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(Based on joint work with Ronnie Hermens and Gijs Leegwater.) The experimental violation of the Bell inequalities is standardly understood as implying some form of nonlocality, either as a violation of Outcome Independence (OI) or of Parameter Independence (PI). The former is seen as compatible with relativity because it does not allow for signalling across entangled pairs, while the the latter is seen as incompatible with relativity because there is a sense in which it allows to signal in principle. Experimental loopholes causing spurious violations of either condition have now been closed, arguably allowing one to draw these conclusions purely on the basis of experimental results – a venture dubbed ‘experimental metaphysics’ by Shimony.
There are well-known qualifications to be made to the significance of these conclusions to some form of nonlocality (e.g. Jones and Clifton), but the most important one is that the derivation of the Bell inequalities assumes also that the distribution of any hidden variables be independent of the (future) measurement settings, a condition known as Measurement Independence (MI). Violations of MI are often seen as conspiratorial, and recent experiments such as the cosmic Bell test (Handsteiner et al.) constrain extremely severely such conspiratorial violations. But there are non-spurious violations of MI in approaches to quantum mechanics based on retrocausation and/or global constraints, which arguably allow one to explain the violations of the Bell inequalities in a local way (cf. Price).
In this talk, we extend the programme of experimental metaphysics to include violations of MI. We first introduce a sense in which also genuine violations of MI allow in principle to signal across entangled pairs. This is a sense of ‘signalling in principle’ that is analogous to but distinct from the one relevant in violations of PI. The putative causal mechanism behind such signalling is also different, being not spacelike but a timelike zig-zag backwards and forwards. Our result relies on the ‘equiprobability theorem’ by Barrett, Kent and Pironio, and generalises it to the case in which no MI is assumed. We then show that the result is quantitatively robust when applied to the setting of the Bell inequalities. With some caveats that we discuss, the upshot is that the experimental violations of the Bell inequalities always imply some form of nonlocality: without signalling and compatible with relativity in the case of OI, with signalling and incompatible with relativity in the case of PI, and with signalling but compatible with relativity in the case of MI – thus completing the programme of experimental metaphysics.