  We consider the superconducting phase in a moving superconductor and show
that it depends on the displacement flux. Generalized constitutive relations
between the phase of a superconducting interference device (SQUID) and the
position of the oscillating loop are then established. In particular, we show
that the Josephson current and voltage depend on both the SQUID position and
velocity. The two proposed relativistic corrections to the Josephson relations
come from the macroscopic displacement of a quantum condensate according to the
(non-inertial) Galilean covariance of the Schr\"{o}dinger equation, and the
kinematic displacement of the quasi-classical interfering path. In particular,
we propose an alternative demonstration for the London rotating superconductor
effect (also known as the London momentum) using the covariance properties of
the Schr\"{o}dinger equation. As an illustration, we show how these
electromotive effects can induce self-sustained oscillations of a torsional
SQUID, when the entire loop oscillates due to an applied dc-current.
