  The tight connection between mass and energy unveiled by Special Relativity,
summarized by the iconic formula $E = mc^2$, 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 paradoxal
situations, here we present a new 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.
