Related papers: Aperiodicity in Quantum Wang Tilings
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…
The quotient cohomology of tiling spaces is a topological invariant that relates a tiling space to one of its factors, viewed as topological dynamical systems. In particular, it is a relative version of the tiling cohomology that…
We consider classical and quantum dynamics of a free particle in de Sitter's space-times with different topologies to see what happens to space-time singularities of removable type in quantum theory. We find analytic solution of the…
The paper develops the idea that the dynamics of both classical and quantum processes is time reversible. It is shown how this classical analogy allows one to define the measure for the path integral in quantum mechanics.
Mathematicians have been interested in non-periodic tilings of space for decades; however, it was the unexpected discovery of non-periodically ordered structures in intermetallic alloys which brought this subject into the limelight. These…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
Quantum mechanics forces us to reconsider certain aspects of classical causality. The 'central mystery' of quantum mechanics manifests in different ways, depending on the interpretation. This mystery can be formulated as the possibility of…
Here we continue with the ideas expressed in "On the strangeness of quantum mechanics" aiming to demonstrate more concretely how this philosophical outlook might be used as a key for resolving the measurement problem. We will address in…
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…
The spin-statistics connection, quantum gravity and other physical considerations suggest that classical space-time topology is not an immutable attribute and can change in quantum physics. The implementation of topology change using…
In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of…
The classical and quantum features of Nambu mechanics are analyzed and fundamental issues are resolved. The classical theory is reviewed and developed utilizing varied examples. The quantum theory is discussed in a parallel presentation,…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
We take quantum theory and replace $\mathbb{C}$ by $\mathbb{C}[\varepsilon]$ where $\varepsilon^2=0$, i.e. we extend quantum theory to the ring of dual complex numbers. The aim is to develop a common language in which to treat continuous…
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical…
We study the dynamics of a two-level quantum system interacting with an external electromagnetic field periodic and quasiperiodic in time. The quantum evolution is described exactly by the classical equations of motion of a gyromagnet in a…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
Viewed as approximations to quantum mechanics, classical evolutions can violate the positive-semidefiniteness of the density matrix. The nature of this violation suggests a classification of dynamical systems based on classical-quantum…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…