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Possible ways of distinguishing mixing lines from isochron lines are explored, including believability, concordance with the geological time scale or other radiometric dates, the presence or absence of mixing hyperbolae, and the believability of daughter and reference isotope homogenization.A model for flattening of "isochron" lines utilizing fractional separation and partial mixing is developed, and its application to the problem of reducing the slope of "isochron" lines without significant time is outlined.It is commonly felt that if all the points lie on a straight line, this is a good indication that the above assumptions are correct.For example, see The Age of the Earth, a book written by G.108-109), "For all practical purposes, the only way to move the isotopic compositions of samples from one isochron to another is by either radioactive decay through time or complete isotopic rehomogenization. Thus the isochron method is self-checking, providing not only the prospect of an age but also a statement on its validity." However, this confident statement is an overstatement. Rock 1 contains p1 parent, d1 daughter, and r1 reference isotope (in the case of rubidium-strontium dating, p is Sr).
At present, we will assume that the decay constants have not changed, recognizing that this assumption can be challenged. One simply measures the parent element and finds the percentage of the parent element that is of the desired isotope.Then we will mix them in proportion so that the proportion of our final rock that is rock 1 is a and the proportion of our final rock that is rock 2 is b.We have that is, all the final rock is either a or b.The isochron method of dating is used in multiple radiometric dating systems.An explanation of the method and its rationale are given.
It is concluded that there is at present a potentially viable explanation for isochron "ages" that does not require significant amounts of time that may be superior to the standard long-age explanation, and that short-age creationists need not uncritically accept the standard long-age interpretation of radiometric dates.