Information-Causality Field and the Unified Field Theory Based on 11-Dimensional T^3 Torus Fractal Geometry -- Paper IV: Deterministic Foundation of Quantum Mechanics: Topological Network Computing on T^3 x Z_900 Lattices, Algebraic Derivation of Tsirelson's Bound 2√2, and Vacuum Strain DualityInformation-Causality Field and the Unified Field Theory Based on 11-Dimensional T^3 Torus Fractal Geometry -- Paper IV: Deterministic Foundation of Quantum Mechanics: Topological Network Computing on T^3 x Z_900 Lattices, Algebraic Derivation of Tsirelson's Bound 2√2, and Vacuum Strain Duality
We present a deterministic, non-probabilistic reformulation of quantum mechanics by replacing Copenhagen probability amplitudes with topological network computing on a discrete T^3 x Z_900 lattice. The wavefunction energy quantum hν is derived directly as the physical work rate of spatial shear strain modulated by the vacuum restoring speed ratio c = √(ρ/κ). By evaluating the Clauser-Horne-Shimony-Holt (CHSH) operator on the 240 coprime automorphism channels of Z_900, we prove that quantum non-locality and Tsirelson's bound S_max = 2√2 ≈ 2.8284 emerge as pure geometric extremum limits at θ_i = π/4, eliminating the need for infinite-dimensional Hilbert space postulates. Furthermore, fundamental constants and quantum scales including Planck units, the running fine-structure constant α(ρ,κ), the Compton wavelength λ_c, and the Casimir force are reparameterized as deterministic functions of local vacuum stress density ρ/κ.
Information-Causality Field and the Unified Field Theory Based on 11-Dimensional T^3 Torus Fractal Geometry -- Paper IV: Deterministic Foundation of Quantum Mechanics: Topological Network Computing on T^3 x Z_900 Lattices, Algebraic Derivation of Tsirelson's Bound 2√2, and Vacuum Strain DualityInformation-Causality Field and the Unified Field Theory Based on 11-Dimensional T^3 Torus Fractal Geometry -- Paper IV: Deterministic Foundation of Quantum Mechanics: Topological Network Computing on T^3 x Z_900 Lattices, Algebraic Derivation of Tsirelson's Bound 2√2, and Vacuum Strain Duality
We present a deterministic, non-probabilistic reformulation of quantum mechanics by replacing Copenhagen probability amplitudes with topological network computing on a discrete T^3 x Z_900 lattice. The wavefunction energy quantum hν is derived directly as the physical work rate of spatial shear strain modulated by the vacuum restoring speed ratio c = √(ρ/κ). By evaluating the Clauser-Horne-Shimony-Holt (CHSH) operator on the 240 coprime automorphism channels of Z_900, we prove that quantum non-locality and Tsirelson's bound S_max = 2√2 ≈ 2.8284 emerge as pure geometric extremum limits at θ_i = π/4, eliminating the need for infinite-dimensional Hilbert space postulates. Furthermore, fundamental constants and quantum scales including Planck units, the running fine-structure constant α(ρ,κ), the Compton wavelength λ_c, and the Casimir force are reparameterized as deterministic functions of local vacuum stress density ρ/κ.
Title: Quantum Mechanics: The Interpretation of Barcelona Description: For a century, the Copenhagen interpretation has taught us that quantum mechanics is fundamentally probabilistic, that the wavefunction collapses upon measurement, and that there is no reality independent of observation. Einstein rejected this: "God does not play dice." This preprint presents a concrete, testable alternative: the Cosmic Mesh — a discrete, elastic, fractal tetrahedral lattice that constitutes spacetime itself. From this single physical substrate we recover all quantum phenomena without probability, without collapse, and without action at a distance: The wavefunction is a real vibration in the Mesh. Entanglement is the same vibration extended across space. Measurement is a local interaction that does not create reality; it only reveals it. Particles are standing waves trapped in topological knots; light is free vibration. We derive a single deterministic rule that governs all motion: At each discrete time step, a vibration migrates to the neighboring tetrahedron that maximizes the local entanglement gradient (Sk−Si). The fine-structure constant emerges geometrically as: α−1=135+2πϕ5≈137.034 where 135 is the ideal torsional-to-volumetric ratio emerging from the geometry of the tetrahedral lattice (90° + 45°), and 2πϕ/5 is the residual torsional stress from 120º cracks and fractal inheritance (golden ratio ϕ). The Mesh is local, deterministic, and testable. We predict that quantum entanglement decays with distance beyond a fundamental coherence length — a direct, falsifiable test of the Copenhagen interpretation. This concise summary is based on the full framework developed in "THE BREATHING UNIVERSE: A Torsional Solid Machine" (Zenodo, 2026). For complete mathematical derivations, including the mechanical origin of lepton masses and the emergence of general relativity, see that work. Keywords: quantum foundations, emergent quantum mechanics, discrete spacetime, topological defects, entanglement, Bell inequalities, Copenhagen interpretation, deterministic quantum theory, elastic lattice, tetrahedral mesh, Weyl curvature imprints, dark matter, cosmological constant, fine-structure constant, golden ratio License: Creative Commons Attribution 4.0 International (CC BY 4.0) Related works: Bertran, A. (2026). THE BREATHING UNIVERSE: A Torsional Solid Machine. Zenodo. Bertran, A., Jussà, E., Vila, M. (2025). The Universe's Geometric Inertia – The Jussà-Vila Ansatz. Zenodo.
