  Einstein's unpublished 1927 deterministic trajectory interpretation of
quantum mechanics is critically examined, in particular with regard to the
reason given by Einstein for rejecting his theory. It is shown that the aspect
Einstein found objectionable - the mutual dependence of the motions of
particles when the (many-body) wavefunction factorises - is a generic attribute
of his theory but that this feature may be removed by modifying Einstein's
method in either of two ways: using a suggestion of Grommer or, in a physically
important special case, using a simpler technique. It is emphasized though that
the presence or absence of the interdependence property does not determine the
acceptability of a trajectory theory. It is shown that there are other grounds
for rejecting Einstein's theory (and the two modified theories), to do with its
domain of applicability and compatibility with empirical predictions. That
Einstein's reason for rejection is not a priori grounds for discarding a
trajectory theory is demonstrated by reference to an alternative deterministic
trajectory theory that displays similar particle interdependence yet is
compatible with quantum predictions.
