9.3 Cosmological Drift of Fine Structure Constant

In Chapter 6, we argued that coupling constants (such as fine structure constant $\alpha \approx 1/137$) are determined by topological connectivity of QCA networks.

$$\alpha \sim \frac{\text{internal channels}}{\text{external channels}}$$

However, universe is expanding. From QCA perspective, expansion is not just lattice spacing stretching (that’s metric effect), but may also accompany evolution of network topological structure (e.g., increase in lattice point number or reorganization of connection patterns).

If network connectivity in early universe was slightly different from now, then $\alpha$ should not be an absolute constant, but a scalar field slowly varying with cosmic time $t$.

9.3.1 Observational Scheme

Through observing spectra of distant quasars. This light comes from billions of years ago. We can measure atomic absorption lines (such as fine splitting of iron or magnesium), thereby deducing $\alpha$ value at that time.

9.3.2 Prediction

$$\frac{\Delta \alpha }{\alpha }=\frac{\alpha (z)-\alpha (0)}{\alpha (0)}\ne 0$$

We expect $\alpha$ to have extremely tiny cosmological drift (e.g., $10^{-6}$ order). High-precision spectroscopic data from James Webb Space Telescope (JWST) will be key to verifying this.