What Is Bremermann's Limit?

In 1962, mathematician and biophysicist Hans Bremermann proposed a ceiling on how fast any physical system could process information, based on combining relativity (mass-energy equivalence) with the quantum time-energy uncertainty relation. The Bremermann information-processing bound states that a system with energy E cannot process information faster than R ≤ 2E/(πħ ln 2) bits per second. For one kilogram of mass converted entirely to computing energy, that works out to roughly 1.36 × 10⁵⁰ bits per second — a number since cited in arguments about the ultimate limits of brute-force computation and cryptographic key strength.

A heuristic, not a derivation

Bremermann’s original argument wasn’t a rigorous proof from first principles; it was a plausibility estimate, combining two established physical relations in a way that gave a physically reasonable-sounding number. The Registry records it with an epistemic status of literature-asserted rather than independently confirmed, because its universality depends on assumptions about how the bound applies to real computing hardware that the original paper didn’t fully justify.

A rigorous version arrived decades later

In 1998, Norman Margolus and Lev Levitin derived a closely related bound properly from quantum mechanics: a quantum system with average energy E above its ground state can pass through at most 2E/(πħ) mutually distinguishable states per second — the same structural formula as Bremermann’s, without his ln 2 factor, but now with an actual quantum-mechanical proof behind it rather than a heuristic combination. The Margolus–Levitin theorem is what physicists now treat as the fundamental version of this limit.

Why it’s here

Bremermann’s bound is a useful case study in the Registry’s own methodology: an early, widely cited claim that turned out to be an approximation of a later, more rigorously derived result. Both are tracked, with their evidence and epistemic status stated plainly rather than collapsed into a single number.

Primary source

Margolus & Levitin, “The maximum speed of dynamical evolution,” Physica D 120 (1998) ↗