We formalize a bilocal extension of the Classical Transition Operator within the framework to resolve the Einstein–Podolsky–Rosen (EPR) nonlocality paradox. By treating the electron () and positron () not as discrete, spatially isolated entities, but as dual, time-symmetric observational projections of a singular topological -cell, quantum entanglement is shown to be a strict artifact of dimensional reduction. Introducing a dynamic phase shift governed by an external Minkowski 4-potential , we employ the 4‑dimensional Stokes’ theorem to map the phase accumulation directly onto the classical Maxwell field tensor . This geometric mapping naturally derives the covariant Lorentz force equation. We demonstrate that the apparent “spooky action at a distance” is an artifact of the coordinate time projection, whereas the physical metric of the system remains strictly local and invariant within the absolute phase time .
We formalize a bilocal extension of the Classical Transition Operator within the framework to resolve the Einstein–Podolsky–Rosen (EPR) nonlocality paradox. By treating the electron () and positron () not as discrete, spatially isolated entities, but as dual, time-symmetric observational projections of a singular topological -cell, quantum entanglement is shown to be a strict artifact of dimensional reduction. Introducing a dynamic phase shift governed by an external Minkowski 4-potential , we employ the 4‑dimensional Stokes’ theorem to map the phase accumulation directly onto the classical Maxwell field tensor . This geometric mapping naturally derives the covariant Lorentz force equation. We demonstrate that the apparent “spooky action at a distance” is an artifact of the coordinate time projection, whereas the physical metric of the system remains strictly local and invariant within the absolute phase time .
We formalize a bilocal extension of the Classical Transition Operator within the framework of Phase Dynamics to resolve the Einstein–Podolsky–Rosen (EPR) nonlocality paradox. By treating the electron () and positron () not as discrete, spatially isolated entities, but as dual, time-symmetric observational projections of a singular topological -cell, quantum entanglement is shown to be a strict artifact of dimensional reduction. Introducing a dynamic phase shift governed by an external Minkowski 4-potential , we employ the 4‑dimensional Stokes’ theorem to map the phase accumulation directly onto the classical Maxwell field tensor . This geometric mapping naturally derives the covariant Lorentz force equation. We demonstrate that the apparent “spooky action at a distance” is an artifact of the coordinate time projection, whereas the physical metric of the system remains strictly local and invariant within the absolute phase time .
We formalize a bilocal extension of the Classical Transition Operator within the framework of Phase Dynamics to resolve the Einstein–Podolsky–Rosen (EPR) nonlocality paradox. By treating the electron () and positron () not as discrete, spatially isolated entities, but as dual, time-symmetric observational projections of a singular topological -cell, quantum entanglement is shown to be a strict artifact of dimensional reduction. Introducing a dynamic phase shift governed by an external Minkowski 4-potential , we employ the 4‑dimensional Stokes’ theorem to map the phase accumulation directly onto the classical Maxwell field tensor . This geometric mapping naturally derives the covariant Lorentz force equation. We demonstrate that the apparent “spooky action at a distance” is an artifact of the coordinate time projection, whereas the physical metric of the system remains strictly local and invariant within the absolute phase time .
We formalize a bilocal extension of the Classical Transition Operator within the framework of phase dynamics to resolve the Einstein–Podolsky–Rosen (EPR) nonlocality paradox. By treating the electron () and positron () not as discrete, spatially isolated entities, but as dual, time-symmetric observational projections of a singular topological -cell, quantum entanglement is shown to be a strict artifact of dimensional reduction. Introducing a dynamic phase shift governed by an external Minkowski 4-potential , we employ the 4-dimensional Stokes’ theorem to map the phase accumulation directly onto the classical Maxwell field tensor , naturally deriving the covariant Lorentz force equation and its sign asymmetry without free parameters. Furthermore, we prove that the positron is a reactive topological "echo" of the primary forward phase step, introducing a sub-temporal causal delay bound by the Compton scale (), which resolves the cosmological baryon asymmetry problem.
We formalize a bilocal extension of the Classical Transition Operator within the framework of Phase Dynamics to resolve the Einstein–Podolsky–Rosen (EPR) nonlocality paradox. By treating the electron () and positron () not as discrete, spatially isolated entities, but as dual, time-symmetric observational projections of a singular topological -cell, quantum entanglement is shown to be a strict artifact of dimensional reduction. Introducing a dynamic phase shift governed by an external Minkowski 4-potential , we employ the 4-dimensional Stokes’ theorem to map the phase accumulation directly onto the classical Maxwell field tensor , naturally deriving the covariant Lorentz force equation and its sign asymmetry without free parameters. Furthermore, we prove that the positron is a reactive topological "echo" of the primary forward phase step, introducing a sub-temporal causal delay bound by the Compton scale (), which resolves the cosmological baryon asymmetry problem. Finally, we demonstrate that annihilation is not the destruction of matter, but the geometric collapse of the projection Jacobians and — extracting the system from Minkowski spacetime and returning it to the pure phase metric , where energy is absolutely conserved and probability vanishes.
This paper provides a strictly local, deterministic, and geometric derivation of quantum entanglement within the framework of Finsler-Maxwell Thermo-Relativistic (TR) Gravity. By extending the 4-dimensional positional space-time manifold to the 8-dimensional phase space of the Finsler tangent bundle TM, we demonstrate that quantum entanglement is not a non-local "spooky action at a distance." Instead, it is a manifestation of topological contiguity along the vertical fibers of velocity, frequency, and temperature. We prove that the measurement-induced correlation wave propagates at a superluminal coordinate velocity (V_intrication approx 2.603 * c) from a Riemannian perspective, yet remains strictly causal and subluminal (V_intrication < V_lim) within the conformally broadened Finslerian light-cone matrix. This approach provides a self-regularizing, geometric resolution to the Einstein-Podolsky-Rosen (EPR) paradox without violating local Lorentz covariance, showing that quantum correlations are encoded directly within the intrinsic non-zero bundle torsion.
Imagine a cube in space. Collapse one dimension and the loss is obvious—it becomes a square, its depth erased. Now place that cube in spacetime and collapse time instead. The shape looks unchanged, yet all traces of motion and cause have vanished. What once unfolded through sequence now appears as simultaneous influence across space, giving the illusion of instant action at a distance. We resolve apparent quantum nonlocality by identifying it as a dimensional reduction artifact. The Born rule's projection from complex amplitudes to real probabilities discards phase information—specifically, temporal dynamics encoded in the Schrödinger equation's exp(-iEt/ℏ) factor—creating the illusion of instantaneity, paralleling how Newtonian gravity's neglect of time produced apparent action-at-a-distance. EPR correlations satisfying Bell's constraints in probability space emerge from strictly local operations in amplitude space. The correlation E(a,b) = -cos(2(a-b)) arises geometrically from local rotations of quadratures relative to a shared phase reference φ, which cancels in correlation calculations. Computational verification across five million measurements reveals differential sensitivity: phase jitter reduces visibility (12% at 20% jitter) while measurement noise has negligible effect, indicating φ encodes physical temporal structure. The model predicts dual balanced homodyne detection will show quadratures rotating with φ while correlations remain invariant, providing direct experimental validation of this local amplitude-based description. Full simulation code implementing the quadrature detector model is provided in Supplementary Materials.