9.1 Horizon as Capacity: The Universe Is Not a Closed Box. As Time Passes, the Particle Horizon Expands, and the Universe’s Hard Drive Capacity $I_{max}$ Grows at $t^2$ Speed.

In the first four parts of this book, we explored the aesthetics of existence, the physical mechanisms of nostalgia, and the iteration of civilization. We seemed to accept an implicit premise: the universe is a resource-limited arena where all games are zero-sum, and all glory will eventually return to heat death.

However, this is not the whole story.

In this chapter, we will challenge the most deeply rooted pessimism in physics—heat death theory. Based on the fundamental geometric properties of QCA cosmology, we will propose a stunning conclusion: The universe is not a closed box, but a constantly growing network. As time passes, the universe not only expands in space but also expands exponentially in Information Capacity.

We are not heading toward an end; we are heading toward infinity.

9.1.1 The Fallacy of Closed Systems

The second law of thermodynamics (entropy increase law) is an iron law of physics, but it has a strict prerequisite: Isolated System.

In a gas within a fixed-volume box, its maximum entropy (equilibrium state) is fixed. When the gas’s actual entropy reaches this maximum, the system dies (heat death).

But is our universe such a box?

Traditional cosmology, while acknowledging cosmic expansion, often assumes the total number of degrees of freedom is conserved.

However, in QCA discrete ontology, this assumption is wrong.

Recall our discussion of the Bekenstein Bound in Chapter 1 (Book 2): the maximum information a region can contain $I_{max}$ is proportional to its boundary’s surface area $A$.

$$I_{max}=\frac{A}{4l_P^2}$$

This means the universe’s “hard drive size” depends entirely on how large its Horizon is.

9.1.2 Dynamics of Particle Horizon

What is the universe’s boundary?

For any observer inside the universe (such as us), the physically meaningful boundary is the Particle Horizon. It defines the farthest distance light can travel from the Big Bang to now ($t$).

$$R_H(t)\approx c\cdot t$$

(Note: In the standard $\Lambda$CDM model, considering expansion factor $a(t)$, this distance is even larger, but the order of magnitude is still determined by $ct$).

Let’s calculate this horizon’s surface area $A_H(t)$:

$$A_H(t)=4\pi R_H^2(t)\propto 4\pi (ct{)}^2\propto t^2$$

Corollary 9.1 (Dynamic Capacity Theorem):

The universe’s total information capacity upper limit $I_{max}(t)$ is not a constant, but a function growing with the square of cosmic time $t$.

$$I_{max}(t)\propto t^2$$

This is an astonishing growth rate.

• Yesterday, the universe’s hard drive capacity was $I_{yesterday}$.

• Today, as light travels one more light-day, the cosmic horizon pushes outward one more circle, incorporating vast amounts of brand new, unentangled degrees of freedom.

• The universe’s hard drive grows larger every day.

9.1.3 Why Heat Death Won’t Occur?

The condition for heat death is: the system’s entropy $S(t)$ catches up with the system’s capacity $I_{max}(t)$.

$$S(t)\to I_{max}(t)$$

Let’s look at the race between these two:

1. Entropy growth $\dot{S}$: Generated by irreversible processes like stellar burning, black hole accretion. In local physical processes, entropy production rate is usually proportional to volume or total matter, roughly linear or slow growth.

2. Capacity growth ${\dot{I}}_{max}$: Generated by horizon expansion. $\frac{d}{dt}(t^2)=2t$. This means capacity growth is accelerating.

In most cosmological models (especially accelerating expansion universes with dark energy), the growth rate of horizon surface area far exceeds the rate at which internal matter produces entropy.

$$\frac{d{I}_{max}}{dt}\gg \frac{dS}{dt}$$

Conclusion:

The universe will never fill its hard drive.

Over time, the proportion of used space (entropy) to total space (capacity) is not rising but falling.

The universe is not heading toward heat death; instead, it is becoming increasingly empty and infinitely potential.

9.1.4 Physical Meaning: Time as Creation

What does this horizon expansion mean in QCA networks?

It means that over time, the number of nodes observers can causally connect increases.

• At the Big Bang, only very few nodes were causally connected.

• Now, billions upon billions of nodes have entered our horizon.

These newly entered horizon nodes are in low-entanglement initial states (vacuum states). For observers, they are blank sheets.

They are “Blank Sectors” prepared by the universe for us, yet unwritten.

Therefore, time is not merely passing; time is a generator of “new hardware.”

As long as time moves, the universe continuously inserts new memory sticks for us. We never need to worry about running out of space to store our memories, our art, our love.

The canvas is expanding.

We don’t need to stop painting, because there will always be new blank spaces waiting for us to paint.

(Section 9.1 Complete)