Motivation for Part II

Lukas Burgholzer, Robert Wille

Peter Millington

Lukas Burgholzer, Robert Wille

James L Park

This portion of the essay concludes a two-part paper, Part I of which appeared in an earlier issue of this Journal. Part II begins with a careful study of the quantum description of real experiments in order to motivate a proposal that two distinct quantum theoretical measurement constructs should be recognized, both of which must be distinguished from the concept of preparation. The different epistemological roles of these concepts are compared and explained. It is then concluded that the only possible type of “quantum measurement theory” is one of little metaphysical interest and that quantum measurement seems problematical only when viewed from an overly narrow classical perspective.

Juno Ryu

In this article, a new topological way to define first quantization procedure is overviewed. Technical ingredients and metaphysical ideas used throughout this series of works are introduced in a way as non-technical as possible for motivating both physically and mathematically interested readers. This overview contains schematic summary of part II and part III of this series.

Christopher John Isham, Jeremy Butterfield

In a previous paper, we have proposed assigning as the value of a physical quantity in quantum theory, a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a valuation illuminates the Kochen-Specker theorem; and in part mathematical---the valuation arises naturally in the topos theory of presheaves. This paper discusses the conceptual aspects of this proposal. We also undertake two other tasks. First, we explain how the proposed valuations could arise much more generally than just in quantum physics; in particular, they arise as naturally in classical physics. Second, we give another motivation for such valuations (that applies equally to classical and quantum physics). This arises from applying to propositions about the values of physical quantities some general axioms governing partial truth for any kind of proposition.