More Really is Different

TL;DR

This paper proves that macroscopic properties of infinite Ising lattices cannot be fully derived from microscopic laws, highlighting the importance of emergent behavior and the limitations of microscopic theories in explaining macroscopic phenomena.

Contribution

It provides a rigorous proof that emergent macroscopic properties cannot be solely deduced from microscopic descriptions in certain physical systems.

Findings

Macroscopic properties of infinite Ising lattices are not derivable from microscopic laws.

Emergent behavior is fundamental in understanding complex physical systems.

Even a complete microscopic theory may not fully explain macroscopic phenomena.

Abstract

In 1972, P.W.Anderson suggested that `More is Different', meaning that complex physical systems may exhibit behavior that cannot be understood only in terms of the laws governing their microscopic constituents. We strengthen this claim by proving that many macroscopic observable properties of a simple class of physical systems (the infinite periodic Ising lattice) cannot in general be derived from a microscopic description. This provides evidence that emergent behavior occurs in such systems, and indicates that even if a `theory of everything' governing all microscopic interactions were discovered, the understanding of macroscopic order is likely to require additional insights.