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It is theoretically and experimentally shown that photons emitted bystatistically independent incoherent classical light sources and measured inthe far field in spatially separated modes may display spatial correlationsakin to path-entanglement of photons produced by quantum sources. By measuringhigher order photon-correlations at different locations, i.e., $m$ photons inone mode and one photon in another mode, we experimentally demonstrate for $m\geq 6$ a violation of Bell-type inequalities for spatial degrees of freedom.The spatial correlations among the photons can be understood from stateprojection where the detection of the first $m$ photons projects the sourcesonto a state which emits the subsequent photon in a strongly correlated manner.From this perspective the entanglement and violation of Bell's inequalitiesappears as a consequence of nonvanishing cross correlations betweennoncommuting quadrature phase components of the two spatially separated fieldsafter $m$ photons have been recorded. In this way we show that classicalsystems may produce spatial field correlations violating local realistictheories.

Nonlocal photon correlations and violation of Bell inequalities for spatially separated classical light fields