Free Will Relative To The Simulator

If A can calculate an exact future slice of B, then B has no alternative future. What happens when B becomes A?

Aug 17, 2025

This idea has followed me for years. Suppose one physical system can calculate an exact future slice of another. At that point, where exactly could free will hide?

Call the systems A and B. Give them the same physics. Inside A, build a simulator of B. Feed it B's physical laws and constants, its constraints, and its complete state before the event. Then ask for B at a particular region R and future time t.

The target is one small region where one decision happens. Its simulation must capture everything that can causally reach that region before t. That may be enormous. It is at least a more precise problem than rebuilding all of spacetime.

This kind of nesting already exists in crude form. Matter has arranged itself into structures that hold compressed representations of matter. A thermostat models temperature. A guidance system models motion. A brain models its surroundings. A physics simulation models a tiny, chosen piece of reality.

\begin{aligned} x_B(R,t)&=S_A\!\left(L_B,C_B,x_B(t_0);R,t\right),\\ d_B&=D\!\left(x_B(R,t)\right). \end{aligned}

$S_A$: the exact simulator operating inside A
$L_B$: the physical laws and constants governing B
$C_B$: the constraints and boundary conditions of B
$x_B(t_0)$: the complete physical state of B at the starting time
$R,t$: the target region and future time
$x_B(R,t)$: the exact physical state of the target slice
$D$: the operation reading the decision from that state
$d_B$: the decision made inside B

A calculates one future slice of B from information available before it.

By exact, I mean four-dimensional accuracy: the actual physical state at that coordinate in B's spacetime.

If that equality is exact, B has one state at R and t and one decision inside it. B may still weigh options and experience choice. A already contains the answer. Under the same inputs, a second decision has nowhere to enter. Libertarian free will in B is false.

Then make B a copy of A. If the simulator works for any system governed by those laws, A has no magical exemption. The difficult case is placing an exact simulation of A inside A: the simulator becomes part of the state, its prediction may alter the decision, and a full copy appears to demand the resources of the thing being copied. A limit on self-prediction can still leave the underlying history fixed.

I first started circling this question around 2015. In 2021, I tried to force it into mathematics and drew the page below. In 2025, I came back to it seriously. I am still on it. Some questions have absolutely no respect for working hours.

The 2021 page where I tried to make the question sit still.

The 2021 page tried to express this through dimensionality, uncertainty, and comparable infinities. I would now remove the infinity argument. A proper subset can have the same cardinality as the whole, so cardinality tells me almost nothing about physical cost. The useful quantities are causal reach, information, precision, memory, energy, and time.

Our simulations are narrow and abstract. Newtonian mechanics can predict a projectile or roulette wheel from measured conditions. Weather models, molecular dynamics, quantum simulators, and digital twins reach into harder territory. They remain finite-precision models of selected observables. Still, each one shows that part of reality can model another part well enough to know something before it happens.

To turn the intuition into a proof, I still owe four things:

Complete input. Laws, constants, and constraints do not choose a history alone. The simulator also needs the causally complete prior state without smuggling the future result into its boundary conditions.
Exact local scope. I need to define the causal domain of R and t and show that its information can be represented. Approximate prediction is impressive, but it cannot carry this proof.
Fast-forwarding. The simulator must return the result before B reaches it. Some systems may be computationally irreducible or contain questions that no algorithm can decide.
Self-application. The same construction must survive when the target has the simulator's own physics, while accounting for resources, feedback, and the prediction becoming part of the predicted state.

So my claim is conditional and sharper than the version I had before. An exact pre-event simulator of B would rule out libertarian free will in B. A physically universal simulator, applicable to the same kind of system that contains it, would extend the result to A. Proving either machine can exist is the work.

The theorem reaches the gap. The premises still have to cross it.

That is the question I actually care about: can a universe contain a smaller physical process that calculates an exact future slice of itself? The remaining problem belongs to physics, information, computation, and self-reference. I am still on it.

(I love that AI automatically inferred that the poor dude contemplating this nonsense had to be a monk in a robe with a Shaolin haircut. Sometimes I feel that way too.)