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Radioactive half lives can be shown to be unchanged over extended periods of time.
Secular equilibrium - Wikipedia
Here is an example.
http://www4vip.inl.gov/gammaray/catalogs/ge/pdf/u234_new.pdf
Due to secular equilibrium, the amounts of U-234 can be measured by U-234 and also can be measured by the amounts of Th-230 present. The half lives of both have to constant to measure the amount of parent from the daughter.
This can viewed strictly mathematically with a system of differential equations for the entire decay chain. You can show that initial half lives must be correct to produce the values we see now.
For those who state that they could have been different in earths past and are different now, they cant change. It can be shown mathematically and measured in a laboratory that half lives have to be constant over time.
The 240,000 year half life of U-234 must be correct because of it being secular equilibrium of Th-230 and its 74,000 year half life.
You do not know how much parent and daughter isotopes were present in the original sample. Also there is research that suggests that solar neutrino emissions may influence the rate of decay. There is no audit trail by which to test the constancy of rates over time and to check for contamination.
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