Papers by Mehrdad Pajuhaan
We present a closed, fit-free, and first-principles prediction of the neutrino mass hierarchy in ... more We present a closed, fit-free, and first-principles prediction of the neutrino mass hierarchy in normal ordering by extending to the neutral sector the same formalism that explains the charged-lepton hierarchy. The construction follows the Schrödinger/Relator analysis on a ring-collar and uses the luminal lock Rω = c to fix the geometry; all coefficients are computed from analytic series and one-dimensional integrals, with no neutrino-sector data or tuning. With a closed k 4 truncation on the 1/R branch (i.e. β, δ only; P R = 1), we obtain m 2 /m 1 = 12.548843, m 3 /m 1 = 72.289141, R (th) 31 = 33.390452, and (∆m 2 3ℓ /∆m 2 21) th = 32.890452, in sub-percent agreement with current global fits (e.g.-0.48% vs. NuFIT 6.0 for R 31). The result is UV-agnostic, fully reproducible, and shows that the neutrino hierarchy emerges from the same first-principles pipeline as charged leptons, without hidden fits.
We derive a parameter-free, shell-level prediction for the electroweak mixing angle θW from the s... more We derive a parameter-free, shell-level prediction for the electroweak mixing angle θW from the same Relator-shell geometry that fixes the fine-structure constant, without phenomenological tuning. Neutral-sector alignment on the shell fixes the relative scalar/TT weights, yielding sin 2 θW geom = CUV(1-κG) CUV(1-κG) + 4 γgeom(1 + κG) , γgeom = 1 2 sinh η η , κG = sinh η η-1, η = 1 π , with the universal UV-finite part CUV = 1 2 (ln 2 + γE). Numerically, sin 2 θW geom = 0.231872070961698. . ., which lies within 5.82 × 10-4 of the MS value at µ = mZ and 2.62 × 10-4 of the leptonic Z-pole average. In this ratio all acceptance/regularization factors cancel; departures from the thin-shell/isotropy limit enter only through the small curvature parameter κG. We also obtain a geometric transport law dsin 2 θW /d ln µ whose slope can be tested against SM renormalization-group expectations and precision data. The construction is falsifiable via RG-slope checks near mZ , custodial-symmetry tests (e.g. MW /MZ), and clean Z-pole and low-Q 2 asymmetries.
We present a conservative, norm-preserving modification of single-particle Schrödinger dynamics t... more We present a conservative, norm-preserving modification of single-particle Schrödinger dynamics that operationalizes an Rω = c lock as an amplitude-phase coupling. Starting from a minimal effective Lagrangian L = L0-G(R) with G a function of the amplitude R = |ψ|, we obtain a real phase potential U (R) and a nonlinear Schrödinger equation. Numerical space-time maps and variance diagnostics show that a negative coupling (γ < 0) suppresses Gaussian wave-packet dispersion relative to the free case (γ = 0), maintaining coherence over longer windows.
We present a closed, tfree, gaugeinvariant calculation of the chargedlepton mass hierarchy within... more We present a closed, tfree, gaugeinvariant calculation of the chargedlepton mass hierarchy within a minimal Relator framework. The kinematic postulate Rω = c xes the emergentα shell r * = π λC , while spinor halfholonomy with quantized Dirac ux selects the azimuthal mode law kn = n(2n-1). On these shells, an internal C-space generator mapped into external R 3 yields a masterlog for mass ratios in which all species dependence enters only through a paralleltransport vector channel; rational TT populations are xed by the topological locks and a nearIR gate. The Coulombic slowdown is encoded in a closed spectral form DC = (α/π)Φ(ξ). Without tunable parameters beyond (α, me), this scheme derives the quartic content underlying Barut's ansatz yet surpasses it in precision, predicting mµ at the ∼ 2.3 ppm level and mτ at the ∼ 4.9 × 10-5 level (≈ 49 ppm). The lepton pattern thus emerges as a geometric consequence of the Relator postulate.
