“The Common Logical Structure of Classical and Quantum Mechanics (and All Scientific Theories)”

Gabriele Carcassi

Abstract: In this presentation we will see that the logical structures of classical and quantum theory are both instances of a common structure that is necessary to all scientific  theories (i.e. theories connected to experimental verification). We will see that the seeming incompatibility of classical logic with quantum mechanics stems from muddling temporal or statistical considerations. These issues can be resolved by clarifying the full meaning of the statements, which will require us to consider all statistically relevant statements, and not only those about single-shot measurements. Once this is done, a complete parallel can be made (e.g. both theories provide both a distributive and non-distributive lattice) in terms of basic and well-known mathematical structures. We will see that, in general, if one wants to describe a physical theory where each statement is linked, at least in line of principle, with an experimental test, a similar structure necessarily emerges.