Billiard-Ball Computer: Reversible Logic via Elastic Collisions

Inputs (bits)

Launch speed 1.4

Ball radius 0.35

AND detector

no collision yet

Output ports (this cycle)

Live readouts

Cycle

Collisions

Total KE

0.00

Balls in flight

How it works

Two equal-mass "bit" balls launch from opposite top corners along crossing diagonal paths. If only one is present it sails straight through to its own exit port. If both are present, they collide elastically exactly where the paths cross — and the fact that a collision happened is itself the logic output:

collision occurs  ⇔  A = 1  AND  B = 1

The collision itself follows the standard equal-mass elastic-collision law (conserves momentum and kinetic energy exactly, so nothing is dissipated as heat):

n̂ = (r_A − r_B) / |r_A − r_B|      (line of centers)
v_A' = v_A − [(v_A − v_B)·n̂] n̂
v_B' = v_B + [(v_A − v_B)·n̂] n̂

A, B buttons — arm each input ball for the next cycle (0 = not launched, 1 = launched).
Fire cycle — launches the armed balls from their corners; Auto-clock repeats this every ~1.6 s, cycling through all four input combinations.
Speed / radius — change flight time and collision cross-section without changing the logic.
Total KE readout stays essentially flat through a collision — a direct, visible demonstration that this "conservative logic" primitive computes without the k_BT·ln 2 minimum energy Landauer's principle charges an irreversible bit erasure.

This is Fredkin & Toffoli's 1982 billiard-ball model of computation, the founding thought-experiment behind reversible and adiabatic nanocomputing: real nanoscale devices (ballistic electron waveguides, single-electron shuttles, adiabatic CMOS) chase the same zero-dissipation ideal by keeping every logic step time-reversible instead of erasing information.

Ball A Ball B

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