Related papers: Extended probability theory and quantum mechanics …
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
In this article the propagation of pointlike event probabilities in space is considered. Double-Slit experiment is described in detail. New interpretation of Quantum Theory is formulated.
We enhance the standard formalism of quantum theory to enable events. The concepts of experiment and of measurement are defined. Dynamics is given by Liouville's equation that couples quantum system to a classical one. It implies a unique…
The major conceptual difficulties of quantum mechanics are analyzed. They are: the notion "wave-particle", the probabilistic interpretation of the Schroedinger wave \psi-function and hence the probability amplitude and its phase, long-range…
In the following we revisit the frequency interpretation of probability of Richard von Mises, in order to bring the essential implicit notions in focus. Following von Mises, we argue that probability can only be defined for events that can…
Within ordinary ---unitary--- quantum mechanics there exist global protocols that allow to verify that no definite event ---an outcome to which a probability can be associated--- occurs. Instead, states that start in a coherent…
How can quantum mechanics be (i) the fundamental theoretical framework of contemporary physics and (ii) a probability calculus that presupposes the events to which, and on the basis of which, it assigns probabilities? The question is…
We develop and defend the thesis that the Hilbert space formalism of quantum mechanics is a new theory of probability. The theory, like its classical counterpart, consists of an algebra of events, and the probability measures defined on it.…
Conceptual problems in quantum mechanics result from the specific quantum concept of reality and require, for their solution, including the observer's consciousness into quantum theory of measurements. Most naturally this is achieved in the…
The notion of context (complex of physical conditions) is basic in this paper. We show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space,…
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…
In this work we first propose to exploit the fundamental properties of quantum physics to evaluate the probability of events with projection measurements. Next, to study what events can be specified by quantum methods, we introduce the…
Kolmogorov's setting for probability theory is given an original generalization to account for probabilities arising from Quantum Mechanics. The sample space has a central role in this presentation and random variables, i.e., observables,…
We study the role of context, complex of physical conditions, in quantum as well as classical experiments. It is shown that by taking into account contextual dependence of experimental probabilities we can derive the quantum rule for the…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
Recent results suggest that quantum mechanical phenomena may be interpreted as a failure of standard probability theory and may be described by a Bayesian complex probability theory.
We show that a new interpretation of quantum mechanics, in which the notion of event is defined without reference to measurement or observers, allows to construct a quantum general ontology based on systems, states and events. Unlike the…
We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability…