Related papers: A Collection of Probabilistic Hidden-Variable Theo…
The hidden-variables premise is shown to be equivalent to the existence of generic filters for algebras of commuting propositions and for certain more general propositional systems. The significance of this equivalence is interpreted in…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
An axiomatics for indistinguishability of elementary particles in terms of hidden variables is presented in a manner which depart from the standard approaches usually given to hidden variables. Quantum distribution functions are also…
Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's…
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
Hidden variables are extra components added to try to banish counterintuitive features of quantum mechanics. We start with a quantum-mechanical model and describe various properties that can be asked of a hidden-variable model. We present…
We extend to any maximally entangled state of a bipartite system whose constituents are arbitrarily (but finite) dimensional the result, recently derived for two-dimensional constituents, that hidden variable theories cannot have local…
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…
The main result presented in this article is that probability can fundamentally be characterized as a subset of conditional expectation induced by a plausible preorder on random quantities. This is justified by the fact that probability is…
We use a simple relational framework to develop the key notions and results on hidden variables and non-locality. The extensive literature on these topics in the foundations of quantum mechanics is couched in terms of probabilistic models,…
It is shown that Bell's counterfactuals admit joint quasiprobability distributions (i.e. joint distributions exist, but may not be non-negative). A necessary and sufficient condition for the existence among them of a true probability…
A very simple but useful almost sure convergence theorem of probability is given.
We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
Bell's theorem proves only that hidden variables evolving in true physical time can't exist; still the theorem's meaning is usually interpreted intolerably wide. The concept of hidden time (and, in general, hidden space-time) is introduced.…
This study has the purpose of addressing four questions that lie at the base of the probability theory and statistics, and includes two main steps. As first, we conduct the textual analysis of the most significant works written by eminent…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
It has recently been questioned whether the Kochen-Specker theorem is relevant to real experiments, which by necessity only have finite precision. We give an affirmative answer to this question by showing how to derive hidden-variable…
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.