UnRAVeL Survey Lecture: Erich Grädel: Hidden Variables in Quantum Mechanics and Logics of Dependence and Independence

Thursday, April 29, 2021, 4:30pm

Speaker: Erich Grädel

 

Abstract:

Hidden-variable models have been proposed since the 1920s as an alternative to the dominant interpretation of quantum mechanics, with the goal to explain and remove certain counterintuitive aspects of quantum mechanics.

We show that logics of dependence and independence, based on team semantics,  provide adequate frameworks for reasoning about hidden-variable models and their purely probabilistic or relational abstractions.

Common desirable properties of hidden-variable models can be defined in an elegant and concise way in dependence and independence logic. The relationship between different properties and their simultaneous realisability can thus be formulated and proven on a purely logical level, as problems of entailment and satisfiability of logical formulae.

Connections between probabilistic and relational entailment in dependence and independence logic allow us to simplify proofs. In many cases, we can establish results on both probabilistic and relational hidden-variable models by a single proof, because one case implies the other, depending on purely syntactic criteria.

We also discuss the famous "no-go“ theorems by Bell and Kochen-Specker and provide a purely logical variant of the latter, introducing non-contextual choice as a team-semantical property.

 

The talks of the UnRAVeL survey lecture 2021 will be given via Zoom every Thursday from 16:30 to 18:00:

Zoommeeting

Meeting ID: 960 4371 5437

Passcode: 039217