Related papers: Some mathematical issues regarding a new approach …
A general theory based upon 7 postulates is introduced. The basical notions are theoretical variables that are associated with an observer or with a group of communicating observers. These variables may be accessible or inaccessible. From…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
The Bell experiment is discussed in the light of a new approach to the foundation of quantum mechanics. It is concluded from the basic model that the mind of any observer must be limited in some way: In certain contexts, he is simply not…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
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 list of basic axioms of quantum mechanics as it was formulated by von Neumann includes only the mathematical formalism of the Hilbert space and its statistical interpretation. We point out that such an approach is too general to be…
In this conceptual paper, we discuss quantum formalisms which do not use the famous Axiom of Choice. We also consider the fundamental problem which addresses the (in)correctness of having the complex numbers as the base field for Hilbert…
We discuss some conceptual issues that any approach to quantum gravity has to confront. In particular, it is argued that one has to find a theory that can be interpreted in a realist manner, because theories with an instrumentalist…
Standard quantum mechanics unquestionably violates the separability principle that classical physics (be it point-like analytic, statistical, or field-theoretic) accustomed us to consider as valid. In this paper, quantum nonseparability is…
The relational version of the modal interpretation offers both a consistent quantum ontology and solution for quantum paradoxes within the framework of nonrelativistic quantum mechanics. In the present paper this approach is generalized for…
The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This…
This paper calls attention to the current state of the probability (P) domain which presents weak points at the mathematical level and more significant flaws at the application level. Popper notices how fundamental issues raised in quantum…
There has been a body of works deriving the complex Hilbert space structure of quantum theory from axioms/principles/postulates to deepen our understanding about quantum theory and to reveal ways to go beyond it to resolve foundational…
A resolution of the quantum measurement problem(s) using the consistent histories interpretation yields in a rather natural way a restriction on what an observer can know about a quantum system, one that is also consistent with some results…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are the multi-time probability distributions estimated from the results of…
A different approach towards quantum theory is proposed in this paper. The basis is taken to be conceptual variables, physical variables that may be accessible or inaccessible, i.e., it may be possible or impossible to assign numerical…
Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…
This paper provides theorems aimed at shedding light on issues in the foundations of quantum mechanics. These theorems can be used to propose new interpretations to the theory, or to better understand, evaluate and improve current…
The widely accepted basis for quantum computing advantage is derived from the entanglement and superposition properties of the probabilistic interpretation of the underlying quantum mechanical formalism which in turn is widely accepted…
Why are the laws of physics formulated in terms of complex Hilbert spaces? Are there natural and consistent modifications of quantum theory that could be tested experimentally? This book chapter gives a self-contained and accessible summary…