Quantum Probability and Quantum Potential Approach to Quantum Mechanics

Bassano Vacchini

Germano Resconi, Santanu Kumar Patro, Amrit Šorli

In this paper, we present the quantum mechanics as a reactive system. To show this, “holography” is introduced as a reactive system. Illumination of the object and reference beam create sources (hologram) that are activated by the same reference beam, which is reacted in a way to produce the image. Controlled chemical system reacts to the external or internal change generated new sources (chemical product) that diffuse in the body environment, and establishes a new equilibrium. The droplets bouncing on a vertical vibrating fluid bath that simulates the main quantum phenomena is a reactive system between droplets and vibrating fluid. It is shown that quantum mechanics is a probabilistic reactive system between quantum potential and pseudo kinetic energy in which an integral is the Fisher information. Information and probability are the key points in quantum mechanics. Quantum mechanics can be built by only the probability normalization properties and associated information without assuming any other hypothesis. With joint probability and Fisher information by Euler Lagrange equation, we can find the quantum potential and the continuity equation. With only probability approach, it is possible to give a meaning to the Schrodinger equation without any thermo-dynamical model of quantum mechanics. The reactive system can be denoted as a morphogenetic system where the form is generated by some designed rules or properties.

Abner Shimony

Sang Pyo Kim

We apply the de Broglie-Bohm interpretation to the Wheeler-DeWitt equation for the quantum FRW cosmological model with a minimal massless scalar field. We find that the quantum FRW cosmological model has quantum potential dominated solutions that avoid the initial and the final cosmological singularities. It is suggested that the quantum potential and the back-reaction of geometry and matter fields may change the property of the cosmological singularities of the Universe. 1 E-mail: sangkim@knusun1.kunsan.ac.kr 1 Introduction One of the most prominent classical-mechanical problems that quantum mechanics can solve is the classical singularity. For example, an electron of an atom suffers from the instability that due to the infinitely negative Coulomb potential and the electron in a zero-momentum state should fall into the infinite potential 2 . In quantum mechanics, however, the s-wavefunction (zero orbital angular momentum state) of the electron has zero probability at the singula...

Yakov Bloch

Abstract Bohmian mechanics is a deterministic account of quantum phenomena in terms of particle trajectories. Guided by a quantum force, the gradient of a quantum potential, trajectories bend to account for quantum interference. The quantum potential is expressible in terms of weak values, complex numbers that characterize quantum systems for which both the initial and final states are predetermined. In Berry and Shukla (2010 J. Phys. A: Math. Theor. 43 354024), the typical probabilities of weak values were calculated. In this paper, expressing the quantum potential in terms of weak values, we find the typical probability distribution of the quantum potential for randomly selected states. The latter allows the calculation of the typical probability of semiclassical superoscillation, a generalization of superoscillations (functions that oscillate faster than their fastest Fourier component) to functions that are not band-limited.

Gottfried T. Rüttimann