More Really is Different

Understand

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.