Related papers: How to Secure Valid Quantizations
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
Difficulties and discomfort with the interpretation of quantum mechanics are due to differences in language between it and classical physics. Analogies to The Special Theory of Relativity, which also required changes in the basic worldview…
An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not…
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g.,…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
One interpretation of how the classical world emerges from an underlying quantum reality involves the build-up of certain robust entanglements between particles due to scattering events [Science Vol.301 p.1081]. This is an appealing view…
All objects in 4D spacetime may in principle travel on null paths in a 5D mani-fold. We use this, together with a change in the extra coordinate and the signature of the metric, to construct a simple model of a classical universe and a…
In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented…
In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…
In view of the enormous difficulties we seem to face in quantizing general relativity, we should perhaps consider the possibility that gravity is a fundamentally classical interaction. Theoretical arguments against such mixed…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable…
This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties and the problem of quantum measurement. A considerable progress has…
Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or…
We present two possible criteria quantifying the degree of classicality of an arbitrary (finite dimensional) dynamical system. The inputs for these criteria are the classical dynamical structure of the system together with the quantum and…
We give a general overview of various flavors of the equivalence principle in classical and quantum physics, with special emphasis on the so-called weak equivalence principle, and contrast its validity in mechanics versus field theory. We…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
After some historical remarks concerning Schroedinger's discovery of wave mechanics, we present a unified formalism for the mathematical description of classical and quantum-mechanical systems, utilizing elements of the theory of operator…