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Theoretical Frameworks for Macroscopic Phase Translation: Reconciling Quantum Tunneling, Decoherence, and Higher-Dimensional Topologies

S Lawal Paul

Published Jul 21, 2026• 0 citations
Publisher

Abstract

This report provides the mathematical foundation and the exact physical mechanisms required to achieve macroscopic phase translation. By synthesizing the macroscopic quantum coherence of Bose-Einstein Condensates (BECs) governed by the nonlinear Gross-Pitaevskii equation, the suppression of environmental entanglement via the Caldeira-Leggett master equation, the mitigation of electrostatic repulsion using Debye screening mechanics, and the topological circumvention of three-dimensional space utilizing five-dimensional Randall-Sundrum brane-world models and Morris-Thorne wormhole metrics, the insurmountable potential barrier is effectively reduced to zero. By redefining the macroscopic object not as a collection of classical particles, but as a heavily correlated, highly isolated quantum waveform capable of accessing localized extra dimensions, the difficult concepts of high-energy physics are channeled into a blueprint for rendering solid matter permeable.

DOI
10.5281/zenodo.21479227

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This report provides the mathematical foundation and the exact physical mechanisms required to achieve macroscopic phase translation. By synthesizing the macroscopic quantum coherence of Bose-Einstein Condensates (BECs) governed by the nonlinear Gross-Pitaevskii equation, the suppression of environmental entanglement via the Caldeira-Leggett master equation, the mitigation of electrostatic repulsion using Debye screening mechanics, and the topological circumvention of three-dimensional space utilizing five-dimensional Randall-Sundrum brane-world models and Morris-Thorne wormhole metrics, the insurmountable potential barrier is effectively reduced to zero. By redefining the macroscopic object not as a collection of classical particles, but as a heavily correlated, highly isolated quantum waveform capable of accessing localized extra dimensions, the difficult concepts of high-energy physics are channeled into a blueprint for rendering solid matter permeable.
Abstract This paper takes quantum coherence as a unifying framework to establish a streamlined physical model that spans microscopic quantum phenomena, macroscopic motion, the four fundamental interactions, and conscious perception. Changes in an object’s motion state are fundamentally the transition and reconstruction of the system’s overall coherent mode. Electromagnetism, gravity, friction, contact forces, and the strong/weak interactions are all forms of coherent coupling at different scales. Macroscopic continuous motion is a sensory illusion of high-speed transitions between discrete coherent states, synthesized into a smooth temporal sequence by consciousness. Decoherence corresponds to the release of phase constraints, accompanied by energy release. From a dimensional perspective, the high-dimensional quantum coherent field is the underlying reality, and the macroscopic classical world is its low-dimensional projection after decoherence and conscious integration. Macroscopic physics is a simplified version of quantum physics, just as conventional calculus is a simplified version of its deeper mathematical foundations. This framework achieves a unified explanation of matter, force, energy, consciousness, and spacetime dimensions, with rigorous logical simplicity and self-consistency.
This paper presents a mathematical formalism for the generation of emergent electrodynamic properties from the internal structure of quantum vortices in Bose-Einstein condensates (BECs) and the screening of transverse Tkachenko waves. From the local energy balance of the condensate, the physical boundary of the vortex core is determined as R = σ, where the kinetic energy of the flow per particle reaches the background chemical potential. Analytical integration of the Gross-Pitaevskii density profile yields the structural redistribution of the vortex mass deficit between the core (47.30%) and the outer halo (52.70%). By analyzing the local displacement of the vortex, wherein the Magnus force is balanced by the Ginzburg-Landau elastic restorative force, we derive the screening of the effective mass density of the Bose-condensate and the emergent permeability coefficient κ_BEC. Sensitivity analysis conducted for various variational coefficients σ_core = γξ demonstrates that the microscopic permeability of the vortex core lies within the interval 4.20 ≤ κ_individual ≤ 7.01, while the macroscopic permeability lies within 1.25 ≤ κ_BEC ≤ 1.48. Utilizing coarse-grained wave equations and the Lagrangian formalism, we derive the frequency screening formula for Tkachenko waves. The theoretical results are compared with JILA experimental data and Simula's numerical solutions, demonstrating high quantitative agreement.
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Quantum decoherence represents a fundamental challenge in the development and application of quantum technologies. This paper investigates the theoretical foundations of quantum decoherence, moving beyond the traditional view of it as a simple, isolated process. We argue that decoherence is a complex phenomenon arising from the interplay of multiple physical mechanisms at various scales. The core of this work is the development of a multi-scale model that integrates microscopic quantum effects – such as displacement, impurities, and time evolution – with macroscopic decoherence effects related to circuit design and material selection. We propose a framework for analyzing and simulating decoherence, recognizing the need for a more comprehensive mathematical description. This paper lays the groundwork for future research aimed at refining our understanding of decoherence and ultimately improving the robustness of quantum systems. ---
We show theoretically the existence of a metastable state and the possibility of decay to the ground state through macroscopic quantum tunneling in two-component Bose-Einstein condensates with repulsive interactions. Numerical analysis of the coupled Gross-Pitaevskii equations clarifies the metastable states whose configuration preserves or breaks the symmetry of the trapping potential, depending on the interspecies interaction and the particle number. We calculate the tunneling decay rate of the metastable state by using the collective coordinate method under the WKB approximation. Then the height of the energy barrier is estimated by the saddle point solution. It is found that macroscopic quantum tunneling is observable in a wide range of particle numbers. Macroscopic quantum coherence between two distinct states is discussed; this might give an additional coherent property of two-component Bose condensed systems. Thermal effects on the decay rate are estimated.