Why quantum correlations are shocking

A simple minimalist argument is given for why some correlations between quantum systems boggle our classical intuition. The argument relies on two elementary physical assumptions, and recovers the standard experimentally-testable Bell inequality in a form that applies equally well to correlations between six-sided dice and between photon polarizations. The first assumption, that measurement selection in a first lab leaves the measurement statistics in a remote lab invariant (no-signaling), has been empirically verified, and is shown to be equivalent to the existence of a corresponding joint probability distribution for quantities measured in the first lab. The observed violation of the Bell inequality is then equivalent to the failure of a second assumption, that measurement selection in the remote lab leaves such a joint distribution invariant. Indeed, the degree of violation lower-bounds the variation of the joint distribution. It directly follows there are just three possible physical mechanisms underlying such violations -- action-at-a-distance (superluminality), unavoidable common factors linking measurement choice and distant properties (conspiracy), and intrinsically incompatible physical quantities (complementarity). The argument extends to all Bell inequalities, and is briefly compared with other derivations.
Comment: 10 pages, 1 figure (accepted version, with minor clarifications)