The Simulator: Computational Constraints and Emergent Quantum Phenomena

Setup

A view from the eyes of "The Simulator" — the entity running the simulation that encompasses all the agents and the agents' world. And from the agents' perspective, how limitations manifest themselves as limitations or laws in their world. Original question. If I used AI to create a simulation of a world filled with agents that don't know they're in a simulation, I'd have limited resources — limited cores, RAM, power. How would these limitations project themselves into the simulation, and how would the agent perceive them?

Abstract

This work explores the impact of computational limitations on the simulation of a complex reality populated by sentient agents unaware of their simulated nature. Unlike previous considerations of simulated time as a variable flow, we posit that within the agents' local frames of reference, time progresses uniformly. Instead, limitations manifest as constraints on the complexity, detail, and dynamism of the simulated world.

How Hardware Limits Project Into Agent Experience

Limited computational power manifests as perceptual limits: reduced visual detail, simplified environmental phenomena (less intricate weather), constraints on agent memory and cognitive capacity. Critically, computational limitations show up as lag or delays — not as visible glitches, but as unpredictable events or limits on the agent's own capabilities. Energy constraints limit the overall activity and complexity of the simulated environment: resource scarcity, simplified ecosystems, less frequent or detailed large-scale events, and "standby" or reduced-activity areas. Agents encountering these areas perceive them as barren, lifeless, or unexplored territory. Hardware limitations — storage capacity and world size — manifest as world boundaries ("edge of the map" effects) and repetitive environmental elements (procedural generation tells). Code errors are interpreted by the agents not as software bugs but as anomalies or inconsistencies in the fabric of reality — potentially giving rise to myths, superstitions, or nascent "scientific" theories.

Quantum-Like Phenomena From Computational Constraints

Heisenberg Uncertainty

Limited precision. With finite resources, impossible to represent position and momentum with infinite precision — inherent limits in accuracy mirror the uncertainty principle.

Discretization effects. If the simulation operates on discrete units of space and time (pixels), position is only defined to the nearest pixel.

Computational trade-offs. Calculating one property with high precision requires sacrificing precision in the other.

Planck Length

Fundamental unit of simulation — the smallest unit of space the simulation can resolve. Analogous to pixel size. Simulating below this scale would require prohibitive compute, making it a hard floor.

Speed of Light

Information processing limit. The maximum rate at which information can be processed and propagated within the simulation — limited by communication infrastructure or processing power.

Causality enforcement. Limiting the speed at which information can travel prevents paradoxes and inconsistencies that would arise from FTL communication.

Quantum Tunneling

Arises from the simulation's inability to perfectly resolve the positions and momenta of particles, allowing them to "tunnel" through barriers that would be classically impenetrable.

Entanglement as Shared Representation

Key mechanism — deferred computation:

Saving resources. Instead of simulating every possible state of a particle in superposition, the simulation stores a representation of the superposition itself. No actual computational resources are spent on individual states until needed. This is lazy evaluation from computer science.

Linked superpositions. For entangled particles, the simulation stores a shared representation of their combined superposition encoding the correlation between states.

No actual communication. Crucially, no information transfer occurs between entangled particles when one is observed. The simulation simply retrieves the appropriate values from shared memory based on the observed state of one particle.

Instantaneous correlation, explained. It's not that information is traveling faster than light — the information was already encoded in the shared representation from the beginning.

Collapse of the Wave Function as Computation

When an observation occurs, the simulation finally performs the computation necessary to assign definite values. Randomness within constraints — specific values are chosen randomly but within the probabilities and correlations encoded in the shared representation. Computation is entirely local to the observer; no global synchronization required.

Illustrative Example

Two entangled photons, A and B. The simulation stores a shared representation: if A is measured to have vertical polarization, B will instantly be found to have horizontal polarization, and vice versa. Until a measurement is made, no actual polarization values are assigned. When a measurement is performed on photon A, the simulation randomly chooses either vertical or horizontal (with the appropriate probability). Based on this choice, the simulation instantly assigns the corresponding entangled polarization to photon B — retrieved from the stored correlated state.

Advantages of the Lazy-Evaluation Model

Massive resource savings — deferring computation until observation drastically reduces processing and memory.

Elegant explanation of entanglement — a natural mechanism for "spooky action at a distance."

Consistency with quantum mechanics — reproduces predictions while providing a plausible implementation mechanism.

Why It Matters

Emergent phenomena. These quantum-like effects would be emergent properties of the simulation, not fundamental laws within the simulated world. They arise from the underlying limitations of hardware and software. Agent perception. The agents inside interpret these effects as fundamental laws of nature, just as we do in our own reality. They would develop complex theories to explain them — potentially producing scientific discoveries that mirror our own understanding of quantum mechanics.

By carefully designing the limitations of the simulation, it becomes possible to create a world that exhibits the same quantum phenomena we observe in our own universe. The inversion is what matters: we observe our universe; we can use that observation to infer constraints of the implementing substrate.