As we pointed out in these two articles, radiometric dates are based on known rates of radioactivity, a phenomenon that is rooted in fundamental laws of physics and follows simple mathematical formulas.
Dating schemes based on rates of radioactivity have been refined and scrutinized for several decades.
The latest high-tech equipment permits reliable results to be obtained even with microscopic samples.
Radiometric dating is self-checking, because the data (after certain preliminary calculations are made) are fitted to a straight line (an "isochron") by means of standard linear regression methods of statistics.
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Thus radioactive dating relies purely on assumptions.
The slope of the line determines the date, and the closeness of fit is a measure of the statistical reliability of the resulting date.
Technical details on how these dates are calculated are given in Radiometric dating. As with any experimental procedure in any field of science, these measurements are subject to certain "glitches" and "anomalies," as noted in the literature.
We will deal with carbon dating first and then with the other dating methods.
Carbon has unique properties that are essential for life on Earth.