  It is theoretically and experimentally shown that photons emitted by
statistically independent incoherent classical light sources and measured in
the far field in spatially separated modes may display spatial correlations
akin to path-entanglement of photons produced by quantum sources. By measuring
higher order photon-correlations at different locations, i.e., $m$ photons in
one 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 state
projection where the detection of the first $m$ photons projects the sources
onto a state which emits the subsequent photon in a strongly correlated manner.
From this perspective the entanglement and violation of Bell's inequalities
appears as a consequence of nonvanishing cross correlations between
noncommuting quadrature phase components of the two spatially separated fields
after $m$ photons have been recorded. In this way we show that classical
systems may produce spatial field correlations violating local realistic
theories.
