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arXiv:physics/0103031

New Approach to Entanglement and Quantum Psi Phenomena, Based on Unified Theory of Bivacuum, Particles Duality, Fields & Time

Alex Käiväräinen

Published Mar 12, 2001• 0 citations
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This is Paper VI of the Planck Cube Space Theory series, providing a unified physical realist interpretation of quantum phenomena based on the axiom system of discrete spatial granularity. Key claims: The wavefunction ψψ is the slowly-varying complex envelope of the twist field (radial torsion of Planck cubes), not an abstract probability amplitude. ∣ψ∣2 is the twist density, proportional to the probability of triggering a detector (physical origin of the Born rule). The uncertainty principle arises from spatial discreteness (Δx≥ℓP0) and measurement disturbance. Wave-particle duality is unified as "particle itself (energy cluster) + accompanying twist field". Quantum entanglement originates from the topological identity of a split cubic lattice chain (no energy/information transfer, respecting special relativity). Quantum tunneling reduces to a geometric equipotential channel in the 10−14 Å interval (d=4r0), consistent with experiments. The Schrödinger equation is not a postulate, but an effective evolution equation for the twist field envelope under continuum, long-wavelength, weak-damping approximations. Statistical randomness arises from Planck-scale initial fluctuations, chaotic amplification, and detection coupling — not from intrinsic randomness. This theory does not deny the mathematical validity of quantum mechanics but provides it with a physical carrier, reducing quantum phenomena to the geometric deformations and elastic propagation of the Planck cubic lattice.
We present a unified derivation of three fundamental quantum phenomena from the Al-Ani Fabric Theory. Starting from a single master equation, we derive: (1) the visibility function for wave-particle duality V(I) = 1/[1 + e^{(I-I_c)/ΔI}], (2) the collapse probability for the measurement problem P(r) = |ψ₀|²/[1 + (δ_meas/δ_c)²], and (3) the CHSH correlation S = 2√2. Using three double-slit experiments (Jönsson 1961, Tonomura 1989, Arndt 1999) for calibration, we determine I_c = (2.1±0.3)×10⁶ and ΔI = (1.8±0.4)×10⁶. The predicted CHSH correlation matches modern experiments (Giustina 2015, Shalm 2015) within 1σ. We then make a testable prediction for future high-precision experiments: S = 2.828 ± 0.005.