On the ‘Rigidity’ of the Force Field of a Moving Source

In the present paper, we propose a heuristic and intuitive approach to visualize how force fields “move” when their source moves at a constant velocity [Formula: see text] or accelerates with acceleration [Formula: see text] relative to a stationary observer. Our approach is based on the application of the principle of relativity and the principle of equivalence and holds regardless of the nature of the force field. The results presented here have been derived in the nonrelativistic approximation ([Formula: see text] and [Formula: see text], [Formula: see text] being the interval of time within which we observe the field). We shall show that in both cases of uniform and accelerated motion of the source, the field moves rigidly with the source. Namely, for every observer, however distant from the source, the field is always directed away from (or points towards) the present, instantaneous position of the source. We also show that these results are in agreement with what we know from experimental evidence and full-fledged physical theories (of electromagnetism and gravitation) beyond the nonrelativistic approximation. The proposed approach may be considered as a tool to facilitate students in graduate and undergraduate courses to familiarize themselves with (and self convince of) such a counter-intuitive feature of the force fields.