Nonlinear stochastic and quantum motion from Coulomb forces

Marcel Franz

Luca Ornigotti, Darren W. Moore, Radim Filip

Controllable nonlinear quantum interactions are a much sought after target for modern quantum technologies. They are typically difficult and costly to engineer for bespoke purposes. However controllable nonlinearities may have always been in reach via the natural and fundamental forces between quantum particles. The Coulomb interaction between charged particles is the simplest example. We show that after eliminating the harmonic part of the Coulomb force by an auxiliary linear force, the remaining reciprocal nonlinear part results in a directly observable non-reciprocal nonlinear effect: increase of the signal-to-noise ratio (SNR) of the coherent displacement of one particle, driven by the position noise, or uncertainty in quantum regime, in another particle. This essential evidence of nonlinear forces is present across large ranges of trap frequency and mass scales, as well as visible in both stochastic and quantum regimes.

Roumen Tsekov

David C. Lush

In the de Broglie - Bohm formulation of quantum mechanics, the electron is stationary in the ground state of the hydrogen atom, because the quantum force exactly cancels the Coulomb attraction of the electron to the proton. In this paper it is shown that classical electrodynamics similarly predicts the Coulomb force can be effectively canceled by part of the magnetic force that occurs between two similar particles each consisting of a point charge moving with circulatory motion at the speed of light. Supposition of such motion is the basis of the {\em Zitterbewegung} interpretation of quantum mechanics. The magnetic force between two luminally-circulating charges for separation large compared to their circulatory motions contains a radial inverse square law part with magnitude equal to the Coulomb force, sinusoidally modulated by the phase difference between the circulatory motions. When the particles have equal mass and their circulatory motions are aligned but out of phase, part of the magnetic force is equal but opposite the Coulomb force. This raises a possibility that the quantum force of Bohmian mechanics may be attributable to the magnetic force of classical electrodynamics. It is further shown that non-relativistic relative motion between the particles leads to modulation of the magnetic force with spatial period equal to the de Broglie wavelength.

H. Y. Cui

The first clue, in the theory of relativity, the 4-vector force acting on a particle is orthogonal to the 4-vector velocity of the particle, this orthogonality means that there is some difference between the orthogonality and the usual statement: the Coulomb's force (or gravitational force) acts along the line joining a couple of particles (in usual 3D space), so the direction of 4-vector Coulomb's force is carefully investigated, it is found that Maxwell's equations can be derived from classical Coulomb's force and the orthogonality. The second clue, a 4-vector force has 4 components, because of the orthogonality of 4-vector force and 4-vector velocity, the number of independent components of the 4-vector force reduces to 3, however we prove that 4-vector Coulomb's force can merely provide 2 independent components, this situation means that there is an undefined component accompanying the 4-vector Coulomb's force, hinting that this missing undefined component is a hidden variable. The third clue, the best way to study the hidden variable is to establish a new concept: Z-space, in which the undefined component of 4-vector Coulomb's force can be clearly defined as the hidden variable for the quantum mechanics. At the last, the undefined component is regarded as a fluctuating source that contributes to Lorentz force, so that the quantum wave equation can be derived out in the ensemble space of particle motion from the relativistic Newton's second law.

Hans-Jürgen Mann