9.2 The Eternity of the Unknown: Hardware Expansion Speed Exceeds Information Writing Speed. The Universe Forever Contains Undefined “Blank Sectors,” Novelty Never Depletes.

In the previous section, we derived that the universe’s total information capacity $I_{max}$ grows at least at $t^2$ speed over time. But this only tells us “the hard drive got bigger.” For a civilization dedicated to fighting heat death, a more critical question is: How fast do we fill this hard drive?

If civilization’s computational power explodes exponentially, could there come a day when we’ve written to all quantum bits in the universe, causing “memory overflow,” forcing the universe into cycles or crashes?

This section will compare hardware expansion rate with software writing rate, reaching an optimistic conclusion: In an expanding universe with dark energy, hardware generation rate forever exceeds the rate at which any physical process writes information. This means the universe forever possesses vast, undefined “Blank Sectors”. The Unknown is not temporary fog, but an eternal property of the universe.

9.2.1 The Race: ${\dot{I}}_{max}$ vs. $\dot{S}$

Let’s compare these two in order of magnitude.

1. Hardware expansion speed (${\dot{I}}_{max}$):

   According to holographic principle, capacity depends on horizon area. In the late universe dominated by dark energy ($\Lambda$), the universe enters exponential expansion phase (de Sitter expansion).

   Although the event horizon is fixed, if we consider available degrees of freedom within comoving volume (i.e., number of newly born nodes), its growth is exponential:

   $$N_{qubits}(t)\propto e^{3Ht}$$

   (Note: In QCA’s “node addition” model, physical volume expansion directly corresponds to increase in underlying node count).

2. Information writing speed ($\dot{S}$):

   This is the total rate at which all physical processes in the universe (stellar burning, black hole mergers, civilization computation) produce entropy or information.

   According to Bremermann’s limit (physical upper bound on computation speed) $E/\pi \hslash$, the universe’s total computation rate is limited by total energy $E_{total}$.

   In any causally connected region, matter energy density dilutes with expansion. Even if civilization converts all matter into computers, total power is limited by total matter.

   Therefore, entropy $S(t)$ growth is at most polynomial (or even saturated), or grows linearly with volume (if matter is conserved).

Inequality:

Over long timescales, exponential growth forever defeats polynomial growth.

$$\frac{d{I}_{max}}{dt}\gg \frac{dS}{dt}(\text{as }t\to \infty )$$

Conclusion:

The universe generates “empty qubits” far faster than we can turn “0” into “1.”

Every second, the universe provides us with far more blank paper than the previous second. We never need to worry about running out of paper; we only need to worry that our pens aren’t fast enough.

9.2.2 Blank Sectors: “Undefined” in Physics

What state are these newly added quantum bits that haven’t yet been “polluted” by matter interactions?

In QCA theory, newly inserted nodes must be initialized. The most natural assumption is initialization to Ground State or maximum uniform superposition.

$$|{\psi }_{new}⟩=|0⟩\text{or}\frac{1}{\sqrt{2}}(|0⟩+|1⟩)$$

These regions are called “Blank Sectors”.

• Physical properties: They are in low-entanglement, low-complexity, zero-history states. They are pure Potentiality.

• Geometric distribution: As the universe expands, these blank sectors continuously emerge from microscopic scales and are stretched into macroscopic voids. Most of the universe’s volume is this kind of “unwritten” virgin land.

For observers, this means the universe forever contains vast “non-historical” regions.

We don’t live in a dense block already filled by causal laws; we live in a sparse matrix. The vast majority of state space has not yet been visited.

9.2.3 Physical Mechanism of Novelty: Rejecting Poincaré Recurrence

If universe capacity were fixed, according to Poincaré recurrence theorem, history would eventually repeat. We would experience exactly the same life over and over. That is hell.

However, because $I_{max}(t)$ grows faster than system traversal speed, Poincaré recurrence time $t_{rec}\sim e^{I_{max}}$ grows doubly exponentially.

This means:

The time needed for the system to traverse all possible states forever exceeds the universe’s current age.

The universe forever lacks time to repeat itself.

Every moment, the universe’s total wave function $|\Psi (t)⟩$ is a brand new configuration that has never appeared in the past and will never repeat in the future.

Definition 9.2 (Novelty Conservation):

Due to hardware’s ahead-of-schedule expansion, the universe’s “Novelty Density” (proportion of unexplored phase space) always maintains a high level, even increasing over time.

Conclusion:

We don’t need to worry about “exhaustion of inspiration” or “end of history.”

Because the universe itself is an Open-ended Generative System.

It continuously lays new tracks, waiting for us to drive civilization’s train toward those wastelands that physical laws haven’t yet touched.

The unknown is the universe’s highest reward for free will.

(Section 9.2 Complete)