Cellular Automata in Quantum Mechanics: God does not play dice

A cellular automaton is a grid of cells, each in one of a few possible states, such as on or off. At every tick of a clock, all cells update at once according to a fixed rule that depends only on the cell’s own state and those of its immediate neighbors. The best-known example is John Conway’s Game of Life, where a handful of rules about when cells live or die produce gliders, oscillators, and even structures that can perform any computation. The appeal is that very simple local rules can generate enormously complex behavior.

Gerard ‘t Hooft, the Nobel laureate who helped build the Standard Model, has a bold proposal: quantum mechanics, the strangest theory in physics, might not be the bottom layer of reality. He thinks there is a deterministic theory underneath it.

In his Cellular Automaton Interpretation, the universe at the Planck scale is exactly this kind of system: a vast grid of discrete cells, each updating by fixed local rules.

Quantum behavior, in this picture, comes from how we describe the system. 't Hooft argues there is a privileged “ontological basis,” a set of states describing what actually exists. Superpositions are our bookkeeping, statistical tools for a reality we can’t see in full detail. The wavefunction describes our knowledge, not the world.

This removes several long-standing puzzles. The measurement problem vanishes, since nothing ever “collapses.” There are no branching many worlds. Quantum probabilities become ordinary ignorance, as in classical statistical mechanics.

To get around Bell's theorem, ‘t Hooft embraces superdeterminism: the particles and the experimenter’s measurement settings share the same deterministic history, so their correlations are part of one causal story rather than spooky action at a distance.

The promise goes beyond tidying up interpretation. A superdeterministic theory could restore locality to fundamental physics, putting it back in harmony with relativity. Its discrete, information-based picture may offer a fresh route to quantum gravity, where continuum physics keeps breaking down. It could also be testable. Other prominent physicists have proposed experiments looking for tiny departures from quantum randomness in carefully repeated measurements, and ‘t Hooft has suggested that quantum computers may eventually hit limits that standard quantum mechanics doesn’t predict. If any of that shows up, it would be the biggest shift in physics in a century.

It’s still a research program with major open problems, including reproducing the full Standard Model. But if it works, quantum mechanics would turn out to be an approximation, and physics would be deterministic again.