Carbon 14 dating system
The more accurate carbon clock should yield better dates for any overlap of humans and Neanderthals, as well as for determining how climate changes influenced the extinction of Neanderthals. Yeah sure some bacteria could have been fossilized with the plant, but then were quickly replaced by minerals from fossilization.
There have been many theories in the past that have been disproved. Van Der Merwe Libby ran many tests on items where the age was known, or estimated by other means.
His test results came rather close, to within plus or minus a few hundred years. All organic material has decaying Carbon in it.
Eventually the reaction would reach some equilibrium and the amount of Carbon in the atmosphere would remain constant. If you have a certain amount of a radioactive material, its half-life is the time it takes for half of the material you started out with to decay. It is stated on an autobiography by Emilio Segre that the concept was suggested to Libby by Enrico Fermi at a seminar in Chicago. Libby was a very brilliant scientist and had some wonderful ideas. The older the sample, the more it would be affected.
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