July 18, 2024
Quantum Limits of Knowledge 2021 Monday 29th March, 2021 Branching space-times (BST), due to Belnap (Synthese, 1992), is a rigorous formal framework for representing indeterministic scenarios in spatio-temporal detail. BST has the resources for defining precise notions of modal and probabilistic correlations, aka funny business. Modal funny business is, to put it informally, an unexpected failure of locally possible outcomes to combine to a globally possible joint outcome. Similarly, probabilistic funny business occurs when 13 local outcomes have joint probabilities that do not factor in the way one would expect them to. Given these notions, BST is well suited for representing and analyzing quantum correlation experiments, which are intricate spatio-temporal arrangements that can exhibit strange correlations. In this talk, we consider only modal correlations, such as exhibited in the GHZ experiment. Ever since Einstein, Podolsky, and Rosen (1935), there has been a quest for providing extended descriptions of quantum correlation experiments that avoid the troublesome correlations by adding hidden variables. In BST, we can characterize different ways in which the given surface structure of such experiments can be extended, and for this analysis, it is crucial to spell out what it means to represent a quantum correlation experiment not just as a spatio-temporal happening, but specifically as an experiment. It turns out that in experiments, two types of indeterminism need to be explicitly distinguished. We will show in BST terms which role this distinction plays in deriving “no go” results for hidden variables.