Nonlocality and local causality in the Schrödinger equation with time-dependent boundary conditions

Highlights: • We study a quantum particle placed in an infinite well with a moving wall. • We show that the current density is modified instantaneously when the wall moves. • We indicate how this could be experimentally recorded with weak measurements. • By circumventing the measurement noise this effect could give rise to signaling. • We examine the possible artefacts that could account for this unphysical behavior. - Abstract: 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 Schrödinger 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.