Related papers: Generalized Probabilistic Theories in a New Light
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…
We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the…
Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
This paper addresses the question why quantum mechanics is formulated in a unitary Hilbert space, i.e. in a manifestly complex setting. Investigating the linear dynamics of real quantum theory in a finite-dimensional Euclidean Hilbert space…
A new formulation of quantum mechanics is proposed based on a new principle that can be considered a generalization of the Born rule. The principle is composed of a mathematical expression and an associated interpretation, and establishes a…
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…
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,…
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…
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
Quantum Mechanics (QM) is a quantum probability theory based on the density matrix. The possibility of applying classical probability theory, which is based on the probability distribution function(PDF), to describe quantum systems is…
In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed states. One might expect that this is typical of Hilbert space…
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
In this paper two hypotheses are developed. The first hypothesis is the existence of random phenomena/experiments in which the events cannot generally be assigned a definite probability but that nevertheless admit a class of nearly certain…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
I propose a new class of interpretations, {\it real world interpretations}, of the quantum theory of closed systems. These interpretations postulate a preferred factorization of Hilbert space and preferred projective measurements on one…
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…
In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in…
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…