One of the most famous "paradoxes" in history, predicted by A.
Einstein's special theory of relativity. Take two twins, born on
the same date on Earth. One, Albert, leaves home for a trip
around the Universe at very high speeds (very close to that of
light), while the other, Henrik, stays at home at rests. Special
relativity predicts that when Albert returns, he will find himself
much younger than Henrik.
That is actually not the paradox. The paradox stems from
attempting to naively analyze the situation to figure out why.
From Henrik's point of view (and from everyone else on Earth),
Albert seems to speed off for a long time, linger around, and then
return. Thus he should be the younger one, which is what we see.
But from Albert's point of view, it's Henrik (and the whole of the
Earth) that are travelling, not he. According to special
relativity, if Henrik is moving relative to Albert, then Albert
should measure his clock as ticking slower -- and thus Henrik is
the one who should be younger. But this is not what happens.
So what's wrong with our analysis? The key point here is that
the symmetry was broken. Albert did something that Henrik did
not -- Albert accelerated in turning around. Henrik did no
accelerating, as he and all the other people on the Earth can
attest to (neglecting gravity). So Albert broke the symmetry, and
when he returns, he is the younger one.