Examining relativistic quantum eld theory we claim that its description of subnuclear phenomena can be understood most adequately from a semiotic point of view. The paper starts o with a concise and non-technical outline of the rmly based aspects of relativistic quantum eld theories. The particular methods, by which these dierent aspects have to be accessed, can be described as distinct facets of quantum eld theory. They dier with respect to the rela-tion between quantum elds and associated particles, and, as we shall argue, should be interpreted as complementary (semiotic) codes. Viewing physical theories as symbolic constructions already came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic eld from mechanics; most notably, as we will point out, with the work of Helmholtz, Hertz, Poincare, and later on Weyl. Since the epistemological questions posed there are heightened with regard to quantum eld theory, we considerably widen their approach and relate it to recent discussions in the philosophy of science, like structural realism and quasi-autonomous domains.
Examining relativistic quantum eld theory we claim that its description of subnuclear phenomena can be understood most adequately from a semiotic point of view. The paper starts o with a concise and non-technical outline of the rmly based aspects of relativistic quantum eld theories. The particular methods, by which these dierent aspects have to be accessed, can be described as distinct facets of quantum eld theory. They dier with respect to the rela-tion between quantum elds and associated particles, and, as we shall argue, should be interpreted as complementary (semiotic) codes. Viewing physical theories as symbolic constructions already came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic eld from mechanics; most notably, as we will point out, with the work of Helmholtz, Hertz, Poincare, and later on Weyl. Since the epistemological questions posed there are heightened with regard to quantum eld theory, we considerably widen their approach and relate it to recent discussions in the philosophy of science, like structural realism and quasi-autonomous domains.
When a physical theory is in its early stages of development, it presents many concepts and constructs that may not be necessary for its interpretation, or may simply be equivocal. As the theory is developed by the physics community, it hopefully passes through a depuration process that washes away many of these constructs and introduces others not initially devised. This process can be viewed, and modeled, as a semiotic process by which the suggested interpretations of the theory, initially dispersed in the space of concepts, taper off in a way that leaves only a small number of possibilities, ideally only one. However, to qualify this process and impose semiotic and epistemological constraints on the depuration process, it seems natural to consider a physical theory as an excerpt of a language and its suggested interpretations as texts, endowed with syntactics and semantics. In this paper we present this framing of general physical theories and apply the resulting semiotic and epistemological constraints we uphold to the special case of quantum mechanics, which shows particular resistance to interpretation tapering. We then show that the findings of this paper are especially important for allowing one to form a hierarchy of interpretations of the same formal structure of a physical theory, even in the case of an experimental underdetermination of these interpretations, which is precisely the case for quantum mechanics. This result is particularly important for more modern physical theories, which are becoming increasingly more abstract and difficult to interpret.
The mathematical description of quantum systems univocally identies their nature. In other words we treat a system as quantum if we describe its behaviour adopting Hilbert spaces and structures thereof, as prescribed by the postulates of quantum theory. The choice of using quantum systems as the elementary systems of physics can be justied in terms of informational principles, thanks to results of the last decade. Such results come as the conclusion of a research program that lasted almost one century, with the aim of reformulating quantum theory in terms of operational principles. This achievement now poses a new challenge, that we face here. If the systems of quantum theory are thought of as elementary information carriers in the rst place, rather than elementary constituents of matter, and their connections are logical connections within a given algorithm, rather than space-time relations, then we need to nd the origin of mechanical concepts—that characterise quantum mechanics as a theory of physical systems. To this end,we will illustrate howphysical laws can be viewed as algorithms for the update of memory registers that make a physical system. Imposing the characteristic properties of physical laws to such an algorithm, i.e. homogeneity, reversibility and isotropy, we will show that the physical laws thus selected are particular algorithms known as cellular automata. Further assumptions regarding maximal simplicity of the algorithm lead to two cellular automata only, that in a suitable regime can be described by Weyl’s dierential equations, lying at the basis of the dynamics of relativistic quantum elds. We will nally discuss how the same cellular automaton can give rise to both Fermionic eld dynamics and to Maxwell’s equations, that rule the dynamics of the electromagnetic eld. We will conclude reviewing the discussion of the relativity principle, that must be suitably adapted to the scenario where space-time is not an elementary notion, through the denition of a change of inertial reference frame, and whose formulation leads to the recovery of the symmetry of Minkowski space-time, identied with Poincar´e’s group. Space-time thus emerges as one of the manifestations of physical laws, rather than the background where they occur, and its features are determined by the dynamics of systems, necessarily equipped with dierential equations that express it. In brief, there is no space-time unless an evolution rule requires it.
