  Spin correlations of $e^{+}e^{-}$ pair productions of two colliding photons
are investigated and explicit expressions for their corresponding probabilities
are derived and found to be \textit{energy} (speed) dependent, for initially
\textit{linearly} and \textit{circularly polarized} photons, different from
those obtained by simply combining the spins of the relevant particles, for
initially \textit{polarized} photons. These expressions also depend on the
angles of spin of $e^{+}$ (and/or of $e^{-}$), for initially {\it linearly
polarized} photons, but not for {\it circularly polarized} photons, as a
function of the energy. It is remarkable that these explicit results obtained
from quantum field theory show a clear violation of Bell's inequality of Local
Hidden Variables theories at all {\it energies} beyond that of the threshold
one for particle production, in support of quantum field theory in the
relativistic regime. We hope that our explicit expression will lead to
experiments, of the type described in the bulk of this paper, which can monitor
energy (and speed) in polarization correlation experiments.
