A Problem from Quantum Theory

Isham, C J, Butterfield, J

We discuss some ways in which topos theory (a branch of category theory) can be applied to interpretative problems in quantum theory and quantum gravity. In Section 1, we introduce these problems. In Section 2, we introduce topos theory, especially the idea of a topos of presheaves. In Section 3, we discuss several possible applications of topos theory to the problems in Section 1. In Section 4, we draw some conclusions.

Francis J. Narcowich

J. Anandan

Abstract Department of Physics and Astronomy University of South Carolina, Columbia, SC 20208, USA [AF] Two of the most important unsolved problems in theoretical physics are the problem of quantizing gravitation and the measurement problem in quantum theory. It is possible that the solution of each one needs the other. Since we have successful quantum theories of electroweak, and strong interactions, the solution to the problem of the collapse of the wave function, known as the measurement problem, may lie in the yet unknown quantum theory of the remaining interaction, namely quantum gravity. On the other hand, the numerous unsuccessful attempts to construct a quantum theory of gravity for more than six decades on the assumption that the present linear quantum theory is correct suggests that perhaps not only general relativity but also quantum theory should be modified in order to construct of satisfactory quantum theory of gravity.

Piotr Garbaczewski, Robert Olkiewicz

Holger Lyre

Quantum theory is a tremendously successful physical theory, but nevertheless suffers from two serious problems: the measurement problem and the problem of interpretational underdetermination. The latter, however, is largely overlooked as a genuine problem of its own. Both problems concern the doctrine of realism, but pull, quite curiously, into opposite directions. The measurement problem can be captured such that due to scientific realism about quantum theory common sense anti-realism follows, while theory underdetermination usually counts as an argument against scientific realism. I will also consider the more refined distinctions of ontic and epistemic realism and demonstrate that quantum theory in its most viable interpretations conflicts with at least one of the various realism claims. A way out of the conundrum is to come to the bold conclusion that quantum theory is, possibly, wrong (in the realist sense).

Paolo Vanini