Up to this point, our study of quantum mechanics has concerned itself with the behaviour of particles that inhabit a Galilean spacetime. For many purposes, in atomic, molecular and condensed matter physics, this theory is quite adequate. We saw in earlier chapters, however, that our actual spacetime has a structure which is much closer to that of the Minkowski spacetime of special relativity and that more general structures must be considered when gravitational phenomena are signicant. From a purely theoretical point of view, it is therefore important to formulate quantum theory in a way which is consistent with these more general spacetimes. The benets of constructing a relativistic quantum theory actually go far beyond the aesthetic satisfaction of making our geometrical and quantum-mechanical reasoning compatible. For one thing, we shall discover that the relativistic theory provides a deeper understanding of spin and the distinction between fermions and bosons, which in the non-relativistic theory appear simply as facts of life that we must strive to accommodate. Also, of course, there are many situations in which relativistic eects become observable, for which non-relativistic theory provides no explanation. The most obvious are high-energy scattering experiments, in which particles acquire kinetic energies comparable with or greater than their rest energies mc2, and the correct 4-momentum (3.33) must be used. There are, however, more subtle eects, such as the spin-orbit coupling that is essential for interpreting atomic spectra, which are also of relativistic origin.
Beginning in 1900 with 1-iax Planck's hypothesis of quanta, physics has been embarked on a course which has raised serious questions about the true nature of physical reality, about the foundational assumptions and structures of science, and about the relationships between physical reality and physical theory. In particular, attempts to give a physical interpretation to quantum theory seem to result in "pictures" of nature which are paradoxical. A subatomic entity is described by the theory as exhibiting the properties and behavior of both particle-like phenomena and wavelike phenomena. Since it seems unreasonable that a single entity could be both a point-like mass and a wave spread out through a region of space, quantum theory would seem to be less than satisfactory or less than complete at the interpretational level. The purpose of this dissertation is to investigate the underlying causes of this paradox. The dissertation proceeds by reviewing the development of quantum theory and the emergence of the paradox. Next, the problem of physical interpretation is examined and several of the more significant existing interpretations are discussed and analyzed. Finally, the foundations of science and the general structure of scientific theory are examined in a search for the origins of the paradox. As a result of these investigations and analyses, it is concluded that the paradoxical nature of the physical interpretation of quantum theory is the consequence of certain paradigms and preconceptualizations about physical reality which have been incorporated into the theory at the foundational level. These fundamental assU14ptions produce, within quantum theory, a forced marriage of the plenum and atomic views of physical reality. They also produce an ambiguity with respect to the nature of causality which is charaeteristic of the theory. These problems are reflected in the mathematical formalisms and physical concepts of the theory as well as in its metaphysical foundations. Lastly, methods of resoling the paradox are discussed. It is argued that a successful solution is possible, but that it would involve the creation of a new metaphor-an extension of the present language--which would lead science to a deeper, subquantum level in terms of which the present paradox would vanish.
Abstract One can consider the developments in quantum field theory from the point of view of foundational problems posed about physical reality at both the epistemological and ontological levels, or as a ‘laboratory’ to study the actual methodology of the scientific enterprise. I shall address both of these issues in this paper. My contention is that at the foundational level there is essentially nothing new in quantum field theory that is not already present in non-relativistic quantum mechanics. This is quite different in emphasis from the view expressed by Redhead (1983a). Even in quantum mechanics most of the difficulties which arise are generated by the realist’s inclination to take the formalism too literally as representing physical reality, often in a modified or distorted classical view. More serious consideration of Bohr’s philosophical framework of complementarity may prove fruitful for coping with this problem, which is not new to quantum field theory, being already the central interpretative problem of quantum mechanics. On the other hand, as a source to illustrate how theories arc constructed and established in actual scientific practice, quantum field theory does provide a wide range of useful examples. Here too, although there are many technically fascinating topics (such as renormalization), quantum field theory is pretty much (meth odological) business as usual. Much more interesting, essentially new, methodological departures are seriously proposed (with varying degrees of credibility) by some rival or alternative developments in modern theoretical physics, such as the S-matrix programme, with its bootstrap conjecture, or cosmology, with various forms of the anthropic principle (Gale 1983) and with the inflationary universe scenario (Guth 1981 ).
Up to this point, our study of quantum mechanics has concerned itself with the behaviour of particles that inhabit a Galilean spacetime. For many purposes, in atomic, molecular and condensed matter physics, this theory is quite adequate. We saw in earlier chapters, however, that our actual spacetime has a structure which is much closer to that of the Minkowski spacetime of special relativity and that more general structures must be considered when gravitational phenomena are significant. From a purely theoretical point of view, it is therefore important to formulate quantum theory in a way which is consistent with these more general spacetimes. The benefits of constructing a relativistic quantum theory actually go far beyond the aesthetic satisfaction of making our geometrical and quantummechanical reasoning compatible. For one thing, we shall discover that the relativistic theory provides a deeper understanding of spin and the distinction between fermions and bosons, which in the non-relativistic theory appear simply as facts of life that we must strive to accommodate. Also, of course, there are many situations in which relativistic effects become observable, for which nonrelativistic theory provides no explanation. The most obvious are high-energy scattering experiments, in which particles acquire kinetic energies comparable with or greater than their rest energies mc2, and the correct 4-momentum (3.34) must be used. There are, however, more subtle effects, such as the spin-orbit coupling that is essential for interpreting atomic spectra, which are also of relativistic origin.