I think the two points of view for cosmic ray generated muons is the
best example. I want to mention another that is of fairly recent origin.
There is considerable interest now in measuring the distances to other
galaxies using type Ia supernovae (Ia SNe) as standard candles. These
supernovae are of an identifiable subclass distinguished from other SNe
by their spectra and by the time evolution of their brightness (called
the "light curve"). Principally because Hubble can reach deeper into
the cosmos than Earth based telescopes could, but now augmented by the
very large telescopes now being constructed, it has become possible to
reach and detect Ia SNe in very distant galaxies. These galaxies show a
large red shift which *can be* attributed to their rapid recession from
our galaxy. Since the light curves of these SNe can be measured over
the weeks to months following their discovery, these standard candles
also constitute relatively reliable clocks moving away from us at high
speed, and we can read the progress of time on these clocks. The time
dilation effect has been seen now in some of the more distant of these
Ia SNe, a verification of time dilation in a system of macroscopic
scale over a relatively long time period.
Those interested in looking further into this are directed to:
astro-ph/9707260, astro-ph/9605134, and astro-ph/9602124.