Related papers: Foundations of non-commutative probability theory …
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
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…
We show that the quantum-mechanical probability distribution involving complex probability amplitudes can be derived from three natural conditions imposed on a relativistically invariant probability function describing the motion of a…
The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of…
It is shown that the standard Kolmogorov model for probability spaces cannot in general allow the elimination but of only a small amount of probabilistic redundancy. This issue, a purely theoretical weakness, not necessarily related to…
In the modern quantum mechanics of cosmology observers are physical systems within the universe. They have no preferred role in the formulation of the theory nor in its predictions of third person probabilities of what occurs. However,…
We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases…
Quantum randomness evidently transcends the classical framework of random variables defined on a single comprehensive Kolmogorov probability space. One prominent example is the quantum double-slit experiment due to Feynman (1951, 1966). A…
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…
We compare two approaches to embedding joint distributions of random variables recorded under different conditions (such as spins of entangled particles for different settings) into the framework of classical, Kolmogorovian probability…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions…
It is well-established that quantum probability does not follow classical Kolmogorov probability calculus. Various approaches have been developed to loosen the axioms, of which the use of signed measures is the most successful (e.g. the…
The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of…
Within the Kolmogorov theory of probability, Bayes' rule allows one to perform statistical inference by relating conditional probabilities to unconditional probabilities. As we show here, however, there is a continuous set of alternative…
Often it is assumed that a quantum state or a phase-space distribution must be normalizable. Here it is shown that even if it is not normalizable, one may be able to extract normalized observational probabilities from it.
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…
First the crucial but very confidential fact is brought into evidence that, as Kolmogorov himself repeatedly claimed, there exists no abstract theory of probabilities, simply because the factual concept of probability is itself unachieved:…
For Kolmogorov test we find natural conditions of uniform consistency of sets of alternatives approaching to hypothesis. Sets of alternatives can be defined both in terms of distribution functions and in terms of densities.
We develop an analogue of probability theory for probabilities taking values in topological groups. We generalize Kolmogorov's method of axiomatization of probability theory: main distinguishing features of frequency probabilities are taken…