Relativistic paradox exposing the ubiquity of hidden momentum

The tight connection between mass and energy unveiled by special relativity, summarized by the iconic formula E=mc², has revolutionized our understanding of nature and even shaped our political world over the past century through its military application. It is certainly one of the most exhaustively tested and well-known equations of modern science. Although we have become used to its most obvious implication---mass-energy equivalence ---it is surprising that one of its subtle---yet, inevitable---consequences is still a matter of confusion: the so-called hidden momentum. Often considered as a peculiar feature of specific systems or as an artifact to avoid paradoxical situations, here we present a relativistic ``paradox'' which exposes the true nature and ubiquity of hidden momentum. We also show that hidden momentum can be forced to reveal itself through observable effects, hopefully putting an end to decades of controversy about its reality.