3.3 Physical Implementation of Free Will: Creating Unpredictable Futures in Deterministic Physical Laws Using Computational Irreducibility

In the previous two sections, we defined the self as a self-referential loop in the QCA network and memory as a topologically protected standing wave. So far, we have constructed a stable observer model with identity. However, this observer still seems to be a passive bystander, or at most an automaton running according to a fixed program. This raises the most central and thorny question in consciousness research: Free Will.

If the universe’s underlying rules $\hat{U}$ are deterministic, did the initial state $|{\Psi }_0⟩$ of the Big Bang 138 billion years ago already lock in every detail of me writing this sentence and you reading it at this moment? If so, isn’t the so-called “choice” just a self-deceiving illusion?

This section will propose a physical compatibilist answer based on Computational Irreducibility in computational theory. We will prove: Determinism not only does not exclude freedom, but is the foundation for free will to exist. Freedom is not the ability to violate physical laws, but the ability to be unpredictable by external systems in advance.

3.3.1 Prediction Paradox: Why Can’t Even God Spoil the Ending?

Classical determinism (Laplace’s demon) promises an illusion of omniscience: as long as we know the current microscopic state and evolution laws, we can calculate any future moment.

But in the QCA universe, this promise breaks down.

Stephen Wolfram’s research shows that for QCA systems like our universe in “Class IV” (complex class), their evolution processes are computationally irreducible.

• Reducible systems: Like planetary orbits. We can use the formula $x(t)=x_0+vt$ to jump directly to the state ten thousand years later without simulating every second in between.

• Irreducible systems: Like life or thought. To determine the system’s state after $T$ steps, the only way is to let the system (or its simulator) run step by step $T$ times. There is no shortcut.

Theorem 3.3 (Prediction Paradox Theorem):

In a QCA universe following light path conservation, no physical entity (including the observer itself or external supercomputers) can obtain complete information about the system at time $T$ with $100\%$ accuracy before time $t<T$.

Proof:

1. Assume there exists a prediction machine $\mathcal{P}$ that attempts to predict system $\mathcal{S}$’s state at time $T$ at time $t$.

2. For precise prediction, $\mathcal{P}$ must simulate every logic gate operation of $\mathcal{S}$.

3. To run faster than $\mathcal{S}$ itself (i.e., give results at $t_{pred}<T$), $\mathcal{P}$’s computation speed must exceed $\mathcal{S}$.

4. According to the light path conservation theorem, $v_{int}\le c$. System $\mathcal{S}$ (part of the universe itself) already runs at maximum physical computing power $c$.

5. Therefore, $\mathcal{P}$ cannot be faster than $\mathcal{S}$. The fastest simulator is the universe itself.

Conclusion: The future is predetermined, but the future is unknowable.

This unknowability does not stem from randomness (like rolling dice), but from computational cost. Your future is not “spoiled” but executed by you personally.

3.3.2 Freedom as “From Self”: Algorithmic Origin of Behavior

If the future is unpredictable, does this mean it is “free”?

Here, we need to redefine “freedom.”

• Freedom $\ne$ Randomness: If your behavior is completely random (determined by quantum noise), you are just a die, not a free agent. You cannot be responsible for random behavior.

• Freedom $=$ Algorithmic Autonomy: Your behavior is determined by your internal algorithmic structure (memory, personality, values), not by externally imposed instructions.

Under the QCA framework, “you” are that specific topological knot structure.

When an external stimulus is input, the output depends on the internal winding of this knot.

• If the output is completely determined by input (reflection), you are a machine.

• If the output is jointly determined by input and your internal state (historical memory), and this decision process is computationally irreducible (must go through your thinking), then you are free.

Definition 3.3 (Physical Definition of Free Will):

Free will is the irreducible causal power possessed by a high information mass ($M_I$) subsystem.

When an observer faces a choice, the universe must wait for the observer’s internal computation to complete before determining the next step of evolution. In this sense, observers are the “critical path” in the universe’s computational process.

3.3.3 Top-Down Causation: Future Determines Present

We mentioned in Chapter 8 that observers not only run but also model.

When a system has internal models about “self” and “future” and adjusts “present behavior” based on “expected future” (by minimizing free energy), causality is reversed at the macroscopic level.

• Physical Layer (Bottom): $t\to t+1$. Past determines future (push).

• Consciousness Layer (Top): $Goal(t+\Delta t)\to Action(t)$. Future determines present (pull).

For example, you decide to wake up early tomorrow (future goal), so you set an alarm now (present behavior).

Although this process is still executed by underlying unitary evolution at the microscopic level (just as software logic is ultimately executed by transistors), at the macroscopic dynamics level, it manifests as Top-down Causation.

Consciousness, as a high-order topological structure, constrains and guides the evolution paths of underlying particles.

3.3.4 Conclusion: Not Only Players, But Also Screenwriters

We have completed a difficult philosophical leap in this chapter.

We acknowledge the determinism of physical laws while saving the dignity of free will.

We are not passive NPCs (non-player characters), mechanically reciting scripts.

We are subroutines in this giant program of the universe that have obtained “self-modification permissions” (Self-modifying Code).

• Computational irreducibility guarantees our unpredictability.

• Self-referential loops guarantee our autonomy.

• Top-down causation guarantees our purposefulness.

This game, although the rules (physical laws) are fixed, the course of the game (history) is calculated step by step by us—countless entangled observers.

In this sense, we are both actors and screenwriters.

(End of Chapter 3)