Creationists have always claimed that isochrons represent “mixing lines” (i.e., straight lines that yield geologically meaningless ages). However, concordance between different isochron dating systems is a good argument against this interpretation. On the other hand, Paul Giem disputed this assertion. He developed a mathematical model which supposedly outlines a possibility how matching isochron dates can be obtained through mixing. He added:
As far as I know, one cannot find this derivation in textbooks, and so those with the proper competence are urged to follow the math closely looking for errors.
But math is simply beyond me. Is there anyone who can spot some basic errors in his derivations?
Good question again for @davidson, @Joel_Duff and the @physicists.
I would agree. Whatever mechanisms Giem tries to find for isochron dating is not going to work for non-isochron methods. Also, each decay chain is independent of the others, so it is difficult to see how independent methods would agree with one another if radiometric dating is not accurate.
For those interested, Roger Wiens wrote an amazing webpage devoted to explaining radiometric dating with the christian audience in mind.
Radiometric Dating:A Christian Perspective
The best source I know of for walking through how isochron dating works, and how it accounts for possible sources of error (whether a reader is Christian or not), is The Bible, Rocks, and Time by Davis Young and Ralph Stearley (pgs 388-443). I took seventeen pages of type written notes when I read this book!
As far as the particular work of Giem goes, it represents one of myriad “just so” stories that essentially say “but what about THIS for undermining confidence in dating?”, while ignoring studies and data that demonstrate not only the reliability of radiometric dating, but also why (for Christians) the only other option is a deceptive God. I would not argue that it might be possible under extremely unique and precise conditions of mixing to get a flattened “isochron line,” but such conditions would never be normative. It is equivalent to the argument that ten tree rings and ten sediment layers COULD have all formed in the same year, thus only appearing to provide independent evidence of ten years of record. Is is possible? Sort of, maybe. Is it worth spending a lot of time refuting?
Maybe not. However, mixing and wall-rock contamination are quite common. But if I am not mistaken, this is irrelevant as long as the dissolved daughter and/or parent isotopes are subsequently homogenized in the magma, right? Because isochron dating hinges upon the assumption that the isotopic ratios were homogenous when the molten rock crystallized.
Isn’t this better phrased: “rests on the observation that isotope ratios are homogenized.”?
A further (and significant) argument against mixing lines is that if mixing was a common cause of the observed “isochrons,” there should be many examples where the slope of the plotted line is negative. The absence (or at least extreme rarity) of such plots means the higher occurrence of radiogenic isotopes is due to decay, not due to mixing with rock with variable mixtures of isotopes.
If I am understanding this correctly it would seem that mixing between rocks would need to occur in a way that is coordinated with fossils, and coordinated across the entire Earth. For example, non-avian dinosaur fossils are not above rocks that date to 65 million years or younger, and this is true across the Earth. So how would this proposed mechanism work across the entire Earth so that no non-avian dinosaur fossil is found in rock that dates younger?
@swamidass I don’t think there is much evidence to suggest that homogenization is a general trend. In fact, Davidson et al (2005) questioned this assumption:
The occurrence of significant isotope variation among mineral phases in Holocene volcanic rocks questions a fundamental tenet in isochron geochronology—that the initial isotope composition of the analyzed phases is identical.
@davidson I’ve heard that argument before but creationists just love to respond to literally every argument that was ever made by an “evolutionist”. More specifically, I found this objection:
One might question why we do not have more isochrons with negative slopes if so many isochrons were caused by mixing. This depends on the nature of the samples that mix. It is not necessarily true that one will get the same number of negative as positive slopes. If I have a rock X with lots of uranium and lead daughter isotope, and rock Y with less of both (relative to non-radiogenic lead), then one will get an isochron with a positive slope. If rock X has lots of uranium and little daughter product, and rock Y has little uranium and lots of lead daughter product (relative to non-radiogenic lead), then one will get a negative slope. This last case may be very rare because of the relative concentrations of uranium and lead in crustal material and subducted oceanic plates. I note that there are some isochrons with negative slopes.
@T_aquaticus Good point.
I would be curious to see examples of the negative slopes. My first suspicion is that they are barely negative (though I could be wrong).
BTW - the Davidson et al 2005 citation is Jon Davidson - not me (just to avoid confusion)
This article does not dispute the general trend of homogenization. It notes exceptions and suggests ways of cross checking. What did I miss?
@swamidass and @davidson This topic bugged me for the past 2 weeks and so I decided to do a little bit of research. I found a handful of publications that specifically addressed/discussed mixing in connection with isochron dating and I came to the conclusion that mixing does not pose a serious threat to the dating methods. I even wrote a relatively short article about this: Magma mixing and Isochron dating – Teaching the consensus
I am on a family vacation at the moment, but did take a quick look at the linked article. It looks good. Effort appreciated!
This conversation was picked up with @PaulGiem himself, over here: Paul Giem: Isochron Dating Rocks and Magma Mixing .