Every radiometric date is the same line: the daughter that has accumulated against the parent that remains. If nothing entered or left the crystal, the ratio is a clock — and the whole of geochronology is arguing about whether that "if" holds.
A single measurement needs you to assume how much daughter was there to begin with. An isochron does not: plot several minerals from the same rock, each normalised to a stable isotope, and they fall on a line. The slope is the age and the intercept is the initial ratio — the assumption becomes a measurement.
Radiocarbon is reported by a convention rather than by the best physics, and has been since 1962: ages use Libby's half life of 5568 years, not the measured 5730, so that old and new dates stay comparable. The correction is applied afterwards, by calibration — which is why a radiocarbon age is quoted as "BP" and a calendar age is something else.
BP counts from 1950, the year the convention was fixed and before the bomb tests changed the atmosphere. Beyond about ten half lives — some 50 000 years — there is too little left to measure, and that is the honest limit of the method.
Zircon holds two uranium decay chains with very different half lives. Plot one against the other and every closed system must sit on a single curve — concordia. A grain that has lost lead falls off it, and the line the discordant grains make points back at both the true age and the disturbance.
A date is not the age of the rock. It is the moment that mineral became closed to that element — and different minerals close at different temperatures, so a single sample can honestly yield several different ages, all correct.
| system | closes near | so it dates |
|---|
Which is why several systems on one rock is not redundancy — it is a cooling history. Ages that fall in the right order tell you how fast the rock came up.
A magnitude computed from a rupture in Earthquakes and an age from a faulted horizon are the two halves of a palaeoseismic trench: how big, and how often.