Bell mini conference RDG.pptx
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1) The document discusses Marian Kupczynski's paper on whether John Bell would choose contextuality or nonlocality today based on graphical models representing random variables. 2) It presents a graphical model showing source hidden variables, context dependent instrument hidden variables, and Alice and Bob's outcome variables that may be correlated. 3) It notes that assuming the instrument hidden variables are uncorrelated leads to the CHSH inequality holding, while allowing them to be correlated allows any four joint probability distributions, and discusses Kupczynski's consideration of the detection loophole.
Bell mini conference RDG.pptx
- 1. Richard D. Gill, Bell mini-conference February 11 2023 Comment on Contextuality or Nonlocality: What Would John Bell Choose Today? by Marian Kupczynski Entropy 2023, 25, 280 (13pp.). https://doi.org/10.3390/e25020280
- 2. Entropy 2023, 25, 280 (13pp.). https://doi.org/10.3390/e25020280
- 3. Random variables are represented by nodes in a DAG Their joint probability distribution is built up by composing conditional distributions of the variable in each node given its node parents (Variables in root nodes are statistically independent of one another) Why this works: the nodes of a DAG can be ordered so that all arrows are pointing the same way Express in a graphical model
- 4. i, j 1, 2 i, j Ai(1, i) Bj(2, j) ~ ~ Settings (may be correlated) Source hidden variables (may be correlated) Context dependent instrument hidden variables (may be correlated) Alices outcome +/1 Bobs outcome +/1 Notice:
- 5. If the instrument hidden variables i, j are allowed to be statistically dependent, then any four joint probability distributions of pairs of setting outcomes (Ai, Bj) are allowed If the instrument hidden variables are assumed to be uncorrelated, then CHSH holds (Gill and Lambare) MKs escape route: the detection loophole. Outcome can also be zero, and MK goes on to study correlations conditional on two non-zero outcomes The cause of the muddle: bad notation The dilemma Kupczynksis quandrary