Complementarity Principle

Physics: Bohr complementarity (1928): wave and particle aspects cannot be observed simultaneously — they are mutually exclusive. Heisenberg uncertainty: ΔxΔp ≥ ℏ/2 (position-momentum); ΔEΔt ≥ ℏ/2 (Mandelstam-Tamm; energy-time). Robertson relation for general observables: ΔAΔB ≥ |⟨[A,B]⟩|/2. Entropic uncertainty: H(x) + H(p) ≥ log(eπ) (Bialynicki-Birula). Incompatible observables don't commute: [x̂,p̂] = iℏ. In QM, a CSCO (complete set of commuting observables) can be simultaneously measured. EPR (1935): claimed QM incomplete; Bell (1964): proved local hidden variables incompatible with QM predictions.