  The kinematics of particles refer to events and tangent vectors, while that
of waves refer to dual gradient planes. Special relativity [1-3] applies to
both objects alike. Here we show that spacetime exchange symmetry [7] implicit
in the SIdefinition of length based on the universal constant c has profound
consequences at low velocities. Galilean physics, exact in the limit c \to
\infty, is mirrored by a dual so-called Carrollian superluminal kinematics
[4-6] exact in the limit c \to 0. Several new results follow. The Galilean
limit explains mass conservation in Newtonian mechanics, while the dual limit
is a kinematical prerequisite for wavelike tachyonic motion [8, 9]. As an
example, the Land\'e paradox [19, 20] of waveparticle duality has a natural
resolution within special relativity in terms of superluminal, particlelike
waves. It is emphasized that internal particle energy mc^2 can not be ignored,
while kinetic energy leads to an extended Galilei group. We also demonstrate
that Maxwell's equations have magnetic and electric limits covariant under
Galilean and Carrollian symmetry.
