6.1 Quantum Cellular Automaton (QCA)
When you sit in a movie theater, watching smooth images on the screen: cars racing, clouds drifting, protagonists crying. Your eyes tell you everything is continuous and smooth. But if you walk up to the screen and observe with a magnifying glass, you’ll find that “smoothness” is just an illusion. You see only pixels of three colors: red, green, blue. These pixels themselves don’t move; they just change brightness in place according to specific rules.
Our universe is likely the same.
In Part II, we reconstructed relativity using smooth geometric language. We talked about “flowing rates,” “rotating vectors.” This is perfect for describing the macroscopic world. But when we try to apply this language to extremely tiny scales—Planck scale ( meters)—the smoothness of geometry collapses.
This is like trying to draw a perfect circle on a computer screen. No matter how high your resolution, if you zoom in enough, that circle’s edge will always become jagged steps.
In our geometric reconstruction framework, this “jaggedness” is not error; it is the universe’s ontological truth.
The Universe’s Refresh Rate
In Chapter 1, we introduced Axiom A1: the universe evolves at a constant rate. Macroscopically, this manifests as continuous flow; but microscopically, we need to introduce a new concept: Quantum Cellular Automaton (QCA).
Don’t be intimidated by this complex term. Its core idea is very simple: The universe is composed of countless tiny, discrete “logic units.”
Imagine space is not an empty box, but a vast three-dimensional grid. At every grid point there is a tiny quantum system—we can think of it as a “qubit” or a “miniature Hilbert Space.”
This is like the universe’s pixels.
This completely changes our understanding of “motion.” In classical physics, when an electron moves from point A to point B, we imagine it sliding through intermediate space like a marble. But in the QCA picture, the electron doesn’t move. What actually happens is grid point A “dimmed” (lost the electron’s state), while adjacent grid point B “brightened” (gained the electron’s state).
So-called motion is actually information transmission.
This explains that mysterious “evolution rate ” we mentioned in Chapter 2. In the QCA model, time does not flow continuously, but jumps frame by frame. The universe has a fundamental “clock tick” (Tick). In every clock tick, every grid point updates its state according to its neighbors’ states through a fixed rule (unitary operator).
Therefore, the universe is not “evolving,” but computing.
We not only view physics as geometric projection, but further, as a kind of computational projection (Computational Projection). From this perspective, the continuous rotation of Hilbert Space is actually the statistical average of countless tiny logic gate operations at the macroscopic level.
The Ghost of Discreteness
You might ask: “If the universe is really pixelated, why can’t I see the grid? Why don’t I feel the world ‘stuttering’?”
The answer lies in scale.
The pixel density at this layer is astonishing. According to estimates, one cubic meter of vacuum contains approximately Planck grids. For comparison, humanity’s sharpest displays have only hundreds of pixels per inch.
Because pixels are too small, update frequency too fast ( times per second), our senses—even our most precise particle colliders—cannot detect the underlying granularity. The “smooth spacetime” we see is actually a low-resolution approximation emerging from underlying discrete structures.
Just as water appears as continuous fluid but is essentially discrete water molecules; spacetime appears as a continuous stage but is essentially a discrete qubit network.
Acknowledging the universe’s discreteness (QCA nature) solves a problem that has plagued physics for years: the elimination of infinities.
In standard quantum field theory, when we calculate interactions between two particles approaching infinitely close, we often get “infinity” results. This is because we assume space can be infinitely divided. But in a QCA universe, you cannot approach infinitely close. Like on a screen, two bright points can only be adjacent at closest, not overlapping. This natural geometric cutoff (Cutoff) makes all physical calculations finite and reasonable.
So when we say “underlying pixels,” we are not making a metaphor. We are describing a reality more fundamental than “strings” or “membranes”: the minimal unit of information processing.
But if the universe is composed of fixed grids, a huge problem follows: Since grids are stationary, why does light speed appear the same in all directions? Shouldn’t walking diagonally and horizontally on the grid have different distances?
This is the famous “Lorentz symmetry breaking” problem. But in the next section we will see that QCA has a magical ability to perfectly disguise itself as isotropic continuous space at the macroscopic level, leaving only extremely tiny traces.
（Next, we will enter section 6.2 “Causality as Network Speed,” exploring how the speed-of-light limit naturally emerges as a logical necessity (Lieb-Robinson bound) in this pixelated universe.）