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The Thermodynamic Determinism of the Feynman Path Integral: Resolving Quantum Superposition via Fluid Dynamics

Mukesh Vidyabhushan Singh

Published Aug 28, 2026• 0 citations
Publisher

Abstract

This paper outlines a highly respectful, complementary, and local-realist framework designed to bridge the elegant mathematical predictions of standard quantum mechanics with the physical, load-bearing principles of continuum mechanics and fluid dynamics. We focus specifically on the celebrated Feynman path integral formulation, which postulates that a quantum particle simultaneously traverses all possible trajectories between two points. By re-modeling the spatial manifold as a continuous, pre-stressed, and compressible hydrodynamic medium—the Universal Lattice (Bv approx 10^113 Pa)—we demonstrate that a "particle" is not a dimensionless 0D point-mass making probabilistic choices, but a highly pressurized, localized standing-wave droplet (acoustic soliton) possessing 3D volumetric geometry. Within this framework, the "sum over histories" is physically reinterpreted as the natural, deterministic propagation of a fluid wave-front physically exploring and meshing the available spatial geometry. We show that Feynman's Action ($S$) represents literal thermodynamic work scaled by the natural frequency of the spatial lattice ($S = U_v / \nu$). Furthermore, we demonstrate that wave-function "collapse" is a strictly deterministic return to hydrostatic equilibrium along the path of least mechanical resistance. Finally, we establish that the conversion of volumetric strain energy into surface tension at the yield boundary is a physical manifestation of the Divergence Theorem, and that the optimization of this pathway is mathematically isomorphic to artificial neural network gradient descent. This approach unites standard quantum mathematics with applied engineering, providing a unified, load-bearing foundation for both.

DOI
10.5281/zenodo.22137216

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Researchers, developers, and students can visually explore the hydrodynamic vacuum flux across the celestial bodies at: Interactive 3D EFM Volumetric Profiler: https://marabutmarabut.github.io/Theory-of-Gravity Official GitHub Repository: https://github.com/MarabutMarabut/Theory-of-Gravity

