相关论文: A Stepwise Planned Approach to the Solution of Hil…
As the first step in an approach to the solution of Hilbert's sixth problem, a general scheme of mechanics, called `supmech', is developed integrating noncommutative symplectic geometry and noncommutative probability theory in an algebraic…
Supmech, the universal mechanics developed in the previous two papers, accommodates both quantum and classical mechanics as subdisciplines (a brief outline is included for completeness); this feature facilitates, in a supmech based…
Operating in the framework of `supmech' (a scheme of mechanics which aims at providing a concrete setting for the axiomatization of physics and probability theory as required in Hilbert's sixth problem; integrating noncommutative symplectic…
This series of papers is devoted to an open-ended project aimed at the solution of Hilbert's sixth problem (concerning joint axiomatization of physics and probability theory) proposed to be constructed in the framework of an all-embracing…
Supmech, an algebraic scheme of mechanics integrating noncommutative symplectic geometry and noncommutative probability, subsumes quantum and classical mechanics and permits consistent treatment of interaction of quantum and classical…
We derive the Hilbert space formalism of quantum mechanics from epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. An…
We introduce Superstate Quantum Mechanics (SQM), a theory that considers states in Hilbert space subject to multiple quadratic constraints, with ``energy'' also expressed as a quadratic function of these states. Traditional quantum…
We explore further the suggestion to describe a pre- and post-selected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically…
We formulate the dynamics of the generic quantum system S_{c} comprising a microsystem S and a macroscopic measuring instrument I, whose pointer positions are represented by orthogonal subspaces of the Hilbert space of its pure states.…
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…
A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and…
Non-unitary quantum mechanics has been used in the past to study irreversibility, dissipation and decay in a variety of physical systems. In this letter, we propose a general scheme to deal with systems governed by non-Hermitian…
According to the stochastic-quantum correspondence, a quantum system can be understood as a stochastic process unfolding in an old-fashioned configuration space based on ordinary notions of probability and `indivisible' stochastic laws,…
Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…
We describe a scheme of quantum mechanics in which the Hilbert space and linear operators are only secondary structures of the theory. As primary structures we consider observables, elements of noncommutative algebra, and the physical…
Schroedinger equation on a Hilbert space ${\cal H}$, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space $P {\cal H}$. Separable states of a bipartite quantum system form a…
Recently there has been much interest in deriving the quantum formalism and the set of quantum correlations from simple axioms. In this paper, we provide a step-by-step derivation of the quantum formalism that tackles both these problems…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
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…