  A careful look at an allegedly well-known century-old concept reveals
interesting aspects in it that have generally avoided recognition in
literature. There are four different kinds of physical observables known or
proclaimed as relativistic invariants under space-time rotations. Only
observables in the first three categories are authentic invariants, whereas the
single "invariant" - proper length - in the fourth category is actually not an
invariant. The proper length has little is anything to do with proper distance
which is a true invariant. On the other hand, proper distance, proper time, and
rest mass have more in common than usually recognized, and particularly, mass -
time analogy opens another view of the twin paradox.
