THE PRINCIPLE OF SUPERPOSITION. The need for a quantum theory Classical mechanics has been developed continuously from the time of Newton and applied to an ...

I show that the standard approach to modeling phenomena involving microscopic classical electrodynamics is mathematically inconsistent. I argue that there is no conceptually unproblematic and consistent theory covering the same phenomena to which this inconsistent theory can be thought of as an approximation; and I propose a set of conditions for the acceptability of inconsistent theories.

I have argued that the standard ways of modeling classical particle-field interactions rely on a set of inconsistent assumptions. This claim has been criticized in (Muller forthcoming). In this paper I respond to some of Muller's criticism.

Mathias Frisch provides the first sustained philosophical discussion of conceptual problems in classical particle-field theories. Part of the book focuses on the problem of a satisfactory equation of motion for charged particles interacting with electromagnetic fields. As Frisch shows, the standard equation of motion results in a mathematically inconsistent theory, yet there is no fully consistent and conceptually unproblematic alternative theory. Frisch describes in detail how the search for a fundamental equation of motion is partly driven by pragmatic considerations (like (...) simplicity and mathematical tractability) that can override the aim for full consistency. The book also offers a comprehensive review and criticism of both the physical and philosophical literature on the temporal asymmetry exhibited by electromagnetic radiation fields, including Einstein's discussion of the asymmetry and Wheeler and Feynman's influential absorber theory of radiation. Frisch argues that attempts to derive the asymmetry from thermodynamic or cosmological considerations fail and proposes that we should understand the asymmetry as due to a fundamental causal constraint. The book's overarching philosophical thesis is that standard philosophical accounts that strictly identify scientific theories with a mathematical formalism and a mapping function specifying the theory's ontology are inadequate, since they permit neither inconsistent yet genuinely successful theories nor thick causal notions to be part of fundamental physics. (shrink)

In this article the Dirac equation is used a guideline to see the historical emergence of the concept of quanta, associated with the quantum field. In P. Jordan’s approach, the electron as quanta results from the quantization of a classical field described by the Dirac equation. The concept of quanta becomes a central piece in the applications of the theory and is seen as fundamental in the intelegibility of the interaction between fields, being the Fock space the natural mathematical structure (...) that permits maintaining the quanta concept when considering interactions. This doesn’t seem to avoid the apparent impossibility of using the concept of quanta – and with it the common interpretation of quantum field, when interacting fields are considered together as one complete system. In this article it is defended that the type of analysis that leads itself to so drastic conclusions is avoidable if a clear distinction is made of the theoretical framework and particular models used in the empirical corroboration of the theory. When dealing with models there is really no complete interacting fields, and what we have is a description of interaction between distinct fields. In this situation the concept of quanta is central in the description of interacting fields. (shrink)

The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is (...) Heisenberg's `quantum-theoretical Umdeutung (reinterpretation) of classical observables', which lies at the basis of quantization theory. Similarly, Bohr's correspondence principle (in somewhat revised form) and Schroedinger's wave packets (or coherent states) continue to be of great importance in understanding classical behaviour from quantum mechanics. On the other hand, no consensus has been reached on the Copenhagen Interpretation, but in view of the parodies of it one typically finds in the literature we describe it in detail. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), in the limit N goes to infinity of a large system with $N$ degrees of freedom (at fixed h), and through decoherence and consistent histories. The first limit is closely related to modern quantization theory and microlocal analysis, whereas the second involves methods of C*-algebras and the concepts of superselection sectors and macroscopic observables. In these limits, the classical world does not emerge as a sharply defined objective reality, but rather as an approximate appearance relative to certain ``classical" states and observables. Decoherence subsequently clarifies the role of such states, in that they are ``einselected", i.e. robust against coupling to the environment. Furthermore, the nature of classical observables is elucidated by the fact that they typically define (approximately) consistent sets of histories. This combination of ideas and techniques does not quite resolve the measurement problem, but it does make the point that classicality results from the elimination of certain states and observables from quantum theory. Thus the classical world is not created by observation (as Heisenberg once claimed), but rather by the lack of it. (shrink)

— Niels Bohr, 19231 “There must be quite definite and clear grounds, why you repeatedly declare that one must interpret observations classically, which lie absolute ly in thei r essenc e. . . . It must belong to your deepest conviction—and I cannot understand on what you base it.”.

The lowest order processes described within quantum electrodynamics are free from the problems of infinites in the theory, and can be dealt with disregarding the need for charge and mass renormalization. This might indicate that the space-time description of these processes is not only consistent but also could give a privileged insight to the functioning of models provided by the theory. The Møller scattering is as R. P. Feynman considered, a prototype for the development of his rules of quantum electrodynamics (...) and his overall space-time approach. The study of Møller scattering might then provide the must straightforward way to the understanding of the space-time description of interactions provide by quantum electrodynamics. This method is much less powerful than might be expected at first, pointing to the intrinsic limitations of the theory in what regards the modelling of the temporality in interaction processes. (shrink)