Carbon 14 in fossils?

There are only three quite technical instances where a half-life changes, and these do not affect the dating methods we have discussed.1. Only one technical exception occurs under terrestrial conditions, and this is not for an isotope used for dating. According to theory, electron-capture is the most likely type of decay to show changes with pressure or chemical combination, and this should be most pronounced for very light elements. The artificially-produced isotope, beryllium-7 has been shown to change by up to 1.5%, depending on its chemical environment (Earth Planet. Sci. Lett. 171, 325-328, 1999; see also Earth Planet. Sci. Lett. 195, 131-139, 2002). In another experiment, a half-life change of a small fraction of a percent was detected when beryllium-7 was subjected to 270,000 atmospheres of pressure, equivalent to depths greater than 450 miles inside the Earth (Science 181, 1163-1164, 1973). All known rocks, with the possible exception of diamonds, are from much shallower depths. In fact, beryllium-7 is not used for dating rocks, as it has a half-life of only 54 days, and heavier atoms are even less subject to these minute changes, so the dates of rocks made by electron-capture decays would only be off by at most a few hundredths of a percent.

That diamond dated 58,000 years old.

If something dates 5,800 years old is that 1/10 background level?I think we have a problem here.