  Physical interpretations of the time-symmetric formulation of quantum
mechanics, due to Aharonov, Bergmann, and Lebowitz are discussed in terms of
weak values. The most direct, yet somewhat naive, interpretation uses the
time-symmetric formulation to assign eigenvalues to unmeasured observables of a
system, which results in logical paradoxes, and no clear physical picture. A
top-down ontological model is introduced that treats the weak values of
observables as physically real during the time between pre- and post-selection
(PPS), which avoids these paradoxes. The generally delocalized rank-1
projectors of a quantum system describe its fundamental ontological elements,
and the highest-rank projectors corresponding to individual localized objects
describe an emergent particle model, with unusual particles whose masses and
energies may be negative or imaginary. This retrocausal top-down model leads to
an intuitive particle-based ontological picture, wherein weak measurements
directly probe the properties of these exotic particles, which exist whether or
not they are actually measured
