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.
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.
The apparent nonlocality of quantum mechanics and the EPR paradox arise from a single temporal category error: the Born rule deliberately erases the quantum system’s own proper time τ (Schrödinger’s Clock — the oriented global phase e^{−iEτ/ℏ}) and thereby renders probability space completely atimeless. When Bell tests later timestamp detection events with an external classical experimenter time t_exp and apply a coincidence window, they forcibly substitute one temporal coordinate for another that no longer exists. Null time ≠ zero time. This substitution creates the illusion of instantaneous (zero-time) collapse. In reality the temporal interval is not zero — it is null: the coordinate itself was projected away. Every consistent recording system outside physics — double-entry bookkeeping, temporal databases, GPS — avoids this paradox by maintaining two independent times: transaction/system time τ and posting/coordinate time t_exp. Quantum mechanics is intrinsically bitemporal. The Born rule is the only projection in physics that collapses these two columns into one, manufacturing apparent nonlocality. Retaining the dual-time structure of the amplitude representation restores strict relativistic locality and causality. Most dramatically, devices that preserve quadrature data can perform coincidence-free Bell tests by post-selection alignment of independent measurements using the residual shared phase — demonstrated explicitly in Elliott G. H. (2025), DOI 10.5281/zenodo.17612223. The universally required coincidence window in probability-space Bell tests is therefore the direct experimental proof of this temporal collapse — a classical substitute for the quantum system time that was destroyed. Quantum nonlocality is not fundamental; it is an artefact of single-time bookkeeping applied to a dual-time theory. Technical foundation (amplitude-space model and phase-jitter signatures): Elliott G. H., “A Local Amplitude-Based Resolution of the EPR Paradox via Dimensional Embedding”, Zenodo, DOI 10.5281/zenodo.17516855 (2025). Experimental demonstration (coincidence-free resynchronisation): Elliott G. H., “Coincidence-Free Bell Tests via Post-Selection Alignment of Independent Quadrature Measurements”, Zenodo, DOI 10.5281/zenodo.17612223 (2025). Keywords: quantum nonlocality, EPR paradox, Bell theorem, Born rule, bitemporal, dual time, system time, experimenter time, Schrödinger’s Clock, null time, coincidence window, coincidence-free Bell test, dimensional reduction, quantum foundations
We resolve the quantum nonlocality paradox by identifying a fundamental category error: the misinterpretation of null time (temporal coordinate absence) as zero time (instantaneous signaling). The Born rule's projection from amplitude space to probability space deliberately discards the dynamical phase ϕ_d(t) = e^{-iEt/ℏ}—Schrödinger's clock—that encodes the system's temporal evolution. This erasure leaves measurement events without temporal coordination, forcing experiments to employ classical coincidence windows as substitutes for the destroyed quantum timing information. We demonstrate that Bell-type correlations emerge from strictly local propagation of synchronized dynamical phases from a common source to each detector, with the apparent nonlocality arising only after temporal information destruction. The model reproduces all quantum predictions while restoring local causality, revealing that quantum mechanics is fundamentally local in its amplitude-space representation. Keywords quantum nonlocality, Bell theorem, EPR paradox, Born rule, temporal erasure, dynamical phase, Schrödinger's clock, local causality, amplitude space, coincidence windows, post-selection alignment, rotational invariance
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 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 .
The Einstein-Podolsky-Rosen (EPR) nonlocality puzzle has been recognized as one of the most important unresolved issues in the foundational aspects of quantum mechanics. We show that the problem is more or less entirely resolved, if the quantum correlations are calculated directly from local quantities, which preserve the phase information in the quantum system. We assume strict locality for the probability amplitudes instead of local realism for the outcomes and calculate an amplitude correlation function. Then the experimentally observed correlation of outcomes is calculated from the square of the amplitude correlation function. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state. Apart from resolving the EPR puzzle, this approach shows that the physical interpretation of apparently “nonlocal” effects, such as quantum teleportation and entanglement swapping, are different from what is usually assumed. Bell-type measurements do not change distant states. Yet the correlations are correctly reproduced, when measured, if complex probability amplitudes are treated as the basic local quantities. As examples, we derive the quantum correlations of two-particle maximally entangled states and the three-particle Greenberger-Horne-Zeilinger entangled state.