Holocene radiometric dating
This limit is currently accepted by nearly all radiocarbon dating practitioners.
It follows that the older a date is, even within this 'limit', the greater are the doubts about the date's accuracy.
The tiny initial amount of C14, the relatively rapid rate of decay (the half-life of C14 is currently about 5700 years) and the ease with which samples can become contaminated make radiocarbon dating results for samples "older" than about 50,000 years effectively meaningless.
It is the supposed accuracy of the new method that allows measurements sensitive enough to date objects claimed to be more than twenty or thirty thousand years old.
A recent test by the British Science and Engineering Research Council has shown that the accuracy of the new technique is greatly overrated.
The carbon dioxide is absorbed by plants, and the plants are eaten by animals, thus contaminating every living thing on earth with radioactive carbon. As time passes, the C14 in its tissues is converted back into nitrogen.
If we know what the original ratios of C14 to C12 were in the organism when it died, and if we know that the sample has not been contaminated by contact with other carbon since its death, we should be able to calculate when it died by its C14 to C12 ratio.