Environmental Decoupling: Reconciling SNe Ia Time Dilation with Null Variations of $α$

TL;DR

The paper shows that the positive time-dilation signal observed in SNe Ia can coexist with null measurements of $\alpha$ in precision spectroscopy if local bound systems shield themselves from the global GCT time flow. Using a GCT metric with $N(t) \propto a^{b/4}$, AD and MM impose background scalings $\Delta \lambda/\lambda \propto (1+z)^{b/2}$ and $\Delta k/k \propto (1+z)^b$, respectively, while a strong environmental shielding yields $|b_{\text{local}}| \lesssim 10^{-5}$. The shielding factor $\gamma = b_{\text{local}}/b_{\text{bg}}$ is constrained to $\lesssim 1.5\times10^{-4}$, implying a suppression by ~6000 in local absorbers and resolving the apparent tension without modifying local physics. The framework predicts that fully virialized systems show negligible local time variation, while partially virialized environments could reveal residual signals, offering a testable avenue for future observations across gravitationally diverse environments.

Abstract

The Generalized Cosmological Time (GCT) framework interprets the observed time dilation in Type Ia supernovae (SNe Ia) as a manifestation of a generalized lapse function in the background metric, favoring a parameter value b \approx 0.04. However, precision spectroscopic measurements of the fine-structure constant αvia the alkali doublet (AD) and many-multiplet (MM) methods predominantly yield null results. In this work, I demonstrate that this discrepancy is not a sensitivity limitation but a fundamental physical consequence of distinguishing between global coordinate time and local proper time. By inverting the GCT scaling relations, I establish that spectroscopic data constrain the effective parameter to |b_{\text{local}}| \lesssim 10^{-5}, revealing a tension of three orders of magnitude against the background value. I resolve this by invoking the principle of environmental shielding. I argue that dense, virialized gas clouds maintain a static local metric that is dynamically decoupled from the background cosmological time flow, strictly analogous to the detachment of bound systems from the Hubble expansion. Consequently, atomic spectra probe a shielded local frame where physical constants remain invariant, whereas SNe Ia observations measure the accumulated geometric time dilation of photons traversing the expanding background. This framework reconciles the positive dilation signals in geometric probes with the stability of fundamental constants in local bound systems without modifying local physical laws.

Figures (1)

• Figure 1: Schematic representation of the dual interpretation of cosmological observables within the GCT framework. (Top) Path Dependence: Photons from SNe Ia propagate through the expanding cosmological background, accumulating the full time dilation effect ($b \approx 0.04$) associated with the background lapse function. (Bottom) Environmental Shielding: Quasar absorption lines are imprinted within dense, gravitationally bound gas clouds. In these screened environments, the effective lapse function decouples from the cosmic flow ($b_{\text{eff}} \approx 0$), preserving the local values of physical constants. The resulting signal is a null measurement, reflecting the static nature of the local frame.