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So when I say radiometric dating, I'm specifically referring to U-Pb, Ar-K and Rb-SR rather than C14 as I think these are more accurate when it comes to corroborating an older earth. I've heard people mention how all of these methods rely on certain assumptions, even isochron dating, which is why they might not be as accurate as we may think. I'll list a few I've heard parroted:

  1. Assuming starting parent-daughter ratios

  2. Assuming its a closed system

  3. Assuming the decay rate is constant

Here's a creationist link that expands on these 3 (disclaimer--I'm not a creationist, I know AiG is pretty much all pseudoscience, but its difficult for me to find secular sources that provide as in-depth of an analysis as they have): https://answersingenesis.org/geology/radiometric-dating/radiometric-dating-problems-with-the-assumptions/

So any help figuring out how important these assumptions are in relation to determining an accurate age for the Earth would be appreciated!

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The assumptions are either observably valid, tested, or logical. When creationists say they are uncertain they are obscuring the fact that these assumptions are almost always routinely tested.

  1. starting parent-daughter ratios: these are in some cases (40Ar/39Ar, Rb/Sr) determined by isochron analysis, and in others tested by dual decay chains 238U->206Pb and 237U->208Pb using concordia analysis. This is completely routine as part of any dating technique and a non-linear relationship on an isochron plot, or a discordant dataset on a concordia diagram invalidates the assumption for that analysis.

  2. closed system behaviour: Whether a system is closed depends on environmental conditions. Numerous experiments are dedicated to understanding the limits of open system behaviour (= closure temperature) by measuring diffusivities.

U-Pb concordia diagrams or isochron plots can be used to evaluate open or closed system behaviour for every analysis. In some cases the open system behaviour of different daughter isotopes in different minerals is used to evaluate temperature evolution through time.

  1. Observable changes to decay rates are negligible (<1%) and have not been observed for isotopes used in geochronology. The creationist argument is essentially that decay rates were faster in the past to account for why geochronology yields an age of the earth of 4.5 billion years as opposed to 6000 years. The difference is a factor of 750 000, never mind a few %. About 50% of Earth's heat budget results from radioactive decay. If decay rates were 750 000 times higher, as much more heat would have been produced from decay that Earth would be in a vapor or plasma state, and not forming any kind of rock. We do have crustal rocks with geochronological ages of ~4 billion years, meaning they were cool enough to crystallise zircon when they formed.

Summary- these assumptions are important, and they are routinely tested. The constancy of decay rates is difficult to test but is observationally constant between the different isotopes used in geochronology. The creationist assumption that all decay rates changed by a factor of 750 000 is absurd.

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