Related papers: An impossibility theorem for Parameter Independent…
A 1964 paper by John Bell gave the first demonstration that quantum mechanics is incompatible with local hidden variables. There is an ongoing and vigorous debate on whether he relied on an assumption of determinism, or instead, as he later…
We establish an equivalence between two seemingly different theories: one is the traditional axiomatisation of incomplete preferences on horse lotteries based on the mixture independence axiom; the other is the theory of desirable gambles…
We develop a framework that leverages the smoothed complexity analysis by Spielman and Teng to circumvent paradoxes and impossibility theorems in social choice, motivated by modern applications of social choice powered by AI and ML. For…
Free choice (or statistical independence) assumption in a hidden variable model (HVM) means that the settings chosen by experimenters do not depend on the values of the hidden variable. The assumption of context-independent (CI) mapping in…
Conventional quantum mechanics with a complex Hilbert space and the Born Rule is derived from five axioms describing properties of probability distributions for the outcome of measurements. Axioms I,II,III are common to quantum mechanics…
In the book [4] the general problem of reconstructing the Hilbert space formulation in quantum theory is discussed from the point of view of what I called conceptual variables, any variables defined by a person or by a group of persons.…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
The hidden-variable question is whether or not various properties --- randomness or correlation, for example --- that are observed in the outcomes of an experiment can be explained via introduction of extra (hidden) variables which are…
Whether the complex numbers of standard quantum theory are experimentally indispensable has remained open for decades. Real quantum theory (RQT), obtained by replacing complex amplitudes with real ones while retaining the usual…
The Bell inequality constrains the outcomes of measurements on pairs of distant entangled particles. The Bell contradiction states that the Bell inequality is inconsistent with the calculated outcomes of these quantum experiments. This…
Cromwell's rule (also known as the zero priors paradox) refers to the constraint of classical probability theory that if one assigns a prior probability of 0 or 1 to a hypothesis, then the posterior has to be 0 or 1 as well (this is a…
In 1935 Einstein, Podolsky and Rosen (EPR) pointed out that Quantum Mechanics apparently implied some mysterious, instantaneous action at a distance. This paradox is supposed to be related to the probabilistic nature of the theory, but…
It was shown by Bell that no local hidden variable model is compatible with quantum mechanics. If, instead, one permits the hidden variables to be entirely non-local, then any quantum mechanical predictions can be recovered. In this paper,…
In the first part of this presentation (sections 2 to 6), I show that Bell's Inequalities provide a quantitative criterion to test "reasonable" Supplementary Parameters Theories versus Quantum Mechanics. Following Bell, I first explain the…
We argue that randomized controlled trials (RCTs) are special even among settings where average treatment effects are identified by a nonparametric unconfoundedness assumption. This claim follows from two results of Robins and Ritov (1997):…
Bell's inequality is derived from three assumptions: measurement independence, outcome independence, and parameter independence. Among these, measurement independence, often taken for granted, holds that hidden variables are statistically…
Previously, we presented a new interpretation of quantum mechanics that revealed it is indeed possible to have a local hidden variable that is consistent with Bell's inequality experiments. In that article we suggested that the local hidden…
Self-testing--the attractive possibility to infer the underlying physics of a quantum device in a black-box scenario--has gained increased traction in recent years, with applications to device-independent quantum information processing.…
In a recent note, Hance and Hossenfelder (arXiv:2211.01331) recall that "locally causal completions of quantum mechanics are possible, if they violate the assumption [called statistical independence or measurement independence] that the…
In 1935, Albert Einstein and two colleagues, Boris Podolsky and Nathan Rosen (EPR) developed a thought experiment to demonstrate what they felt was a lack of completeness in quantum mechanics. EPR also postulated the existence of more…