相关论文: A Collection of Probabilistic Hidden-Variable Theo…

De Finetti's theorem, also called the de Finetti-Hewitt-Savage theorem, is a foundational result in probability and statistics. Roughly, it says that an infinite sequence of exchangeable random variables can always be written as a mixture…

We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…

The paper argues that far from challenging - or even refuting - Bohm's quantum theory, the no-hidden-variables theorems in fact support the Bohmian ontology for quantum mechanics. The reason is that (i) all measurements come down to…

Recently we have introduced a novel characterisation of the distribution of twin primes that consists of three essential elements. These are: that the twins are most naturally viewed as a subsequence of the primes themselves, that the…

We discuss some issues about probability in quantum mechanics, with particular emphasis on the GHZ theorem. We propose the usage of nonmonotonic upper probabilities as a tool to derive consistent joint upper probabilities for systems where…

This article investigates the difference between the true detection probability and the subjective probability of a uniformly optimal search plan. Its main contributions are multi-fold. First, it provides a set of examples to show that, in…

By examining two counterexamples to the existing theory, it is shown, with mathematical rigor, that as far as scattered particles are concerned the true distribution function is in principle not determinable (indeterminacy principle or…

This expository paper advocates an approach to physics in which ``typicality" is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and physics are reviewed. Their original versions…

Recently, [{arXiv:0810.3134}] is accepted and published. We present ultimate version of no-hidden-variables theorem. We derive a proposition concerning the quantum theory under the existence of the Bloch sphere in a single spin-1/2 system.…

Probabilistic databases (PDBs) introduce uncertainty into relational databases by specifying probabilities for several possible instances. Traditionally, they are finite probability spaces over database instances. Such finite PDBs…

We introduce an algebraic framework for interacting quantum systems that enables studying complex phenomena, characterized by the coexistence and competition of various broken symmetry states of matter. The approach unveils the hidden unity…

Entropic arguments are shown to play a central role in the foundations of quantum theory. We prove that probabilities are given by the modulus squared of wave functions, and that the time evolution of states is linear and also unitary.

We report a rigorous theory to show the origin of the unexpected periodic behavior seen in the consecutive differences between prime numbers. We also check numerically our findings to ensure that they hold for finite sequences of primes,…

Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…

A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…

The purpose of this article is to introduce the concept of invariance and its properties. These properties can be used to check the primality of a number. Combining these properties with the Euler theorem, it is possible to generalize this…

Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…

We generalise the Fundamental Theorem of Calculus to higher dimensions. Our generalisation is based on the observation that the antiderivative of a function of $n$-variables is a solution of a partial differential equation of order $n$…

To begin with, it is pointed out that the form of the quantum probabil- ity formula originates in the very initial state of the object system as seen when the state is expanded with the eigen-projectors of the measured ob- servable. Making…

We prove a uniqueness theorem for an entire function, which shares certain values with its higher order derivatives.