David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 128 (3):343 - 379 (2001)
Since the validity of Bell's inequalities implies the existence of joint probabilities for non-commuting observables, there is no universal consensus as to what the violation of these inequalities signifies. While the majority view is that the violation teaches us an important lesson about the possibility of explanations, if not about metaphysical issues, there is also a minimalist position claiming that the violation is to be expected from simple facts about probability theory. This minimalist position is backed by theorems due to A. Fine and I. Pitowsky.Our paper shows that the minimalist position cannot be sustained. To this end,we give a formally rigorous interpretation of joint probabilities in thecombined modal and spatiotemporal framework of `stochastic outcomes inbranching space-time' (SOBST) (Kowalski and Placek, 1999; Placek, 2000). We show in this framework that the claim that there can be no joint probabilities fornon-commuting observables is incorrect. The lesson from Fine's theorem is notthat Bell's inequalities will be violated anyhow, but that an adequate modelfor the Bell/Aspect experiment must not define global joint probabilities. Thus we investigate the class of stochastic hidden variable models, whichprima facie do not define such joint probabilities. The reasonwhy these models fail supports the majority view: Bell's inequalities are notjust a mathematical artifact.
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Citations of this work BETA
Thomas Müller (2010). Towards a Theory of Limited Indeterminism in Branching Space-Times. Journal of Philosophical Logic 39 (4):395 - 423.
Thomas Muller (2007). A Branching Space-Times View on Quantum Error Correction. Studies in History and Philosophy of Science Part B 38 (3):635-652.
Leszek Wroński & Tomasz Placek (2009). On Minkowskian Branching Structures☆. Studies in History and Philosophy of Science Part B 40 (3):251-258.
Nuel Belnap (2012). Newtonian Determinism to Branching Space-Times Indeterminism in Two Moves. Synthese 188 (1):5-21.
Thomas Müller & Niko Strobach (2012). A Letter on the Present State of Affairs. Synthese 188 (3):469-485.
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