  We investigate the nonlocal dynamics of a single particle placed in an
infinite well with moving walls. It is shown that in this situation, the
Schr\"odinger equation (SE) violates local causality by causing instantaneous
changes in the probability current everywhere inside the well. This violation
is formalized by designing a gedanken faster-than-light communication device
which uses an ensemble of long narrow cavities and weak measurements to resolve
the weak value of the momentum far away from the movable wall. Our system is
free from the usual features causing nonphysical violations of local causality
when using the (nonrelativistic) SE, such as instantaneous changes in
potentials or states involving arbitrarily high energies or velocities. We
explore in detail several possible artifacts that could account for the failure
of the SE to respect local causality for systems involving time-dependent
boundary conditions.
