It’s use gets shakier and shakier as science finds new methods."
Only if your term "carbon dating" itself is misused.
Carbon dating is only one of dozens of different methods for finding ancient ages -- it works back to ~60,000 years:
- "Radiocarbon dating (usually referred to simply as carbon-14 dating) is a radiometric dating method.
It uses the naturally occurring radioisotope carbon-14 (14C) to estimate the age of carbon-bearing materials up to about 58,000 to 62,000 years old."
"The older a sample is, the less 14 C there is to be detected, and because the half-life of 14 C (the period of time after which half of a given sample will have decayed) is about 5,730 years, the oldest dates that can be reliably measured by this process date to around 50,000 years ago, although special preparation methods occasionally permit accurate analysis of older samples."
This site lists dozens of methods, including radiometric dating.
