  Despite the widely-held premise that initial boundary conditions (BCs)
corresponding to measurements/interactions can fully specify a physical
subsystem, a literal reading of Hamilton's principle would imply that both
initial and final BCs are required (or more generally, a BC on a closed
hypersurface in spacetime). Such a time-symmetric perspective of BCs, as
applied to classical fields, leads to interesting parallels with quantum
theory. This paper will map out some of the consequences of this
counter-intuitive premise, as applied to covariant classical fields. The most
notable result is the contextuality of fields constrained in this manner,
naturally bypassing the usual arguments against so-called "realistic"
interpretations of quantum phenomena.
