2.3 The Breaking of Scale Invariance

“Perfect disguise does not exist. Although the universe desperately tries to mask the truth of light speed growth through synchronous expansion, over extremely long time spans, that ruler used to measure all things—the fine structure constant—will eventually reveal tiny cracks. This crack is the backdoor to new physics.”

In the previous section, we explained why we cannot feel the exponential growth of light speed $c$. This is because our measuring instruments (atomic rulers and clocks) are also deforming synchronously, causing physical laws to exhibit Scale Invariance. It’s like when Alice grows larger, the entire wonderland also grows larger, so she feels unchanged.

But is this “synchrony” covering the entire universe really absolutely perfect?

If the universe’s underlying logic is $e$ (generation) and $\varphi$ (non-resonant growth), then absolute symmetry must be temporary.

Under the precise deduction of Vector Cosmology, we predict: As $\tau$ progresses, scale invariance will undergo tiny, observable breaking.

This breaking will not manifest in rough macroscopic motion; it will manifest in physics’ most refined dimensionless constant—the Fine Structure Constant ($\alpha$).

The Drift of 1/137

The fine structure constant $\alpha$ governs the strength of electromagnetic interactions. Its defining formula melts together light speed $c$, Planck constant $\hslash$, electron charge $e$ (charge quantity), and vacuum permittivity ${ϵ}_0$:

$$\alpha =\frac{e^2}{4\pi {ϵ}_0\hslash c}\approx \frac{1}{137}$$

Physicists have long been puzzled by why it is $1/137$. But in our evolution equation, the more important question is: Will it change?

Let’s look at $c$ in the formula.

According to our equation $c(\tau )\propto e^{k\tau }$, $c$ is in the denominator.

If the evolution rates of charge $e$ and Planck constant $\hslash$ are completely synchronized with $c$ (i.e., following exactly the same $\varphi /\pi$ growth rate), then $\alpha$ will be an absolute constant. The universe will forever maintain “scale invariance.”

But the essence of $\varphi$ (spiral) is “incommensurability”.

Different physical sectors’ evolution rates are difficult to achieve absolute mathematical synchronization.

• $c$ (light speed): Mainly driven by the expansion of the $v_{ext}$ sector.

• $e$ (charge): Mainly maintained by the $v_{int}$ sector (internal $U(1)$ rotation).

As the cosmic spiral unfolds, there will be extremely tiny “shear” between external expansion (space/light speed) and internal rotation (matter/charge).

This shear will cause $\alpha$ to drift slowly:

$$\frac{\dot{\alpha }}{\alpha }\ne 0$$

Evidence from Quasars

This is not merely theoretical prediction. At the frontier of observational astronomy, we have already seen signs of this breaking.

By analyzing absorption spectra of quasars billions of light-years away (i.e., billions of years ago), astronomers (such as Webb et al.) have found that the early fine structure constant $\alpha$ differs from modern laboratory measurements by an order of magnitude of one part per million ($10^{-5}$).

In the standard model, this is regarded as measurement error or “clouds of new physics.”

But in Vector Cosmology, this is fulfillment of prophecy.

• If $\alpha$ has decreased (meaning $c$’s growth is slightly faster than $e^2$): This indicates the universe’s “hardware upgrade” (bandwidth growth) is faster than “software refactoring” (charge coupling).

• If $\alpha$ exhibits spatial dipole anisotropy (increasing at one end of the universe, decreasing at the other): This proves the universe is not only expanding but also spinning. That Néron-Severi great circle is undergoing complex torsion in high-dimensional space.

The drift of $\alpha$ is the footprint left by the Red Queen’s run. It proves that perfect circle is not completely closed; each cycle leaves tiny geometric residuals.

Physical Consequences of Breaking: Countdown to Phase Transition

What use is this tiny drift? Is it just astronomers’ conversation piece?

No. It is the countdown to Phase Transition.

The stability of physical laws depends on constant constancy. If $\alpha$ changes by $4\%$, carbon synthesis in stellar interiors will stop, and life cannot be born.

This hints at a terrifying but also hopeful prospect:

Current physical laws are only temporary “metastable states.”

As light speed $c(\tau )$ grows exponentially, accumulated scale breaking will eventually reach a critical point.

• Quantitative change: $\alpha$ drifts slowly.

• Qualitative change: When $\alpha$ crosses a certain threshold, electrons can no longer be bound by atomic nuclei.

At that moment, all atomic matter will instantly disintegrate. But this is not destruction; this is formatting.

Old material forms (atoms) are eliminated because they cannot keep up with light speed growth.

New material forms (perhaps pure photon crystals, quark-gluon plasma computing clouds) will take their place.

Conclusion: Light in the Crack

So, the breaking of scale invariance is not a bug of the universe; it is a feature.

It is a crack.

If physical laws were ironclad and eternally unchanging, then we would truly be dead things imprisoned in a circle.

It is precisely because constants are drifting, precisely because that 1/137 is trembling slightly, that we confirm the universe is alive.

It is growing, it is changing, it is preparing for the next grand phase transition.

And we—observers at $\tau \approx 1800$—are precisely through measuring this tiny breaking, glimpsing the direction of cosmic evolution.

We need not fear the change of laws.

Just as when water becomes steam, water molecules do not die; they merely gain the freedom to fly.

So do we.

Thus, the task of Volume One [Equations] is complete. We have derived the formula, explained its physical meaning, and even pointed out observational evidence to verify it.

Now, holding this powerful mathematical tool in our hands, it is time to aim it at ourselves.

At which node of cosmic history do we stand? How far are we from that “phase transition moment” that will disintegrate atoms and elevate consciousness?

This leads to the theme of Volume Two: Coordinates. We will no longer talk about distant quasars; we will calculate here, now, this body.