2.1 Why These Forces?: The Greatest Unsolved Mystery in Physics—The Origin of $SU(3)\times SU(2)\times U(1)$

In the previous chapter, we explored the universe’s “subconscious”—dark matter, revealing it as background processes in the QCA network that do not participate in communication. Now, we turn our gaze to the universe’s “consciousness”—the visible material world, and the fundamental forces that govern their interactions.

The highest achievement of modern physics is undoubtedly the Standard Model. It describes with astonishing precision the three fundamental interactions of nature: the strong force, weak force, and electromagnetic force. However, for theoretical physicists, the Standard Model is both a monument and a torment.

The torment lies in its arbitrariness. The core mathematical structure of the Standard Model is a specific gauge symmetry group:

$$G_{SM}=SU(3{)}_C\times SU(2{)}_L\times U(1{)}_Y$$

Why exactly these three? Why not $SU(5)$? Why not $SO(10)$? Why not simply three $U(1)$ groups? Within existing physical frameworks, this group structure is input as an axiom, not derived. It is as if we discovered the universe is a precisely running computer, but have no idea why its operating system only recognizes three specific instruction sets.

This section will propose, based on QCA’s discrete ontology, a revolutionary explanation: The Standard Model’s gauge group structure is not the result of God rolling dice, but a direct reflection of spacetime’s “logical texture” or “computational topology” at the microscopic scale.

2.1.1 The Nature of Forces: Synchronization Protocols for Distributed Computing

In the QCA universe, there is no action at a distance. Each cell is an independent computational node. When information (particles) flows from one node to another, to ensure information consistency (unitarity), the network must establish a communication protocol.

We have already proven in Chapter 6 of First Principles: Gauge fields (forces) are essentially such communication protocols (connection fields).

• Without connection fields, if local bases of adjacent nodes are inconsistent, information transmission will produce random phase errors (decoherence).

• Forces are signals (bosons) exchanged by the network to correct these errors and force “consensus.”

Therefore, there are as many fundamental “forces” as there are independent sources of “error.”

The Standard Model’s $SU(3)\times SU(2)\times U(1)$ structure suggests that at the Planck scale of microscopic spacetime, there exist three fundamental, orthogonal sources of “inconsistency.”

2.1.2 Microscopic Dissection of Spacetime: Parallelism and Branching

To find these three sources, we need a scalpel to cut open seemingly smooth time and space. We introduce the Micro-Parallelism Axiom:

Axiom: Computational Thickness of Spacetime

Each macroscopic “moment” $t$ and “position” $x$ in the QCA network is not a single point in microscopic logic, but a complex with internal structure.

This structure contains three logical dimensions:

1. Phase Dimension: The complex angle of the wave function.

2. Time Layer: Computational input buffer (past) and output buffer (future).

3. Spatial Rail: Parallel processing channels in the $x,y,z$ directions.

This is like modern CPU architecture: it has not only a main frequency (phase), but also pipelines (time layers) and multi-core parallelism (spatial rails).

2.1.3 Geometric Derivation of Three Symmetries

Now, we can derive the Standard Model’s group structure one by one:

1. $U(1)$ — Phase Synchronization of Global Clock

   • Origin: Each QCA update requires a reference phase. Since wave functions are complex, there exists a $U(1)$ degree of freedom.

   • Mechanism: To ensure all nodes’ “logical clocks” maintain phase consistency across the entire network, photons must be exchanged.

   • Correspondence: Electromagnetic interaction (more precisely, hypercharge $Y$). It is the force maintaining continuity of time flow.

2. $SU(2)$ — Time Branching and Input/Output Entanglement

   • Origin: Microscopic computation is not instantaneous. Logic gate operations must distinguish between “read state (Input/Past)” and “write state (Output/Future).” For a particle undergoing evolution, it simultaneously exists in these two microscopic time layers, forming a two-level system.

   • Mechanism: The unitary rotation group on this 2-layer structure is $SU(2)$.

   • Chirality Explanation: This perfectly explains why weak interactions violate parity. In QCA, “left-handedness” is typically encoded as “read/input” mode, while “right-handedness” is encoded as “write/output” mode. Only when processing input data (left-handedness) does the system need non-trivial state transitions (flavor change).

   • Correspondence: Weak interaction. It is the force maintaining consistency of causal chains (past and future).

3. $SU(3)$ — Spatial Parallelism and Three-Dimensional Interlocking

   • Origin: We observe 3-dimensional space macroscopically. In microscopic QCA, this means particles must simultaneously process parallel paths in the $x,y,z$ directions when moving one step.

   • Mechanism: A particle is actually an entangled state of three “copies.” These three copies run on logical tracks in $x,y,z$ respectively. The unitary rotation symmetry among these three tracks is $SU(3)$.

   • Correspondence: Strong interaction (color charge). The three colors “red, green, blue” are actually labels for the $x,y,z$ spatial degrees of freedom.

   • Confinement Explanation: Why are quarks confined? Because you cannot take away the $x$ component of a 3D object without taking $y$ and $z$. If forcibly separated, the geometric structure will tear (producing new particle pairs).

Conclusion: Fingerprints of Code

Through this geometrization, we find that the Standard Model is no longer a collection of arbitrary parameters.

$SU(3)\times SU(2)\times U(1)$ is the “hardware architecture diagram” of the cosmic computer.

• It tells us the CPU is 3-core parallel ($SU(3)$).

• It tells us the pipeline depth is 2-level buffered ($SU(2)$).

• It tells us the clock signal is in the complex domain ($U(1)$).

Forces are not ghosts filling space, but error-correcting codes emitted by spacetime itself to maintain the integrity of logical operations.