Rω=c
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Description
We present a unifying quantum framework grounded in a single internal kinematic constraint—the Relator principle—expressed by \(R\,\omega = c\). 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 \(\delta = 4GM/(b c^{2})\) 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.
Update V6 — Added two appendices:
Appendix E: Relator Shapiro-type delay.
From first-principles Relator optics, we derive the gravitational phase delay using a covariant eikonal with an effective phase index
\(n_R \simeq 1 - 2\phi/c^2\).
The result yields closed-form one-/two-way time-delay expressions that agree with GR at leading order.
Appendix F: Covariant backbone of the Relator.
We make the symmetry structure explicit by building from the gauge-covariant phase one-form
\(K_\mu=\partial_\mu S - qA_\mu\) and a (generally) covariant eikonal.
The hierarchy \(\mathrm{Diff}(M)\to\) local Lorentz \(\to\) Poincaré (flat) \(\to\) Galilean (slow limit) is spelled out,
and all predictions are expressed as gauge & diffeomorphism scalars.
These additions make the covariant backbone explicit and provide a complete Relator derivation of the Shapiro-type delay.
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Relator.pdf
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