Author: Marco Lindenbeck Title: Deterministic Quantum Mechanics: Replacing the Copenhagen Pillars of Probability and Uncertainty with Discrete Substrate Logistics Description: For a century, the Copenhagen Interpretation has forced theoretical physics to accept a subatomic universe governed by random chance, probabilistic wave functions, and fundamental fuzziness. This paper demonstrates that these principles are not foundational truths of nature, but mathematical artifacts born from a single categorization error: treating the vacuum of space as a continuous, empty void. By applying the ΩGLR framework—defining the vacuum as a discrete, pre-tensioned geometric network (the Topological Substrate) governed by a strict Pythagorean processing limit (c2=u2+v2)—this paper entirely eliminates probability and uncertainty from the atomic scale. By mapping the discrete hardware that underlies quantum software, local realism, determinism, and absolute mechanical causality are fully restored to atomic physics. Key Mechanical Derivations Included: Replacing Schrödinger: The Topological Resonance Equation redefines electron energy levels as deterministic network routing paths. Replacing Heisenberg: The Uncertainty Principle (ℏ/2) is mathematically mapped as the Substrate Resolution Limit—an asymptotic hardware buffer overrun (Bandwidth Saturation). The Bohr Radius & Rydberg Protocol: Re-derived as strict geometric hardware constraints and topological data exhaust. The Photoelectric Effect: Re-derived as localized structural bandwidth saturation. The Casimir Effect: The 1 Atmosphere measurement discrepancy is resolved mathematically via the discrete Bilateral Elasticity Factor (2ϕ−2), eliminating the need for virtual zero-point particles.
We present a quantum framework grounded in micro-causality and spacetime quantization, where spacetime is composed of discrete, causally ordered units rather than a continuous manifold. This intrinsic structure naturally generates fundamental quantum features—wave–particle duality, energy quantization, and the Heisenberg uncertainty principle—without invoking canonical quantization, matter-wave postulates, or harmonic-oscillator models. Consequently, this paradigm eliminates the long-standing paradoxes of wavefunction collapse, self-interference, and non-local spooky correlations in entanglement.Within this causal lattice spacetime, quantum commutation relations emerge from finite shift operators, and the uncertainty principle arises geometrically from non-commutativity at the fundamental level. Unlike standard quantum field theory (QFT), which predicts infinite vacuum energy and requires renormalization, the present framework removes zero-point energy, ultraviolet divergences, and fine-tuning. Moreover, U(1) symmetry is broken geometrically on the lattice, leading to mass generation without a Higgs mechanism.The Casimir effect is reinterpreted as a temperature-dependent imbalance in thermal radiation pressure rather than the consequence of vacuum fluctuations, predicting that the Casimir force should vary with ambient temperature. Experimental confirmation of such dependence would directly support the lattice interpretation and challenge the QFT view of vacuum energy.By unifying key quantum behaviors through discrete causal geometry, this model offers a divergence-free and physically grounded alternative to continuum-based QFT. It opens new avenues for quantum unification, cosmology, and the understanding of fundamental constants, without speculative constructs, singularities, or infinities.
