  Can a large system be fully characterized using its subsystems via inductive
reasoning? Is it possible to completely reduce the behavior of a complex system
to the behavior of its simplest "atoms"? In the following paper we answer these
questions on the negative for a specific class of systems and measurements. We
begin with simple two-particle example, where strong correlations arise between
two apparently empty boxes. This leads to new surprising effects within atomic
and electromagnetic systems. A general construction based on pre- and
post-selected ensembles is then suggested, where the N-body correlation can be
genuinely perceived as a global property, as long as one is limited to
preforming a small set of measurements which we term "strictly local". We
conclude that within time-symmetric quantum mechanics and under certain
boundary conditions, high-order correlations can determine low-order ones, but
not vice versa. Moreover, the latter seem to provide no information at all
regarding the former. This supports a top-down structure in many-body quantum
mechanics.
