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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There are also other radioisotope dating methods like potassium-argon.
As with carbon dating, there are calibration curves. Those were made over long periods of time using samples for which we knew the dates. There will always be some uncertainty associated with those methods too.
For example, you can use tree rings and ^14 C measurements of those samples to make a calibration curve: https://www.ansto.gov.au/news/new-radiocarbon-calibration-curves-for-a-better-dating-method
You can also use other objects of known ages for which we have historical records.
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