  We show that quantum mechanics predicts an Einstein-Podolsky-Rosen paradox
(EPR), and also a contradiction with local hidden variable theories, for photon
number measurements which have limited resolving power, to the point of
imposing an uncertainty in the photon number result which is macroscopic in
absolute terms. We show how this can be interpreted as a failure of a new, very
strong premise, called macroscopic local realism. We link this premise to the
Schrodinger-cat paradox. Our proposed experiments ensure all fields incident on
each measurement apparatus are macroscopic. We show that an alternative
measurement scheme corresponds to balanced homodyne detection of quadrature
phase amplitudes. The implication is that where either EPR correlations or
failure of local realism is predicted for continuous variable (quadrature phase
amplitude) measurements, one can perform a modified experiment which would lead
to conclusions about the much stronger premise of macroscopic local realism.
