  A standard approach in the foundations of quantum mechanics studies local
realism and hidden variables models exclusively in terms of violations of
Bell-like inequalities. Thus quantum nonlocality is tied to the celebrated
no-go theorems, and these comprise a long list that includes the Kochen-Specker
and Bell theorems, as well as elegant refinements by Mermin, Peres, Hardy, GHZ,
and many others. Typically entanglement or carefully prepared multipartite
systems have been considered essential for violations of local realism and for
understanding quantum nonlocality. Here we show, to the contrary, that sharp
violations of local realism arise almost everywhere without entanglement. The
pivotal fact driving these violations is just the noncommutativity of quantum
observables. We demonstrate how violations of local realism occur for arbitrary
noncommuting projectors, and for arbitrary quantum pure states. Finally, we
point to elementary tests for local realism, using single particles and without
reference to entanglement, thus avoiding experimental loopholes and efficiency
issues that continue to bedevil the Bell inequality related tests.
