Related papers: The extension problem for partial Boolean structur…
The standard formulation of Quantum Mechanics violates locality of interactions and the action reaction principle. An alternative formulation in an extended phase space could preserve both principles, but Bell's theorems show that a…
On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the so-called Misra-Bugajski reduction map. We…
Classical mechanics is presented here in a unary operator form, constructed using the binary multiplication and Poisson bracket operations that are given in a phase space formalism, then a Gibbs equilibrium state over this unary operator…
The hilbert-space structure of quantum mechanics is related to the causal structure of space-time. The usual measurement hypotheses apparently preclude nonlinear or stochastic quantum evolution. By admitting a difference in the calculus of…
Both the quantum mechanical and classical Bells experiment are within the focus of this paper. The fact that one measures different probabilities in both experiments is traced back to the superposition of two orthogonal but nonentangled…
The concept of complementarity in combination with a non-Boolean calculus of propositions refers to a pivotal feature of quantum systems which has long been regarded as a key to their distinction from classical systems. But a non-Boolean…
Bell nonlocality and Kochen-Specker contextuality are among the main topics of foundations of quantum theory. Both of them are related to stronger-than-classical correlations, with the former usually referring to spatially separated systems…
It is shown that the Bell inequalities are closely related to the triangle inequalities involving distance functions amongst pairs of random variables with values $\left\{ 0,1\right\} $. A hidden variables model may be defined as a mapping…
The discussion of the foundations of quantum mechanics is complicated by the fact that a number of different issues are closely entangled. Three of these issues are i) the interpretation of probability, ii) the choice between realist and…
We discuss the distinction between the notion of partial observable and the notion of complete observable. Mixing up the two is frequently a source of confusion. The distinction bears on several issues related to observability, such as (i)…
Research in the application of quantum structures to cognitive science confirms that these structures quite systematically appear in the dynamics of concepts and their combinations and quantum-based models faithfully represent experimental…
In spite of all {\bf no-go} theorems (e.g., von Neumann, Kochen and Specker,..., Bell,...) we constructed a realist basis of quantum mechanics. In our model both classical and quantum spaces b are rough images of the fundamental {\bf…
We construct the most general form of our previously proposed nonlinear extension of quantum mechanics that possesses three basic properties. Unlike the simpler model, the new version is not completely integrable, but it has an underlying…
Almost all representations considered in computable analysis are partial. We provide arguments in favor of total representations (by elements of the Baire space). Total representations make the well known analogy between numberings and…
Using a quantum like algebraic formulation we give proof of Kochen-Specker theorem. We introduce new criteria in order to account for the contextual nature of measurements in quantum mechanics.
A problem with an instructive description of measurement process for sufficiently separated entangled quantum systems is well known. More precise and crafty experiments together with new technological challenges raise questions about…
Contextuality, the impossibility of assigning a single random variable to represent the outcomes of the same measurement procedure under different experimental conditions, is a central aspect of quantum mechanics. Thus defined, it appears…
Fully revealing the mathmatical structure of quantum contextuality is a significant task, while some known contextuality theories are only applicable for rank-1 projectors. That is because they adopt the observable-based definitions. This…
Bell's theorem reveals a profound conflict between quantum mechanics and local realism, a conflict we reinterpret through the modern lens of causal inference. We propose and computationally validate a framework where quantum entanglement…
For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…