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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Measuring via the method you describe is only one of the way we are able to date things, with different methods being good for different range and overlapping in some ranges and reinforcing each other.
We known that for example the ratio of Carbon-13 to Carbon-14 in our atmosphere is more or less fixed. Carbon-14 constantly disappears due to decay, but it also gets constantly created new in the upper atmosphere.
Living things breath in and eat things that have breathed in CO2 from the atmosphere and thus the ratio of C-13 to C-14 in living things stays fixed.
Dead things no longer take in new Carbon. So as time goes by the ratio changes. decay still happens but no new C-14 gets added.
By itself this would not be very good as it relies on the assumption that new C-14 was always created at the same rate it is today. Thanks to the existence of other dating methods we can see ho well that assumption does and does not match up with reality and calibrate measurements accordingly.
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