  Time and space translation invariance, giving rise to energy and momentum
conservation, are not only amongst the most fundamental but also the most
generally accepted symmetry assumptions in physics. It is nevertheless prudent
to put such assumptions to experimental and observational tests. In this note,
we take the first step in this direction, specifying a simple periodic time
dependence that violates time translation invariance in QED, and setting
phenomenological constraints on it. In addition to observational and
experimental constraints on time varying couplings, we focus on probes of
violation of energy conservation such as spontaneous production of photon and
electron pairs and the $e \to e \gamma$ process. We discuss similarities and
differences to the discussion of time varying fundamental constants and to the
case of a light bosonic dark matter field that usually also causes oscillating
effects.
