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The British Journal for the Philosophy of Science 2007 58(4):805-867; doi:10.1093/bjps/axm034
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Copyright © The Author 2007. Published by Oxford University Press on behalf of British Society for the Philosophy of Science.

Stochastic Einstein Locality Revisited

Jeremy Butterfield

Trinity College, Cambridge CB2 1TQ, UK

jb56{at}cam.ac.uk


  Abstract

I discuss various formulations of stochastic Einstein locality (SEL), which is a version of the idea of relativistic causality, that is, the idea that influences propagate at most as fast as light. SEL is similar to Reichenbach's Principle of the Common Cause (PCC), and Bell's Local Causality.

My main aim is to discuss formulations of SEL for a fixed background spacetime. I previously argued that SEL is violated by the outcome dependence shown by Bell correlations, both in quantum mechanics and in quantum field theory. Here I reassess those verdicts in the light of some recent literature which argues that outcome dependence does not violate the PCC. I argue that the verdicts about SEL still stand.

Finally, I briefly discuss how to formulate relativistic causality if there is no fixed background spacetime.

1 Introduction
2 Formulating Stochastic Einstein Locality
2.1 Events and regions
2.2 The idea of SEL
2.3 Three formulations of SEL
2.3.1 The formulations
2.3.2 Comparisons

2.4 Implications between the formulations
2.4.1 Conditions for the equivalence of SELD1 and SELD2
2.4.2 Conditions for the equivalence of SELS and SELD2


3 Relativistic Causality in the Bell Experiment
3.1 The background
3.1.1 The Bell experiment reviewed
3.1.2 My previous position

3.2 A common common cause? The Budapest school
3.2.1 Resuscitating the PCC
3.2.2 Known proofs of a Bell inequality need a strong PCC
3.2.3 Two distinctions
3.2.4 Szabó's model
3.2.5 A common common cause is plausible
3.2.6 Bell inequalities from a weak PCC: the Bern school

3.3 SEL in the Bell experiment
3.3.1 PCC and SEL are connected by PPSI
3.3.2 The need for other judgments
3.3.3 Weak vs. strong SELD


4 SEL in Algebraic Quantum Field Theory
4.1 The story so far
4.2 Questions
4.2.1 Our formulations
4.2.2 The Budapest and Bern schools


5 SEL in Dynamical Spacetimes
5.1 SEL for metric structure?
5.2 SEL for causal sets?
5.2.1 The causal set approach
5.2.2 Labelled causal sets; general covariance
5.2.3 Deducing the dynamics
5.2.4 The fate of SEL



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