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This paper outlines a highly respectful, complementary, and local-realist framework designed to bridge the elegant mathematical predictions of standard quantum mechanics with the physical, load-bearing principles of continuum mechanics and fluid dynamics. We focus specifically on the celebrated Feynman path integral formulation, which postulates that a quantum particle simultaneously traverses all possible trajectories between two points. By re-modeling the spatial manifold as a continuous, pre-stressed, and compressible hydrodynamic medium—the Universal Lattice (Bv approx 10^113 Pa)—we demonstrate that a "particle" is not a dimensionless 0D point-mass making probabilistic choices, but a highly pressurized, localized standing-wave droplet (acoustic soliton) possessing 3D volumetric geometry. Within this framework, the "sum over histories" is physically reinterpreted as the natural, deterministic propagation of a fluid wave-front physically exploring and meshing the available spatial geometry. We show that Feynman's Action (SSS) represents literal thermodynamic work scaled by the natural frequency of the spatial lattice (S=Uv/νS = U_v / \nuS=Uv​/ν). Furthermore, we demonstrate that wave-function "collapse" is a strictly deterministic return to hydrostatic equilibrium along the path of least mechanical resistance. Finally, we establish that the conversion of volumetric strain energy into surface tension at the yield boundary is a physical manifestation of the Divergence Theorem, and that the optimization of this pathway is mathematically isomorphic to artificial neural network gradient descent. This approach unites standard quantum mathematics with applied engineering, providing a unified, load-bearing foundation for both.
This paper outlines a strictly local-realist, deterministic alternative to the probabilistic "quantum leap" of Copenhagen-style quantum mechanics. We define the "Leap of Energy" as the pressure-driven, discrete transfer of thermodynamic work across an active, hyperelastic 2D membrane that bounds a stable 3D subatomic wave-core. Under the Wave Infrastructure framework, the vacuum of space is modeled as a continuous, hyper-rigid continuum—the Universal Lattice (B_v approx 10^113 Pa). Fundamental particles are modeled as localized, pressurized 3D standing-wave solitons (acoustic droplets) in hydrostatic equilibrium with the surrounding lattice. We establish the Constant Core Principle, proving that the droplet's internal 3D volumetric strain energy (U_v) remains stable during quantum transitions. The transition itself occurs entirely at the 2D boundary, which acts as a semi-permeable dielectric dam storing "Cosmic Memory" as physical surface tension (gamma). Finally, we derive deterministic, load-bearing mechanisms for photon emission as boundary stress venting, and radioactive decay as boundary tensile failure.
We present a unified theoretical and computational framework that bridges quantum me- chanics and macroscopic astrophysics through deterministic fluid dynamics. By modeling the spacetime vacuum as a viscoelastic medium with an inherent structural yield strength— defined here as the Internal Mesh Tension (γ0), an intrinsic pressure and energy density of the vacuum—we demonstrate that probability waves and gravitational anomalies can be entirely reinterpreted as emergent hydrodynamic phenomena. At the microscopic scale, we introduce the Deterministic Wave Engine (DWE), an N-body computational model where photons are treated as super-cavitating topological vortices (Spindles) possessing invariant helicity. Using massively parallel WebGPU architectures, we simulate 5 × 107 indepen- dent trajectories, proving that Fraunhofer diffraction, quantum tunneling, and entangle- ment emerge strictly from tangential boundary collisions, non-Markovian acoustic echoes, and thermodynamic friction. At the macroscopic scale, we apply the same internal mesh tension (γ0) to formulate a Dissipative Gravitation Model. We validate this mesh drag empirically through A/B testing of standard and retrograde planetary rotators using Gaia DR3 astrometric data. This unified framework provides a purely local-realist, determin- istic alternative to both standard probabilistic quantum mechanics and strictly kinematic interpretations of general relativity.
This monograph provides a deterministic, hydrodynamic foundation for Quantum Mechanics, replacing the probabilistic abstractions of the Copenhagen interpretation. By redefining the cosmic vacuum as a tangible, compressible Bose-Einstein Condensate (BEC), the abstract Schrödinger equation is mathematically mapped directly to the classical Euler fluid momentum equations via the Madelung Transformation. Through this hydrodynamic lens, wave-particle duality is physically resolved: a localized quantum droplet is mechanically steered by the acoustic pressure gradient of its own wake. The Heisenberg Uncertainty Principle is explicitly recontextualized as the irreducible variance of convective diffusion—a microscopic buoy subjected to the continuous turbulence of the vacuum's kinematic viscosity. Furthermore, quantum entanglement is modeled not as an abstract, non-local phenomenon, but as continuous longitudinal phononic resonance. Scaling these sub-atomic continuum mechanics to astrophysics, this framework replaces collisionless Dark Matter and stochastic planetary accretion with macroscopic acoustic nodes, viscous fluid drag, and deterministic tidal thresholds—recently validated by 2026 Chandra observations of pre-ignition EUV thermalization. Ultimately, this demonstrates that quantum mechanics is simply fluid dynamics operating at extreme limits of scale and viscosity.
