Time-Free Description of Motion in Dynamic Systems From Momentum to Entanglement

Rahul Panse

Joseph Jean-Claude

Time has been in increasing trouble in physics. Skeptics are on the rise since many among its former supporters are nowadays acknowledging the notion that time might be unreal or just a local variable. In the Quanto-Geometric Theory, we have proposed new physics and novel solutions in response to the many conundrums facing the field which radically proscribe time in the metric of the physical realms. What is difficult to construct in a program of timeless physics is an interpretation of the evolution of time-independent dynamic systems at all scales. While we already know what that looks like for the quantum world with E. Scrodinger’s Quantum Mechanics, a granular dynamic description of time-independent physics in the macrocosm has probably yet to be achieved. In this proposal, we undertake to substantially muster up a time-free description of motion in dynamic systems from momentum to entanglement, in physics at all scales.

Rahul Panse

Yuri A. Rylov

The formalism of dynamics in the space-time, where motion of free particles is primordially stochastic, is considered. The conventional dynamic formalism, obtained for the space-time, where the motion of free particles is primordially deterministic, seems to be unsuitable. The statistical ensemble of stochastic (or deterministic) systems is considered to be the main object of dynamics. At such an approach one can describe deterministic, stochastic and quantum particles by means of the uniform technique. The quantum particle is described as a stochastic particle, i.e. without a reference to the quantum principles. Besides, by means of this technique one can describe classical inviscid fluid. There are four different versions of the formalism. One of versions uses equations, which describes evolution of the labelling (Lagrangian coordinates at fixed initial conditions for the density and the momentum density. These fixed initial conditions enter in the evolution equations. A nonuniqueness of irrotational flow and the mismatch between the velocity and the momentum density appear at this description. The mismatch is determined by the fluid vorticity and by some arbitrary parameter. Appearance of mismatch may be associated with the turbulence. The united formalism is purely dynamic. Even describing stochastic systems, it does not refer to probability and probabilistic structures.

V. M. Akulin

Y. Ben-Aryeh

The space-time structure of two-photon and three-photon entangled states is analysed and the Wigner functions for these states are developed. The analysis of the Wigner functions is made in real position-momentum space where position goes with time in a retarded frame and the momentum of the photon in free space is proportional to frequency. The entanglement of the photons in frequencies and wave vectors is due to the phase matching conditions. By the use of narrow-band filters the dominant entanglement effect is due to phase matching conditions in frequencies, and under this condition the description of the three-photon entangled state becomes analogous to that of the two-photon. The motion of the entangled photons is seperated into the centre of mass motion and the relative motion between the photons, including two or three degrees of freedom for the two-photon and three-photon, respectively. Under the approximation of narrow-band filters we get for each degree of freedom a Gaussian wave packet in position momentum with the corresponding time frequency in retarded frames.