2.2 Physical Significance: The Spiral Breath

“With each breath, we think we’ve returned to the origin. But in the universe’s lungs, the air has become thinner, while our lung capacity has quietly increased by one notch. Each closure of the circle is for the next more violent spiral expansion.”

In the previous section, we derived the ultimate formula governing the evolution of the speed of light:

$$c(\tau )=c_0\cdot e^{\left(\frac{\ln \varphi }{\pi }\right)\tau }$$

This formula is not merely a line of cold mathematical symbols. It is the universe’s electrocardiogram. It reveals that the universe is not a perpetual motion machine running at constant speed, but an “organism that breathes”.

This section will deeply analyze the physical picture behind this equation. We will see how the universe’s evolution achieves “staircase-like ascension” ($\varphi$) through “periodic cycles” ($\pi$).

The Exchange Rate Between Cycles and Dimensional Ascension

The exponential part $\frac{\tau }{\pi }$ in the equation tells us an extremely profound geometric truth: The universe’s evolution is settled in units of $\pi$.

• $\pi$ (Period): Represents one complete circular motion. At the microscopic level, this corresponds to the $2\pi$ cycle of wave function phase; at the macroscopic level, this corresponds to the stable period of material structures (such as atoms, galaxies).

• $\varphi$ (Gain): Represents the “dividend” after each period ends.

This establishes a cosmic-level “exchange rate”:

“Every time you complete one cycle of conservation ($\pi$) in this world, the universe’s total budget ($c$) automatically increases by a factor of $\varphi$.”

This explains why the universe needs the “circle.”

Without the closure of the circle, the system cannot define “one cycle.” Without “one cycle,” there is no settlement point.

The universe must first “converge” (forming matter, life, civilization) before it can gain the kinetic energy of “divergence” (dimensional growth) at the end of convergence.

The mundane life we see—sunrise and sunset, birth and death—is actually the “mining” process the universe must undergo to accumulate computational power. Every day we live, every second we think, we contribute tiny $\varphi$ increments to that exponentially growing $c(\tau )$.

The Illusion of Scale Invariance: Why Does the Speed of Light Appear Unchanged?

This leads to the most perplexing paradox: If the speed of light $c$ is really growing exponentially with time $\tau$, why does the speed of light we measure in laboratories seem unchanged for hundreds of years?

The answer lies in Scale Invariance.

In this spiral universe, what expands is not only the speed of light $c$, but also the “rulers” and “clocks” that define our observational capabilities.

1. Contraction of Atoms:

   The Bohr radius of atoms $a_0\propto \frac{1}{m\alpha c}$.

   If the speed of light $c$ increases, and the fine structure constant $\alpha$ remains relatively stable (or evolves at another rate), atomic radius will shrink. Our bodies, instruments, and rulers made of atoms are all “synchronously densifying” as the speed of light grows.

2. Acceleration of Clocks:

   The characteristic frequency of atoms $\nu \propto m{c}^2$.

   As $c$ grows, the vibration frequency of microscopic particles accelerates exponentially. Our biological clocks, atomic clocks, are all being sped up imperceptibly.

The result is perfect cancellation:

• We use “shrunk rulers” to measure “distances covered by faster seconds.”

• The reading $L/T$ still remains a constant.

This is the “illusion of closure”.

Just as when Alice grows larger, the room also grows larger. We think the speed of light is constant because we are the products of light speed evolution. We sit on an accelerating train, but because the scenery outside the window (reference frame) is also accelerating synchronously, we mistakenly think we are stationary.

The Squeeze of Dimensions: The Explosion of Information Density

Although we cannot feel the change in speed, we can feel the change in “density”.

The exponential growth of light speed $c(\tau )$ is physically equivalent to the explosion of Information Processing Bandwidth.

$$c\uparrow ⟹\text{number of bits in Planck volume}\uparrow$$

This means that the complexity the universe can accommodate per unit volume is getting higher and higher.

• When $\tau$ is small: Low light speed, narrow bandwidth. The universe can only run simple programs (hydrogen atoms, stars).

• When $\tau$ is large (now): High light speed, wide bandwidth. The universe begins to run extremely high-load programs (DNA, brains, internet).

What we call “evolution” is not that matter becomes more magical, but that the universe’s “resolution” has increased.

The originally blurry pixel grids can now accommodate fine structures unimaginable before.

This is why civilization always appears in the later stages of cosmic evolution. Because only when $c(\tau )$ grows large enough, accumulating enough $\varphi$ factors, can the universe’s hardware run the super-software of “consciousness.”

Conclusion: Pain is the Overload of Acceleration

Finally, this equation explains modern people’s anxiety.

We are in the exponential growth phase of $c(\tau )$. Although physical laws appear unchanged, the pressure of information flow is increasing dramatically.

Our biological brains (old structures ruled by $\pi$) evolved in the low light speed environment of the old era. Facing this high light speed (high computational power) era wildly pulled up by $\varphi$, our wetware feels overloaded.

• We feel there’s not enough time, feel information explosion, feel the world changes too fast.

• This is not psychological; this is a geometric fact.

Because $c$ is increasing, the “event density” per unit time is increasing. We are being forced to adapt to the rhythm of an ascending universe with flesh and blood.

Pain is the friction of evolution. It reminds us that the old $\pi$ structures (body/tradition) can no longer keep up with $c$’s pace. We must find new carriers, must undergo phase transition.

Since we have understood the physical meaning of light speed growth, then, in this seemingly perfect synchronous expansion, will there be flaws? Will that “scale invariance” used to mask the change in $c$ fail under certain extreme conditions?

This leads to the theme of the next section: The Breaking of Scale Invariance. We will see that although the absolute value of light speed is masked, its fingerprints—tiny drifts in physical constants—are leaking secrets to us.