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The Deterministic Wave Engine: Simulating Quantum Analogs and the Tsirelson Bound through Viscoelastic Vacuum Hydrodynamics

Fernando Belmiro do Couto

Published Jun 16, 2026• 0 citations
Publisher

Abstract

We present the Deterministic Wave Engine (DWE), a mathematical experiment and highperformance computational platform that models the vacuum as a physical viscoelastic fluid with structural spatial tension. The objective of this framework is to demonstrate that quantum statistical distributions, such as Born’s Law, can emerge entirely from deterministic, local-realist space-time trajectories. By simulating the 1967 Pfleegor-Mandel experiment without physical slits, we show that interference arises via acoustic memory within the fluidic medium. Furthermore, we replicate the Hong-Ou-Mandel (HOM) effect as a purely deterministic aerodynamic block driven by the mutual induction of topological solitons. Notably, the engine reproduces the quantum mechanical violation of the Bell/CHSH inequality, achieving a stable correlation of S = 2.8273, mathematically aligning with the Tsirelson bound as a direct consequence of continuous thermodynamic friction. Finally, we propose a Hydro-Quantum Processing Unit (HQPU) architecture that enables Quantum Non-Demolition (QND) reading via continuous wake barometry.

DOI
10.17605/osf.io/yfb2d

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We present the Deterministic Wave Engine (DWE), a mathematical experiment and highperformance computational platform that models the vacuum as a physical viscoelastic fluid with structural spatial tension. The objective of this framework is to demonstrate that quantum statistical distributions, such as Born’s Law, can emerge entirely from deterministic, local-realist space-time trajectories. By simulating the 1967 Pfleegor-Mandel experiment without physical slits, we show that interference arises via acoustic memory within the fluidic medium. Furthermore, we replicate the Hong-Ou-Mandel (HOM) effect as a purely deterministic aerodynamic block driven by the mutual induction of topological solitons. Notably, the engine reproduces the quantum mechanical violation of the Bell/CHSH inequality, achieving a stable correlation of S = 2.8273, mathematically aligning with the Tsirelson bound as a direct consequence of continuous thermodynamic friction. Finally, we propose a Hydro-Quantum Processing Unit (HQPU) architecture that enables Quantum Non-Demolition (QND) reading via continuous wake barometry.
# Release v7.0.0: The Fluidic Fraunhofer Convergence & QND Validation We are thrilled to announce the release of **Deterministic Wave Engine (DWE) v7.0.0**, the definitive version of our purely local-realist, GPU-accelerated hydrodynamic wave simulator. This major release marks the completion of the core DWE framework. By modeling the spacetime vacuum as a viscoelastic fluid with an Internal Mesh Tension (γ0\gamma_0γ0​), we have successfully demonstrated *in silico* that the most mysterious quantum phenomena—interference, entanglement, tunneling, and the wave-function collapse—are strictly emergent consequences of classical fluid dynamics, requiring no probabilistic abstraction or superluminal communication. ### 🌊 Major Advancements in v7.0.0 * **The Mechanical "Wave-Function Collapse" (Matrix E):** We have successfully modeled the physics of decoherence. The simulation proves that the disappearance of the interference pattern during measurement is not caused by an abstract "observer effect," but by **Ballistic Mortality**. Introducing a physical sensor into the slit creates thermodynamic friction that zeroes the photon's helicity (ω→0\omega \to 0ω→0), destroying its ability to "surf" the vacuum gradient.* **Quantum Non-Demolition (QND) Barometry:** Introduced the `hqpu` module, demonstrating that a vortex qubit's state (spin) can be read *without* destroying it. By utilizing parallel acoustic barometers to read the "thermodynamic wake" of the photon, the HQPU architecture proves that information can be extracted while perfectly preserving the Fraunhofer interference pattern.* **Perfect Deterministic Fraunhofer Convergence:** Eradicated all artificial Huygens noise and probabilistic shortcuts. The fluid lens (Matrix D) now perfectly herds photons into the Fraunhofer diffraction envelope (cos⁡2⋅sinc2\cos^2 \cdot \text{sinc}^2cos2⋅sinc2) using purely tangential boundary collisions (1/r1/r1/r) and the Quantum Magnus Effect.* **Strict Regime Isolation:** Redesigned the WebGPU WGSL compute shaders to mathematically isolate classical thermodynamic scattering (sand) from high-tension elastic conservation (vacuum). ### 📊 Included Analytical Assets This release includes updated Python scripts in the `analytics/` folder to render publication-ready scientific graphs from the GPU output.Execute the engine binaries and run the Python modules to independently verify the macroscopic emergence of Born's Law, the local-realist violation of Bell's Inequality, and the QND barometric readings.
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.
The double-slit experiment remains the empirical foundation of wave–particle duality. While standard quantum mechanics successfully predicts interference patterns via wave-function evolution and attributes the loss of interference to “decoherence,” it lacks a physical ontology. The Copenhagen interpretation and subsequent models offer mathematical descriptions of probability without identifying the underlying mechanical cause. This paper asserts that quantum mechanics is not a departure from physical realism but the statistical consequence of subatomic hydrodynamics. Under the Quantum Vector Time Field (QVTF) framework, the vacuum is modelled not as an empty geometry but as a continuous, highly pressurised superfluid medium. Subatomic masses are defined as topological vortex-solitons that generate continuous pilot-waves through this medium. We demonstrate that double-slit interference is the strict result of classical hydrodynamic steering, and we define quantum “decoherence” not as mathematical entanglement but as the physical destruction of the guiding wave structure via turbulent injection of measurement probes. By treating the vacuum as a physical fluid, the epistemological paradoxes of quantum mechanics are resolved into deterministic mechanics.
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 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.
This paper presents PPT-Quantum, a deterministic unification of quantum phenomena through the lens of classical fluid dynamics. By identifying the universal medium (vacuum) as a hyper-dense superfluid (ρuniv≈2.3×1017 kg/m3), we demonstrate the mathematical equivalence between the Schrödinger equation and the Euler equations for fluid flow. Key Contributions: Physical Mechanisms: Provides deterministic explanations for superposition, the observer effect, and the double-slit experiment using acoustic pilot-wave steering. Decoherence as Turbulence: Identifies "quantum decoherence" as hydrodynamic turbulence caused by thermal phonons, offering a roadmap for room-temperature Terahertz Phononic Computing. Open-Source Simulations: Included with this submission are two Python-based mathematical models: PPT_Quantum_The_Analytic_Hydrostatic_Pressure_Model___Double_Slit___.py: Simulates pilot-wave navigation and the mechanical impact of thermal turbulence (decoherence). PPT_Quantum_The_Decoherence_Simulator.py: Maps the analytic hydrostatic pressure geometry of the vacuum in a double-slit environment. This work builds upon the foundations laid in PPT-Atoms (Zenodo: 18727144) to complete a scale-invariant model of physical reality.