As a student of geochronology, dating and timekeeping is something that I think about a lot.
Right now the scientifically accepted length of a second is defined by the rotation of an atom of Cesium-133 as read by an atomic clock. The reason that particular isotope is used is because all atoms release energy when heated or otherwise excited (often in the form of visual light, a phenomenon called incandescence) and Cesium-133 gives off energy in a very narrow range of frequencies: 9,192,631,770 Hz, which can accurately be detected by a very sensitive piezoelectric crystal oscillator that vibrates in tune with the energy released by an excited Cs-133. Therefore, the internationally accepted length of a second is a 9,192,631,770 rotations of a Cs-133 atom.
(By the way, if you like science fiction with a heaping helping of science like I do, check out the Science of Superman, a book written by a scientist and baby-boomer that tries to explain how that old-school hero's powers work. Though the book is otherwise impeccable, the one real error I can see in the book is that it calls the universally agreed on length of time for a second to be arbitrary, when actually there is a really good reason why that specific number is used: the Cesium atom gives off energy in that narrow, near microwave frequency.)
Amusingly enough, though the definition of a second may be internationally accepted, the spelling of "Cesium" is not: UK scientists spell it "Caesium." This is why I love science, by the way: you can argue about stupid stuff like spelling but not about an immutable physical property of reality.
Anyone that doubts the absolute necessity of defining a supersmall unit of measurement in science like a second should be directed toward the field of particle physics. One of the more successful attempts at testing and proving Einstein's theory of relativity was made with a particle called a Muon, that only exists for several one-millionths of a second before breaking down. The time dilation effects of relativity are invisible at an everyday scale, but even a slight slowdown in the existence and breakdown of a Muon can be registered. Therefore, the effects of going faster can be seen in the breakdown of these tiny particles.
There are a few ways, though, that timekeeping can be kept in the future.
1) Pulsar rotation.
Pulsars are a type of superdense star that are all that remains after a supernova. This star that is too light to collapse and result in a black hole. Because the star still has the superhigh angular momentum left over, it turns superfast, functioning as something like an electric dynamo, with each rotation releasing a colossal amount of electromagnetic radiation that can be detected from earth. The energy given off by the rotation of a pulsar is done with such regularity and precision that it rivals and matches that of atomic clock. Pulsar rotation is so precise that when they were first discovered by astronomers they thought they might be artificial in origin!
One of the shortest rotational periods of a pulsar detected thus far has been 8 seconds. Sure, Pulsars eventually slow down as their angular momentum decreases, but that takes 10-100 million years so there's plenty of time a pulsar can be used reliably.
I firmly believe that it is human destiny to explore the universe, something only temporarily thwarted by shortsighted politicians that oppose our space program. Because pulsars can be detected over colossal distances, they can be detected in space and in space are a lot more meaningful a unit of measurement of time than terrestrial units based on earth's solar system like days, weeks or months. Because it's based on something cosmic and non-humanocentric, it is a system of measurement of time that can be shared with aliens. Yes, don't look at me like that, that's exactly what I said! I'm thinking big here, long term.
Hey, science fiction writers reading this! You can use this one if you want to, free of charge. Just invite me to your book-signing. It'd do wonders for my rep as a prestigious science genius!
2) Hexadecimal Clocks.
There was always something arbitrary about the 24 hour clock, with its 60 minute hours and 60 second minutes. This awkward system comes to us from the Babylonians, who did their mathematics in base-60.
Remember "metric time" from The Simpsons? Sure, we all thought it was a joke, but there was actually a real effort for a short time during the French Revolution to keep time in decimal units of 10, with 100 decimal seconds in 100 decimal minutes, and 10 decimal hours from noon to midnight. This lasted for a grand total of one year, from 1794-1795, when everyone forgot about the whole thing because it was a monster to convert, with a decimal second being .864 of a traditional second. Incidentally, I'm not a materialistic person, but if I was super-rich, the one place I'd indulge myself is in getting an antique post-Revolutionary decimal clock. Well, that and maybe getting William Defoe's Goblin Glider from the first Spider-Man movie...
Hexadecimal notation on the other hand, has advantages that French decimal time doesn't. For one thing it's a 24-hour clock, with the 24 hour day divided into 16 units, which also makes it a cinch to convert, making one hexhour about 90 traditional minutes and a hexminute around 90 seconds. The number is given as a fraction of the passage of a day in hexidecimal notation. Therefore, the moment before midnight is given as ,FFFF and midnight is ,0000. The hexhour can even be broken down into quarter-units too, at the 0,4,8, and C positions when slipped into the second digit.
Though something tells me this might not catch on among non-math majors...
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