The probabilistic nature of quantum mechanics has long been debated as either an intrinsic property of reality or a limit of human knowledge. We propose a third option: quantum phenomena are the deterministic mechanical consequences of wave propagation through a discrete, stiffness-limited medium---the Golden-Rhombohedral Cosserat Vacuum, a five-fold symmetric quasicrystal we term the quintinuum. Building on our previous derivations of the fine-structure constant (α\alpha α) and gauge symmetries (U(1), SU(2), SU(3)) from vacuum geometry, we now derive the phenomenological behavior of quantum matter. We demonstrate that: (1) Wave-particle duality arises from the interaction between a topological defect (the particle) and its precursor strain field (the wave); (2) The uncertainty principle is a bandwidth limit imposed by the finite stiffness of the vacuum lattice; (3) Quantum non-locality results from longitudinal scalar tension relaxing through a volume-preserving medium. Crucially, by restoring the scalar component of Maxwell's original quaternionic electromagnetism, we derive the propagation speed of this longitudinal tension. We predict the ``Speed of Entanglement'' to be finite but superluminal: \begin{equation*} v_L = c \cdot \varphi^{47} \approx 2.0 \times 10^{18} \text{ m/s} \end{equation*} This framework resolves the paradoxes of the Copenhagen interpretation by replacing abstract postulates with the concrete mechanics of a golden-rhombohedral quasicrystal. The universe is not magic; it is a machine. We have found the gears.
Topological Mechanics derives the complete mathematical content of quantum theory from the TVS23 structured vacuum network V23, a discrete elastic medium with icosahedral symmetry A5 generated by the polynomial x^3 - x - 1 = 0. The Schrodinger equation is not postulated but derived: it is the exact envelope equation of a real material torsion wave (a knot) oscillating at its Compton carrier frequency, with Planck's constant emerging as a derived network quantity. The wavefunction is identified as the complex envelope of this real wave, and its squared modulus as torsional energy density rather than probability. Quantum tunnelling is exhibited directly in a purely classical real field, matching the quantum period to 0.3%. The chemical bond is derived as a shared standing mode of the torsion field across two vacuum cells, restoring binding in H2+ where orbital treatments fail. Electron correlation is identified as topological exclusion between identical electron knots, confirmed as the entire binding mechanism of the H- ion and directionally compressed in H2. Finally, the discreteness of the network is shown to be exactly invisible to long-wavelength probes due to the lack of degree-4 invariants in the A5 symmetry group (isotropic to machine precision).
This paper presents the formal computational verification of the Refresh Rate Hypothesis (RRH), demonstrating that Special Relativistic kinematics, Heisenberg uncertainty, and non-local quantum correlations emerge natively from a discrete, capacity-limited lattice vacuum. Utilizing an optimized three-dimensional Face-Centered Cubic (FCC) matrix operating at 934 volumetric frames per second, we implement a strict local processing budget governing cell updates. When localized wave packets translate across coordinates, their internal phase clocks automatically dilate along Einstein’s exact non-linear Lorentz curve to conserve computational resources, achieving a tracking precision within 2.118e-7% variance. Furthermore, we show that by replacing classical angular phase-readouts with a discrete ontic change-of-basis sieve governed by field-wide phase conservation, the ensemble statistics break the classical Bell bound, exactly saturating the Tsirelson limit (|S| = 2.8284) across an airtight 100-tick spacelike communication horizon. These findings eliminate the 60-year deadlock between discrete space and continuous invariants, providing a fully local, deterministic foundation for unified physics. Key Computational Milestones & Datasets Documented: The RRH Lattice Update Kernel: Implements a discrete fractional accumulator on a 12-neighbor Face-Centered Cubic (FCC) matrix to completely eliminate grid anisotropy and numerical shape-diffusion at fractional velocities. Relativistic Budget Verification: Demonstrates an unquantized clock dilation precision tracking Einstein's curves within a 2.118×10⁻⁷% error margin under high-speed diagonal 0.6c transit. Emergent Quantum Symmetries: Establishes wave-particle double-slit duality with a coherent fringe visibility score of 0.999447, while deriving the Heisenberg Uncertainty Principle as an informational hardware sampling constraint. Causal CHSH Joint Correlation Statistics (Step 5B): Introduces a Paired Conservation Sieve that breaks the classical local ceiling (|S| ≤ 2.0) to capture the absolute Tsirelson limit (|S| = 2.8284) with zero superluminal data cheating.