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DoT: The Duality of Time Postulate

And Its Consequences on General Relativity and Quantum Mechanics

Mohamed Haj Yousef

5.1. Mass as a property of a mode

The original book links inertia with the delay involved in forming a composite record. A physical mass must be identified consistently through acceleration response, rest energy, and dispersion; delay alone does not supply that identification.

Suppose a stable excitation has rest frequency ω0\omega_0 in a calibrated physical time and obeys

ω(𝐤)2=c2𝐤2+ω02.\omega(\mathbf k)^2=c^2\mathbf k^2+\omega_0^2.

(5.1)

With E=ℏωE=\hbar\omega and 𝐩=ℏ𝐤\mathbf p=\hbar\mathbf k, comparison with Eq. (3.12) gives

m=ℏω0c2.m=\frac{\hbar\omega_0}{c^2}.

(5.2)

A dimensionless eigenvalue becomes a mass only after its time scale, action scale, and propagation scale are fixed. The frequency must also belong to a physical excitation above the vacuum, rather than to an arbitrary auxiliary operator.

Internal kinetic and binding contributions enter a composite system’s invariant mass. Higgs couplings supply charged elementary fermion masses in the Standard Model after electroweak symmetry breaking. A generative account must recover the observed spectrum and interactions.

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