2021/10/30 by Norman Margolus, Margolus, Norman
Computer Science · Physics and Astronomy · #Cellular Automata and Lattice Gases (nlin.CG) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mechanical and Optical Resonators #Model Reduction and Neural Networks #Neural Networks and Reservoir Computing #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2111.00297
openalex publication_date 2021/10/30 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
The limited distinctness of physical systems is roughly expressed by uncertainty relations. Here we show distinctness is a finite resource we can exactly count to define basic physical quantities, limits to the resolution of space and time, and informational foundations for classical mechanics. Our analysis generalizes quantum speed limits: we count the distinct (orthogonal) states that can occur in a finite length of unitary change. As in Nyquist's bound on distinct signal values in classical waves, widths of superpositions bound the distinct states per unit length -- and basic conserved quantities are widths. Maximally distinct unitary evolution is effectively discrete -- and this characterizes classical systems. [see also Popular Summary in arxiv ancillary files]