Minimax context principle

Abstract

I show how space-like structures emerge within the topos-based approach to quantum mechanics. With a physical system, or, more generally, with an operationalistic setup a context category is associated being in fact an ordered collection of contexts. Each context, in turn, is associated with certain configuration space. The minimax context principle is put forward. Its basic idea is that among various configuration spaces the `physical space' is the configuration space of a structureless point particle. In order to implement it, two order relations on contexts are introduced being analogs of inner and outer daseinisation of projectors. The proposed minimax context principle captures two characteristic features of physical space: maximal with respect to refining the accuracy, and minimal by getting rid of extra degrees of freedom.

Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications, Kosheleva, O., Shary, S.P., Xiang, G., Zapatrin, R. (Eds.), 9 pages, to appear in March, 2020

References in corpus (4)

• A Topos Foundation for Theories of Physics: I. Formal Languages for Physics
• A Topos Foundation for Theories of Physics: II. Daseinisation and the Liberation of Quantum Theory
• A Topos Foundation for Theories of Physics: III. The Representation of Physical Quantities With Arrows
• Lectures on Topos Quantum Theory