I was in History class the other day and I asked how people are able to get “accurate” dates for how old certain objects are. He said something along the lines of there are certain elements in materials and they decay overtime, half life this so we know roughly how long ago it was made.
I’m a mathematics major and am proficient in physics. I understand the concept of exponential decay and half-life’s. My questions is how do we know how much of a material we are measuring there initially was? To me, without knowing that, we could say that something was made whenever we want it to be made. Clearly I’m missing something but I can’t quite figure it out.
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Along with isotope dating, we use microscopic amounts of atmospheric gas trapped inside polar ice cores, laid down in clear annual layers, to cross check that the ratios of initial isotopes are known. This is cross checked again against tree rings (dendrochronology) that go back thousands of years, as trees that die and fall in peat swamps are very well preserved for many ages.
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