Adopted ideal plane-wave and frequency-reading model

Adopt as physical assumptions of this framework, extending Adopted ideal-clock and ideal-vacuum-light interpretation (ideal vacuum light rays are exactly the future null straight lines, with coordinate speed $c$ in every inertial chart) and Adopted inertial covariance of the model equations (the affine Minkowski model, with the model's equations covariant under proper orthochronous affine Lorentz maps):

(i) Ideal plane wave. An ideal monochromatic light wave in vacuum is modeled, in any inertial chart, by a dimensionless affine phase $\theta$ with future null wave covector $k$ (Affine phase functions and wave covectors on affine Minkowski space, Frame data of a future null wave covector: the unique pair $(\varpi ,s)$ with $\mathrm{\mid }s\mathrm{\mid }=1$): the level sets of $\theta$ are the wave fronts, and the complete ray trajectories of this wave are the constant-phase lines $\lambda \mapsto p+\lambda k^{\mathrm{♯}}$ for $\lambda \in \mathbb{R}$, whose tangents are future null. Their future portions from $p$ have images $p+{\mathbb{R}}_{\ge 0}{k}^{\mathrm{♯}}$. The complete trajectories are ideal light rays in the sense of Adopted ideal-clock and ideal-vacuum-light interpretation; the portions are half-lines. The model is one ideal plane wave: constant wave covector, no medium, no dispersion, no absorption, no modulation or envelope, no boundary or source model, no intensity or polarization model.

(ii) Frequency reading. An ideal observer of the model with four-velocity $U_o=cn$ ($n$ future unit timelike) that receives this wave reads the angular frequency ${\omega }_n:=-ck(n)=-k(U_o)$ and the linear frequency ${\omega }_n\mathrm{/}(2\pi )$ of Null wave covectors, frame frequency data and the observer frequency of an ideal plane wave, that is, minus the rate of change of the phase with respect to the observer's own proper time with the sign convention that this number is positive (The phase rate along a worldline is the wave covector evaluated on the four-velocity, A future timelike vector pairs negatively with every nonzero future causal vector). The reading is attached to the observer's worldline at the event of reception.

(iii) Frequency comparisons. Comparing the frequency of one wave between two ideal observers or between two inertial descriptions means comparing ${\omega }_n$ at specified reception events, or the frame data $(\omega ,s)$ of the same phase function in specified inertial charts; this postulate asserts no Doppler or aberration formula, and comparing events requires propagating the phase along the specified observer worldlines.

(iv) Scope and exclusions. These are adopted idealizations, not deductions from experiment and not claims about nature. No quantum photon model and no identification of energy with $\mathrm{\hslash }\omega$ is made; no claim is made that real light, real clocks, real receivers or real sources are exactly described; dispersive, absorbing, nonlinear or modulated media, finite line width, intensity, polarization, source and detector physics, gravitation, quantum effects and accelerated-observer reception are outside the model. Empirical tests of the model belong to the framework's experimental work and are not asserted here.

No choice principle is used in this formulation; the postulate is an adopted assumption of the model, not a proved assertion.