  Recently, we proposed a non-local relativistic formulation of MOND (Modified
Newtonian Dynamics). The equations of motion were not derived, rather they were
inferred from the result one would obtain by using the Schwinger-Keldysh
formalism. The formalism simultaneously ensures causality of the field
equations and the reality of in-out operator amplitudes. This point was avoided
in our previous paper as its discussion was too far afield. Here we first
demonstrate the features non-local actions generally possess: namely acausal
equations of motion and non-real in-out operator amplitudes; and secondly how
the Schwinger-Keldysh formalism works to provide the characteristics we usually
desire from effective theories.