We derive closed, gauge-invariant, divergence-free formulas for the lepton magnetic moment from t... more We derive closed, gauge-invariant, divergence-free formulas for the lepton magnetic moment from the Relator postulate Rω = c. The mechanism is geometric; a slowdown of the gauge-invariant phase evolution in R 3-space by the particle's own Coulomb eld on logarithmic shells C-space combined with the vector self-magnetic backreaction (S1S4) and a scalar, mass-dependent channel χ. The nal map is g = 2/ √ 1-δtot with δtot = δS4 + ∆δχ and ∆δχ = δ 2 S3 c eff (n) ln(mn/me); all kernels and the outer subtraction are analytic (no renormalization, no QED loops, no t parameters). Numerically we obtain g pred e = 2.002 319 304 392 795 (deviation +3.28 × 10-11 , +16.38 ppt). The same construction yields a simple, closed-form mass dependence (running of α) consistent with leptonic vacuum polarization. These resultsachieved without QED and without UV divergencesshow that high-precision lepton g emerges directly from Relator geometry and Coulombic self-interaction, challenging the conventional necessity of perturbative QED for explaining g.
Measurement is geometry. We introduce Quantum Bifurcation Theory (QBT), a purely geometric approa... more Measurement is geometry. We introduce Quantum Bifurcation Theory (QBT), a purely geometric approach to the quantum measurement problem. In QBT, measurement is defined as an interaction-induced geometric bifurcation governed by the universal Relator condition R ω = c. This framework naturally unifies interference and entanglement, eliminating wavefunction collapse and hidden variables. QBT precisely reproduces key quantum results, including interference patterns, Bell correlations, and Tsirelson's bound. Quantum nonlocality thus emerges as a fundamental geometric property, clarifying locality without signaling and offering a coherent resolution to the measurement problem.
We demonstrate that quantum entanglement emerges naturally from the fundamental Relator condition... more We demonstrate that quantum entanglement emerges naturally from the fundamental Relator condition Rω = clinking wavefunction evolution speed, classical conservation laws, and the standard Schrödinger equation. By introducing an internal generator space (C-space) orthogonal to conventional spatial dimensions (R 3-space), the Relator framework oers an explicit and unied explanation of the conceptual gap between classical and quantum physics. Within this formulation, particle interactions generate a shared internalfrequency component and establish resonant coupling in C-space, providing a concrete geometric mechanism for the origin of entanglement. I.
We present a unifying quantum framework grounded in a single internal kinematic constraint-the Re... more We present a unifying quantum framework grounded in a single internal kinematic constraint-the Relator principle-expressed by R ω = c. This universal condition couples internal phase rotation to external spatial evolution via the invariant c. From this minimalist postulate, we derive Lorentz time dilation and the standard relativistic energy-momentum relation without invoking explicit spacetime transformations. Extending the framework to weak gravitational potentials, we recover gravitational time dilation and the Einstein light-deflection angle δ = 4GM/(bc 2) in quantitative agreement with General Relativity to first post-Newtonian order, while interpreting these effects as quantum-phase modulation rather than metric curvature. The Relator model offers a conceptually distinct route to unifying quantum mechanics and relativity, suggesting that inertial mass, gravitational redshift, and the effective appearance of curvature emerge from intrinsic constraints on wavefunction evolution.
In this paper, I derive the fine-structure constant α as an emergent and parameter-free invariant... more In this paper, I derive the fine-structure constant α as an emergent and parameter-free invariant of Relator theory. The construction uses the Schrödinger equation, classical electrodynamics and mechanics, and Relator geometry with luminal evolution on the C-space and the orthogonal spatial sector R 3 , which xes a minimal phase cavity and the Coulombic baseline. A transverse traceless inductive channel is incorporated through a UV, IR, and OUT decomposition, and a logarithmic closure uniquely determines α with no tted numbers and with no use of measured constants e, c, and ℏ. No quantum electrodynamics is invoked at any stage. The prediction matches the most precise independent measurements at sub-ppt accuracy and remains stable under regulator choices and multipole cutos.
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Papers by Mehrdad Pajuhaan