Bohm Trajectories and Feynman Paths in Light of Quantum Entropy

Abstract

A new definition of quantum entropy by a gauge constraint on a classical Boltzmann manifold is proposed. Bohm potential is derived as Fisher information, in accordance with Bohm-Hiley idea of "Active Information", and the geometries underlying Bohm trajectories and Feynman paths are compared. Given a quantum system, it is shown how the modifications of such geometries are connected to the microstates that quantum entropy provides.

Quantum Mechanics Interpretation on Planck Scale

“…In fact, the stochasticity has a mesoscopic flavor, and one would not expect to find it at a scale of radical discretization. Ambiguities do not decrease with the second quantization, but increase; in general and on all scales, the elegance of the description of physical processes through amplitudes [5] is strongly limited by the probabilistic mortgage. The latter should derive from deeper reasons, and the Born rule should emerge as a sort of "regulator" of the collective dynamics and their degrees of freedom.…”

Bell Length as Mutual Information in Quantum Interference

“…The advent of Bohmian Quantum Mechanics resolves this gap by the quantum potential, which showed to be not only the central expression of the nth "interpretation" but also an "open door" in order to treat non-locality in contexts that are otherwise difficult, such as particle physics, cosmology and quantum information [14]. In particular, it is possible to show that a deep mathematical connection exists between Bohm's quantum potential and Feynman's paths, they complete each other both in the physical meaning and as an efficacious tool [15].…”

“…Despite the density describing the space-temporal distribution of the ensemble of particles associated with the quantum state is a function of the coordinates, the dependence of the Bell length on the coordinates does not imply the necessity of supplementary existence conditions in order to guarantee its positive definite nature. Equations (14) and (15) imply that the quantum lengths-associated to Sbitnev's approach and to Novello's, Salim's and Falciano's approach respectively-deriving from the quantum potential can never be singular, in the sense that the denominator appearing in their expression can become zero only in the classical case.…”

Event-Based Quantum Mechanics: A Context for the Emergence of Classical Information

“…It seems useful to point out here that the use of a Hamiltonian operator does not indicate the motion of anything, but rather it has to be seen as a 'probability gradient', a notion that unifies different formalisms such as Bohm potential and Feynman path integrals [22]. The fact that the application f introduced with the Postulate 1 is "sensitive" to time but not to space generates the well-known phenomenon of the non-separability of entangled amplitudes, well exemplified by the amplitudes of a pair of identical particles of spin 1/2 in a state of singlet.…”