DoT: The Duality of Time Postulate

For a positive invertible response operator $K$ and source $f$, a typical static response is

The rescaling $K\mapsto\lambda K$ changes $C_f$ to $C_f/\lambda$ without changing the carrier dimension. Rescaling $f$ also changes the response. A rank of $137$ therefore does not fix an electromagnetic interaction strength until the operator, source, and absolute normalization have been selected.

The low-energy electromagnetic fine-structure constant is

The 2022 CODATA recommended value is $$\alpha^{-1}=137.035\,999\,177(21),$$ where the parentheses denote the standard uncertainty in the final digits [16]. The structural identification $\alpha_0=1/137$ is therefore a proposed ideal-model value, not the measured coupling. The difference is about $2.63\times10^{-4}$ in relative terms, far larger than the quoted uncertainty. A correction must follow from independent dynamics, with a stated energy regime and renormalization prescription; fitting the residual does not derive it.

Dimensional constants require equal care. The SI assigns exact values [17]: $$\begin{aligned} c&=299\,792\,458\,\mathrm{m\,s^{-1}},\\ h&=6.626\,070\,15\times10^{-34}\,\mathrm{J\,s}. \end{aligned}$$ Replacing $c$ by $300\,000\,000\,\mathrm{m\,s^{-1}}$ is not a new vacuum prediction in those same units. Nor does multiplying a refractive-index ratio by three measure a spatial dimension. A model should predict dimensionless relations or comparisons with operational standards.