Quantum action, non-locality and coherence from classical perception, a new facet of Lagrangian formalism for relativistic dynamics

TL;DR

This paper introduces a novel Lagrangian formalism that unifies classical and quantum descriptions, emphasizing nonlocal correlations, coherence, and energy-momentum transfer across space-like boundaries, with implications for quantum space, decoherence, and cosmology.

Contribution

It presents a new facet of Lagrangian formalism that incorporates nonlocal correlations and coherence in relativistic dynamics, bridging classical and quantum frameworks.

Findings

Coherent evolution of correlated geodesics demonstrates nonlocal energy-momentum transfer.

Nonlocal mitigation explains decoherence criticality in electrodynamic evolution.

Analysis of cosmic recessional kinematics incorporates nonlocal effects of quantum vacuum fields.

Abstract

Classical and quantum mechanical descriptions of physical world are seamlessly abridged within the framework of Lagrangian formalism which, besides revealing the essence of nonlocally correlated dynamic evolution, helps understanding abrupt onset towards perturbation driven correlation breakdown criticality with the manifestation of classical dynamic properties. The abridged formalism takes into consideration a family of ubiquitously correlated paths in their linear combination and shows that the coherently evolved dynamic course of optimum displacement is variationally realizable within arbitrarily selected pair of space-like surface-boundaries, only if the nonlocal correlation implies virtually mediating energy and momentum quanta across instantly evolved volume meeting integral conservations. The coherent evolution characteristics are explored for correlated geodesics of quantum space and for dynamics of particle. As safeguard to coherently mediated system, ubiquitous nonlocal mitigation on external perturbation is explored in explaining decoherence criticality considering the case of electrodynamic evolution. Coherently evolved geodesics endorse quantum space of ultrahigh energy harmonic oscillators, which is exotic to the physical world described by evolution harmonics of comparatively low energies over a wide frequency range. Observable recessional kinematics of cosmic space with its background vacuum field supporting the physical world is analyzed by considering nonlocal mitigation of exotic quantum vacuum field on the gravitationally perturbed space across ubiquitous isolation barrier arising from markedly different quantum orders of the two vacuum fields describable by a common dimensional element like Planck length.