Abstract This paper establishes a rigorous causal analysis of quantum propagator mechanics by mapping thesingle-photon path integral measurements formalized by Wen et al. (2026) onto the physical substrate ofthe Tension Optimized Newtonian Entropy (TONE) framework. By subjecting multi-path coherent su-perpositions and action-dependent phase accumulations to deterministic real-wave kinematic constraintson a Descartes grid, we resolve abstract quantum propagators as effective statistical ledgers operatingover a shared physical surface. Conventional quantum foundations treat Feynman’s path integral as anontological splitting of physical reality where a single particle simultaneously traverses millions of paral-lel trajectories across an infinite, unobserved state space. This investigation provides a non-parametricrefinement of these path distributions by demonstrating that the apparent infinity of allowable routessimply reflects environmental randomness that emerges when initial boundary layer data is completelyabsent. By tracking the localized position-to-time coordinate translations of matter waves inside dis-crete substrate pores, the analytical path ambiguities collapse to predictable wave packet displacementsbounded by a strict Planck-length minimum. Ultimately, the multi-path verification recorded under ex-ternal photon probe measurements is shown to represent standard relative motion under the Heisenberguncertainty principle when an observer lacks the starting position information of a finite wave packet,rather than a fundamental superposition of an infinite number of zero-dimensional point-particle paths.The entire phenomenon of relational coordinate movement is grounded on a local Newtonian timeline,replacing abstract probability clouds with deterministic metric action-reaction conservation laws acrossparallel manifold layers. PACS Numbers: 04.60.-m, 03.65.Ta, 04.20.Cv, 47.10.-gKeywords: Path Integrals, Feynman Propagators, Descartes Grid, Heisenberg Uncertainty, Real-WaveMechanics, TONE FrameworkCopyright Notice: Copyright Pending © 2026 Anthony Santana. All Rights Reserved.DOI: 10.5281/zenodo.22691853
This updated preprint (v2) investigates the fundamental ontological contradiction between macroscopic chemical determinism and microscopic quantum uncertainty. Standard interpretations of quantum mechanics propose a micro-world governed by causeless randomness and probability waves. However, this study argues that the flawless precision observed in macroscopic chemistry and industrial systems necessitates an underlying, strictly deterministic physical reality operating at the hardware level of the universe. To resolve this paradox, the paper introduces the "Cosmic Texture" (Texton) Model, which redefines the universe not as an empty void, but as a continuous, highly elastic, and compressible fluid substratum. Within this framework, quantum uncertainty is not a fundamental law of nature, but the deterministic result of the unmapped hydrodynamic background noise of this texton sea and the inherently destructive nature of measurement methods. Key concepts explored and expanded in this version include: Hydrodynamic Phase Transitions & Baroclinic Vorticity: Rejecting mass-energy duality, the model defines particles as varying physical phases of the texton fluid. Linear compression waves (energy) transition into highly dense, stable, rigid vortices (matter) via baroclinic torque (∇ρ×∇P\nabla \rho \times \nabla P∇ρ×∇P) during high-energy collisions. Charge as Pressure Gradients: Electric charge and attractive forces are redefined mechanically as hydrostatic pressure and central vacuum gradients within the continuous fluid network. Mechanical Wave Collapse (The Observer Effect): The "collapse" of probability waves is explained via classical fluid dynamics. A measurement shockwave causes a diffuse electron cloud to implode into a constricted state. Exceeding its structural carrying capacity, the vortex reflexively expels excess energy (photon emission) and returns to its stable limit cycle. Non-Local Determinism: Bell's non-locality is preserved through the De Broglie-Bohm pilot-wave theory, where the abstract "quantum potential" is physically identified as real hydrostatic pressure and tension gradients within the texton sea. Spin Quantization: The discrete nature of quantum spin is mathematically grounded in Kelvin's Circulation Theorem, demonstrating that topological fluid knots must exist in integer multiples. Empirical & Phenomenological Validation: Moving beyond theoretical frameworks, this study supports its deterministic model with discrete lattice simulations and macroscopic analogs. Crucially, the hydrodynamic behavior of the Cosmic Texture is corroborated by established laboratory evidence, including: Madelung's hydrodynamic formulation of the Schrödinger equation (1927). Yves Couder's macroscopic walking droplet experiments (2006). The Dynamic Casimir Effect (DCE): Demonstrating the mechanical excitation of the fluid substratum. The SLAC E144 Experiment: Providing evidence for wave-to-vortex phase transitions. The Aharonov-Bohm Effect & Superfluid Vortices: Validating vector potentials as physical momentum flow and confirming the macroscopic quantization of limit cycles. This study presents a testable, causal, and purely mechanical alternative to the Copenhagen interpretation, re-establishing absolute causality in theoretical physics.
