory, i.e. inequivalent representations of the algebra of observables of the field in terms of operators on a Hilbert space. The threat is that each representation embodies its own distinctive conception of what a particle is, and how a ‘particle’ will respond to a suitably operated detector. Our main goal is to clarify the subtle relationship between inequivalent representations of a field theory and their associated particle concepts. We also have a particular interest in the Minkowski versus Rindler quantizations of a free Boson field, because they respectively entail two radically different descriptions of the particle content of the field in the very same region of spacetime. We shall defend the idea that these representations provide complementary descriptions of the same state of the field against the claim that they embody completely incommensurable theories of the field.
Philosophical reflection on quantum field theory has tended to focus on how it revises our conception of what a particle is. However, there has been relatively little discussion of the threat to the "reality" of particles posed by the possibility of inequivalent quantizations of a classical field theory, i.e., inequivalent representations of the algebra of observables of the field in terms of operators on a Hilbert space. The threat is that each representation embodies its own distinctive conception of what a particle is, and how a "particle" will respond to a suitably operated detector. Our main goal is to clarify the subtle relationship between inequivalent representations of a field theory and their associated particle concepts. We also have a particular interest in the Minkowski versus Rindler quantizations of a free Boson field, because they respectively entail two radically different descriptions of the particle content of the field in the very same region of spacetime. We shall defend the idea that these representations provide complementary descriptions of the same state of the field against the claim that they embody completely incommensurable theories of the field.
Once I tried to teach some quantum mechanics to a class of law students, philosophers, and art historians. As an advertisement for the course I put together the most sensational quotations I could collect from the most authoritative practitioners of the subject. Heisenberg was a goldmine: “The concept of the objective reality of the elementary particles has thus evaporated…”; “the idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them … is impossible …” Feynman did his part too: “I think I can safely say that nobody understands quantum mechanics.” But I failed to turn up anything comparable in the writings of Bohr. Others attributed spectacular remarks to him, but he seemed to take pains to avoid any hint of the dramatic in his own writings. You don't pack them into your classroom with “The indivisibility of quantum phenomena finds its consequent expression in the circumstance that every definable subdivision would require a change of the experimental arrangement with the appearance of new individual phenomena,” or “the wider frame of complementarity directly expresses our position as regards the account of fundamental properties of matter presupposed in classical physical description but outside its scope.” I was therefore on the lookout for nuggets when I sat down to review these three volumes – a reissue of Bohr's collected essays on the revolutionary epistemological character of the quantum theory and on the implications of that revolution for other scientific and non-scientific areas of endeavor (the originals first appeared in 1934, 1958, and 1963.)
The aim of the research is to develop a dialectical relational-event ontology (DREO), that is, a second-order metaphysical framework designed to resolve the fundamental problems of the philosophy of quantum physics: wave-particle dualism and the irreducible pluralism of interpretations. The scientific novelty of the article lies in the following: for the first time, not just another interpretation of quantum mechanics is proposed, but a meta-framework that dialectically sublates the pluralism of interpretations itself and demonstrates their systemic unity; the category of a "relational event" is introduced as a fundamental unit of being, which marks a transition from substantial metaphysics (debates on the individuality of objects) to a metaphysics of becoming; wave-particle dualism is interpreted not as ontological (two entities) and not as epistemological (N. Bohr's complementarity principle), but as a dialectical contradiction sublated in the concept of "relational potentiality" – a structure of possibilities actualized depending on the perspective; the complementarity of wave and particle for the first time receives ontological status – it is a mode of existence of quantum reality itself as a "pulsation" between modes of actualization; a new model of scientific rationality is substantiated – dialectical pluralism – where truth is not a property of an individual proposition but a property of the entire system of perspectives taken in their dialectical unity, which fundamentally distinguishes DREO from contextual quantum realism (CQR), which remains within the static opposition of "rule – application" and epistemological perspectivism. The key results of the study are the following ideas: a relational event (rather than an object or a relation in itself) is recognized as the fundamental unit of being – a discrete act of transition from the potential to the actual in a specific context of interaction; "particle" and "wave" are interpreted as two extreme, mutually exclusive and simultaneously complementary types of actualization of a single structure of potencies in different perspectives; the multiplicity of incompatible but empirically equivalent interpretations of quantum mechanics is shown not as a flaw in the theory, but as a logical consequence of the relational structure of reality, which requires a multitude of complementary perspectives for its adequate expression. Thus, the century-old opposition between objectivism and relativism in the philosophy of science is removed.
What does not satisfy me in that theory [quantum mechanics], from the standpoint of principle, is its attitude towards that which appears to me to be the programmatic aim of all physics: the complete description of any (individual) real situation (as it supposedly exists irrespective of any act of observation or substantiation). Albert Einstein, Reply to Criticisms [This] implies the impossibility of any sharp separation between the behaviour of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear . In fact, the individuality of the typical quantum effects finds its proper expression in the circumstance that any attempt of subdividing the phenomena will demand a change in the experimental arrangement introducing new possibilities of interaction between objects and measuring instruments which in principle cannot be controlled. Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the objects. Indeed the finite interaction between object and measuring agencies conditioned by the very existence of the quantum of action entails – because of the impossibility of controlling the reaction of the object on the measuring instruments, if these are to serve their purpose – the necessity of a final renunciation of the classical idea of causality and a radical revision of our attitude towards the problem of physical reality. […]
In spite of the recent extraordinary progresses of experimental techniques it does not seem that, after more than seventy years from the birth of quantum mechanics, a unanimous consensus has been reached in the physicist's community on how to understand the "strange" properties of quantons, the wavelike/particlelike objects of the quantum world. In the first paragraph I will briefly recall some results on the problem of decoherence in large quantum systems, which at the same time may be viewed as an attempt of providing a "realistic" physical interpretation of the standard mathematical formulation of the theory. In the following ones I will present a derivation from first principles of the Wigner representation of quantum mechanics in phase space which eliminates altogether from the theory the Schrödinger waves and their questionable properties. This approach leads to the conclusion that the wave/particle duality has nothing to do with "probability waves", but is simply the manifestation of two complementary aspects (continuity vs. discontinuity) of an intrinsically nonlocal physical entity (the quantum field) which objectively exists in ordinary three dimensional space.