An Operationalist Perspective on Setting Dependence

Abstract

A well known logical loophole for Bell's theorem is that it relies on setting independence: the assumption that the state of a system is independent of the settings of a measurement apparatus probing the system. In this paper the implications of rejecting this assumption are studied from an operationalist perspective. To this end a generalization of the ontic models framework is proposed that allows setting dependence. It is shown that within this framework Bell's theorem reduces to the conclusion that no-signaling requires randomness at the epistemic level even if the underlying ontology is taken to be deterministic. The ideas underlying the framework are further used to defend setting dependence against the charges of being incompatible with free will and scientific methodology. The paper ends however with the sketch of a new problem for setting dependence: a necessary gap between the ontic and the epistemic level that may prevent the formulation of a successful setting dependent theory.

How Real are Quantum States in $$\psi$$-Ontic Models?

“…After all, we also do not expect that quantum states will be fundamental in such a theory [8]. The further assumption is that at this level the choice of the measurement is independent of the state of the system [22]. physics, take an approximately analogous position to the statistical mechanics within the framework of classical mechanics.…”

Completely real? A critical note on the claims by Colbeck and Renner

“…6 See(Halvorson, 2019) for further discussion. 7 See for example(Hermens, 2019). 8 It deserves to be noted though that the approach of Colbeck and Renner is rather unorthodox.…”

Teoria de recursos para contextualidade generalizada

“…The definition of a prepare-and-measure scenario takes into account the works of (Duarte and Amaral, 2018), (Hermens, 2019) and (Leifer, 2014). We have then a complete prescription of an operational prepare-and-measure scenario, which will be fundamental for our future considerations.…”

“…Each operational primitive has an ontological counterpart. We will present here the ontological models' framework, following (Hermens, 2019) and (Leifer, 2014). An ontological model constitutes then constructing a pair (Λ, Σ) and the ontological counterparts for the operational primitives (Π, Θ).…”

“…In (Kunjwal and Spekkens, 2015), the authors notice that for finitely defined prepare-and-measure scenarios, the set Λ always has finite cardinality, and therefore he only considers a discrete version of definition 10. In (Morris, 2009) and (Hermens, 2019), the authors notice that there exists a formal and general approach for defining the ontological description for the operational primitives for arbitrary sets Λ: for the measurement procedures, we associate Markov kernels, or also, fuzzy indicator functions; and for the epistemic states, they construct measures µ associated with each preparation procedure.…”