Legacy quantum mechanics relies on abstract probability distributions to explain Wave-Particle Duality, abandoning physical determinism in favor of Statistical Uncertainty. This manuscript resolves that anomaly by defining the Quantum Vacuum as a highly pressurized, structured fluid medium. Under the Electron Flow Model (EFM), elementary particles are not dimensionless mathematical points, but localized fluid solitons propagating through the Universal Vacuum Flux. Our analysis demonstrates that the observed interference patterns in the Double-Slit Experiment are generated by the Macroscopic Physical Bow Waves of the soliton. These Bow Waves sever and recombine after passing through the slits to create a standing wave interference pattern of Pressurized Ridges and Thermodynamic Troughs. The localized particle itself travels strictly through a single path, naturally surfing these pressure ridges to land on the detector screen. This framework moves beyond interpretation by establishing clear, Falsifiable Predictions that structurally distinguish the EFM from standard Quantum Mechanics: Viscous Damping: Predicts an additional mechanical channel of decoherence driven by dynamic fluctuations in the ambient pressure of the vacuum flux, scalable by the fluid bulk viscosity. Absolute Vacuum Pressure Shift: Suggests a measurable fringe compression in orbital cold-atom interferometry relative to sea level, driven by the absolute density of the vacuum flux. The v-Causal Temporal Limit of Delayed Choice: Establishes a concrete 0.51-picosecond switching threshold for tabletop delayed-choice experiments (48 m), scaling linearly to 12.6 nanoseconds at satellite-class baselines (1,200 km). The EFM predicts a physical persistence of the interference pattern—and a breakdown of quantum correlations—if measurement switching occurs faster than the finite acoustic transit time of the fluid tether. The Unified Fluid Cosmos Framework: This paper serves as Manuscript 21 Version 1 in the comprehensive series, Marabūt's Theory of Gravity. It presents the Electron Flow Model (EFM), a generative, fluid-dynamic framework designed to fundamentally replace Albert Einstein's General Relativity and standard Quantum Mechanics. The EFM shatters classical circularity with a single, undeniable foundational premise: Gravity is Pressure, not curvature, and not an intrinsic mass property. Published Manuscripts in this Series: Manuscript 01: The Push-Pull Mechanics of Vacuum Flux (The Foundational Framework) — https://doi.org/10.5281/zenodo.18874694 Manuscript 02: Resolving the Weyl Potential Anomaly — https://doi.org/10.5281/zenodo.19784494 Manuscript 03: Mechanistic Resolution of Jet Deflection in Cygnus X-1 — https://doi.org/10.5281/zenodo.19790983 Manuscript 04: Quantum Mechanics of Stellar Chain Reactions and EVGS Formation — https://doi.org/10.5281/zenodo.19801398 Manuscript 05: The Heliospheric Grand Data Matrix — https://doi.org/10.5281/zenodo.20128776 Manuscript 06: Fluid-Dynamic Reinterpretation of Gravity, Black Holes, and Gravitational Waves — https://doi.org/10.5281/zenodo.20129518 Manuscript 07: Fluid-Dynamic Reinterpretation of the Kinematic Sunyaev-Zeldovich Effect — https://doi.org/10.5281/zenodo.20130259 Manuscript 08: Transcending the Singularity — Electron Void Gravitational Spheres — https://doi.org/10.5281/zenodo.20130801 Manuscript 09: The Final Parsec Problem Solved — https://doi.org/10.5281/zenodo.20134048 Manuscript 10: The Illusion of the Singularity — https://doi.org/10.5281/zenodo.20135533 Manuscript 11: The Illusion of Dark Energy — https://doi.org/10.5281/zenodo.20149141 Manuscript 12: The Illusion of Dark Matter — https://doi.org/10.5281/zenodo.20171372 Manuscript 13: The Illusion of Spacetime — https://doi.org/10.5281/zenodo.20172281 Manuscript 14: The Illusion of Spooky Action — https://doi.org/10.5281/zenodo.20173191 Manuscript 15: The Superluminal Mechanics of the Quantum Vacuum — https://doi.org/10.5281/zenodo.20173755 Manuscript 16: Empirical Validation of the Electron Flow Model — https://doi.org/10.5281/zenodo.20271062 Manuscript 17: Confronting the Cosmic Microwave Background — https://doi.org/10.5281/zenodo.20483713 Manuscript 18: Resolving the CMB Power Spectrum — https://doi.org/10.5281/zenodo.20493520 Manuscript 19: The Foundation of Stellar Dynamics — https://doi.org/10.5281/zenodo.20500168 Manuscript 20: Resolving the Black Hole Information Paradox — https://doi.org/10.5281/zenodo.20535631 Manuscript 21: Hydrodynamic Shockwaves and Wave-Particle Duality — https://doi.org/10.5281/zenodo.20620456 Manuscript 22: Resolving the Quantum Measurement Problem — https://doi.org/10.5281/zenodo.20628003 Manuscript 23: The Origin and Nature of the Vacuum Flux — https://doi.org/10.5281/zenodo.20754253 Manuscript 24: The Illusion of the Quantum Cat — https://doi.org/10.5281/zenodo.20768397 Manuscript 25: The Rock Giant Reclassification — https://doi.org/10.5281/zenodo.20899782 Manuscript 26: The Pioneer Anomaly and Electron Pressure Drag — https://doi.org/10.5281/zenodo.21346600 Data & Code Availability: To accompany this manuscript, we have open-sourced the complete Python mathematical engine and a fully interactive 3D web-based simulation of the EFM Volumetric Profiler. Researchers, developers, and students can visually explore the hydrodynamic vacuum flux across the celestial bodies at: Interactive 3D EFM Volumetric Profiler: https://marabutmarabut.github.io/Theory-of-Gravity Official GitHub Repository: https://github.com/MarabutMarabut/Theory-of-Gravity