What are timestamps and timescales?
A timestamp is not a fact about the universe. It is a count, and a count is meaningless until you say what you were counting and from when.
A timescale supplies exactly three things:
- How long a tick is — the unit.
- When tick zero was — the origin.
- How many ticks have elapsed since — the count.
That is the whole definition. Anything providing all three is a valid timescale, and anything missing one is not a timescale at all, however time-like it looks.
Some examples, one of them ridiculous
UTC is the world’s civil timescale — the one nearly everything is ultimately answerable to, and the one with a peculiarity worth knowing about, since it is not available in real time.
TAI counts SI seconds continuously with no leap seconds, which makes it well behaved for arithmetic and useless for telling somebody what time to be somewhere.
Years since Victoria’s reign is also a valid timescale. The unit is a year, the origin is 1837, and you can count. It is absurd, nobody would use it, and it is entirely legitimate under the definition.
The absurd one earns its place. UTC is so familiar that it is easy to read “timestamp” as meaning something absolute, when it means a count against a convention that people had to agree on and could have agreed differently.
Every pair of timescales is related by a straight line
Because a timescale is only a tick length and an origin, any two of them are related by the simplest relationship there is. Plot one against the other and you get a straight line:
y = mx + b, where:
- m, the slope, is the ratio of tick lengths. Two timescales counting the same-length tick have a slope of 1, and their lines are parallel.
- b, the intercept, is the difference in origins.
That is the entire relationship between any two timescales, and it is worth knowing because it tells you exactly what can differ. If two clocks disagree, the disagreement decomposes into those two parameters and nothing else: a difference in how fast they tick, and a difference in where they started. See elapsed time, where those two turn out to have very different consequences.
Why this matters in practice
Two timestamps are only comparable if they share a timescale, or if you know the offset between theirs. Reconciling records across organizations is largely this problem wearing other clothes.
A timescale can be realized well or badly. UTC is a definition; what your clock actually produces is a realization of it, and the gap between them is everything this site is about. See UTC(k) for who maintains those realizations and how far they sit from the definition.
Some things you time do not need a timescale at all. Measuring how long something took needs a unit and a counter, but no origin and no agreement with anybody — which is a genuinely different and much easier problem. That is elapsed time.