The longest interval of time for some process (eg a heart beat or a human lifetime) is that measured by a clock moving with the observer. It is
called proper time. The length of that interval measured by some other clock in relative motion to that observer is always less than the proper time and as the relative speed approaches that of light, it tends to zero.
The twin paradox (see http://plus.maths.org/issue36/features/aiden) is related. If a twin stays at home and lives for 10 years on his watch while his identical twin goes off on a spacetrip at near light speed, then the travelling twin will return to find that he is
younger than his stay-at-home twin when he is reunited with him on earth.
So the maximal time is given by the proper time measured by a clock moving with you, and the minimum time can be arbitrarily small as the relative speed approaches that of light, or the gravitational field approaches the value needed to
make a black hole.
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