  A relativistically invariant quantum theory first advanced by Bakamjian and
Thomas has proven very useful in modeling few-body systems. For three particles
or more, this approach is known formally to fail the constraint of cluster
separability, whereby symmetries and conservation laws that hold for a system
of particles also hold for isolated subsystems. Cluster separability can be
restored by means of a recursive construction using unitary transformations,
but implementation is difficult in practice, and the quantitative extent to
which the Bakamjian-Thomas approach violates cluster separability has never
been tested. This paper provides such a test by means of a model of a scalar
probe in a three-particle system for which (1) it is simple enough that there
is a straightforward solution that satisfies Poincar\'e invariance and cluster
separability, and (2) one can also apply the Bakamjian-Thomas approach. The
difference between these calculations provides a measure of the size of the
corrections from the Sokolov construction that are needed to restore cluster
properties. Our estimates suggest that, in models based on nucleon degrees of
freedom, the corrections that restore cluster properties are too small to
effect calculations of observables.
