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

Joseph Jean-Claude

Published Apr 29, 2022• 0 citations

Abstract

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.

DOI: 10.33774/coe-2022-qb9d5

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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.

Following a line of research that I have developed for several years, I argue that the best strategy for understanding quantum gravity is to build a picture of the physical world where the notion of time plays no role. I summarize here this point of view, explaining why I think that in a fundamental description of nature we must "forget time", and how this can be done in the classical and in the quantum theory. The idea is to develop a formalism that treats dependent and independent variables on the same footing. In short, I propose to interpret mechanics as a theory of relations between variables, rather than the theory of the evolution of variables in time.

Following a line of research that I have developed for several years, I argue that the best strategy for understanding quantum gravity is to build a picture of the physical world where the notion of time plays no role. I summarize here this point of view, explaining why I think that in a fundamental description of nature we must forget time, and how this can be done in the classical and in the quantum theory. The idea is to develop a formalism that treats dependent and independent variables on the same footing. In short, I propose to interpret mechanics as a theory of relations between variables, rather than the theory of the evolution of variables in time.

Quantum mechanics (QM) is the description of dynamics in the microscopic world of atoms, photons, electrons, etc. Similar to Newton’s law of dynamics, dp/dt = F, which is the statement on the time evolution of the dynamical physical state associated with matter, the Schrödinger equation iħdψ/dt = Hψ is the statement of the time evolution on the quantum physical state of matter, denoted with the function ψ ( x, t ). Though the wavefunction ψ ( x, t ) is not a dynamical quantity like momentum, the role of time in the description of dynamics is similar and straightforward, if the final results are interpreted as the average over a statistical ensemble (collection). In the conventional interpretation of quantum mechanics, the wavefunction is supposed to be the complete description of the physical state of the particle, like an electron or an atom. It is complex-valued, mathematically, and needs two real quantities for its specification. It evolves in ‘magnitude’ and ‘phase’ as the reference clock advances in time. The evolution progresses causally, connecting the past to the present and into the future, as one expects in dynamics. Thus, the variable called ‘time’ in the microscopic world of quantum mechanics is the same as the time that is familiar in our macroscopic world.

Two related problems in relativistic quantum mechanics, the apparent superluminal propagation of initially localized particles, and the dependence of their localization on the motion of the observer, are analyzed in the context of the theory of constraints. Time and energy operators are introduced for the free relativistic particle, and a parametrization invariant formulation is obtained through Dirac constraint theory. The resulting description is of a system constrained in momentum and energy, but not in position or time, for which observables are constants of the motion. The Klein-Gordon equation is recovered on a physical Hilbert space, constructed via integration over the proper time from an augmented Hilbert space, wherein time and energy are dynamical variables...