Abstract
Radiometric rock dating, the methodology of determining the date of formation of a rock sample by the well-established rate of decay of the isotopes contained, depends on accurately determination of the starting points, the original concentrations of the isotopes. Many methods of estimating these beginning concentrations have been proposed, but all rest on tenuous assumptions which have limited their acceptance. This paper attempts to show that the Isochron-Diagram method contains a logical flaw that invalidates it. This most accepted of all methods has two variations, the mineral isochron and the whole-rock isochron. The logically-sound authenticating mechanism of the mineral isochron is applied to the whole-rock isochron, where it is invalid. The long-term stability of the whole-rock is applied to the mineral, where it is inappropriate.
When the isochron data are the result of the rock being a blend of two original species, the diagram is called a mixing line, having no time significance. This paper shows that all whole-rock isochrons are necessarily mixing lines. It is noted that by analogy the mixing-line logic casts strong suspicion on the mineral isochron as well. Since only whole-rock isochrons play a significant role in the dating game anyway, isotopic geochronology can be rather generally discredited.
Keywords:
Age
Geochronology
Isochron
Isotope
Old-earth
Radiometric
Young-earth
Introduction:
Thanks mainly to the fact that they appear to be so constant, the decay rates of radioactive materials have become the primary mechanism for attempting to discover the age of rocks.[5,16] In addition to a constant rate of variation, however, any timing mechanism must also have a calibrated beginning point. A number of methods have been tried to calibrate the "radiometric clock". But they have all required unprovable and apparently unwarranted assumptions. Faure, in his textbook [9] refers to all of them as "assumed values" except for those obtained by the "isochron", or similar linear method.
The linear methods are several, and have in common the reduction of the data to a set which can yield a straight-line plot. Many exceedingly detailed descriptions of these methods are available.[1,2,5,16] A summary description of the Rb-Sr isochron is included below.
Arndts and Overn alerted the creationist community to the fact that in spite of the mathematical rigor of the isochron, it also has unwarranted assumptions, and the data carefully gathered and processed to indicate immense ages can more appropriately be dismissed as indicating the recent mixing of two or more magmas.[1,2,3] Dalrymple[6] challenged our analysis with five points, all of which were promptly and thoroughly refuted.[4]
In Dalrymple's latest book [7] he ignores the entire issue of the whole-rock isochron, only defending the mineral isochron. There is sound logic supporting the mineral isochron, but another fatal flaw. Individual mineral crystals are not closed systems. Even over the few thousands of years available in the young-earth paradigm, they are insufficiently stable to give acceptable data to the geochronologists.
The Rb-Sr Isochron Method
Rubidium and strontium occur as trace elements in many common rock types. Rubidium has two isotopes. ⁸⁵Rb (stable, abundance 72%) and ⁸⁷Rb (radioactive). ⁸⁷Rb decays to ⁸⁷Sr with a half-life of (approximately) 48.8 billion years. Strontium is stable in all natural forms, and in addition to the radiogenic ⁸⁷Sr (7%), has isotopes ⁸⁸Sr (82%), ⁸⁶Sr (10%), and ⁸⁴Sr (<1%).
The general method of dating is to take several samples of the rock, to determine the ratios of the Rb-Sr isotopes in each, and by simultaneous equations determine the probable beginning points for each, from which the age may be determined.[16]
For the sake of compatibility with the available laboratory instruments, the specific ratios chosen are ⁸⁷Rb-⁸⁶Sr and ⁸⁷Sr-⁸⁶Sr. The algebra is equivalent to a simple straight-line diagram as in Figure 1. where points a, b, and c represent the samples.
Here is graphically represented the fact that the amount of daughter isotope increases as the amount of parent increases in the sample. The magnitude of that increase (i.e. the slope of the line) depends on the time allowed for the decay process to transpire, or the age of the rock. If we extrapolate down the line to the zero intercept, we have a representation of a sample with no parent isotope to contribute to the daughter concentration. This must represent the initial daughter concentration.
The slope is the age and the intercept is the initial daughter ratio. The scheme is mathematically sound. We must examine the assumptions.
For a problem to be solvable by simultaneous equations there must be as many independent equations as there are unknowns. The unknowns are the original ⁸⁷Sr-⁸⁶Sr ratio for each sample and the age of each sample. Each sample gives one equation, but introduces two additional unknowns. Regardless of the number of samples, there are never enough equations to cover all the unknowns.[16] These problems must be resolved by the assumptions.
The same age
It is assumed that all samples analyzed together are the same age. The word "isochron" (from the Greek "same time") symbolizes that. We do not dispute this assumption.
The same initial strontium ratio
If all initial ⁸⁷Sr-⁸⁶Sr ratios in the system are assumed to be the same, the scheme can be made to work, as the unknowns are reduced to two, the common age, and the common strontium ratio. Any two samples may now introduce the required two equations, and any more beyond that will simply improve the accuracy and the confidence level. This assumption is outside the experience based on field data, however, where the general case is that every sample has its own unique ratio. However, it can be rationally assumed that each sample we find has its own age and its particular rubidium concentration, which over time may have imparted a unique portion of daughter isotope. The assumed uniform strontium ratios should certainly be valid when applied to a rock system solidifying from a uniform homogenized melt. We must emphasize, however, that this enabling assumption must fail in the absence of an initial homogenized melt.
A "closed" system
If isotopes have migrated in or out of the sample during the aging period, the resulting data have no time significance. Isochrons are thought to be self checking in this regard, since with several samples an open system with random migration should scatter the points off of the straight line. Indeed, it often happens that there is a scatter of data, rendering the isochron worthless. But there are many occurrences of isochrons having acceptably straight-line form that are also rejected. Often "metamorphism" is cited as the probable cause, the system having opened, either partially or completely resetting the clock. [11,19] In order to assure an acceptably closed system, samples as large as 1 meter cubes have been suggested.[20] The assumption of a closed system for many of the isochrons, if they have not been questioned by the geochronologists, will not be challenged here. We note that these are generally obtained on the samples of larger dimensions, that is the whole-rock isochrons.
Independent equations
If the equations are not independent, the problem cannot be solved. This would be the case where all samples on the diagram plot on a single point. Although the single point on the diagram is valid, there is no way of finding a slope or intercept. If the melt were initially homogeneous and remained closed, it could be expected still to be homogeneous, and yield that single-point isochron. This should be the general case of the whole-rock isochron.
The need is to find samples with a variety of initial rubidium content but still having initial strontium ratios that are known to be uniform. The assumed initial homogeneous melt cannot be expected to give whole-rock samples with variable rubidium, but the assumed uniform ⁸⁷Sr-⁸⁶Sr ratios demand such an initial homogeneous melt.
The mineral isochron solves the dilemma. The mineral crystals have done the job in an elegant way. Crystals naturally form around a specific chemical composition, each atom occupying its naturally-assigned site. Foreign atoms just don't fit, either electrochemically or physically, and are strongly rejected. Depending on its concentration in the melt, a foreign element may have more or less acceptance in a crystal, based on its chemical and physical resemblance to one or another of the normal host elements. As the crystals form, each different mineral type accepts a different trace level of rubidium and of strontium. Because of their individual unique chemistry they each extract a different amount of rubidium and of strontium from the melt. The crystals of the individual minerals are used as the rock samples in the mineral isochrons.
Mixing
Often an isochron yields an unacceptable slope, indicating an age much too young or much too old to be compatible with the accepted model. [19] Frequently the slope is negative.[18,14] A common explanation for these cases is "mixing". It has always been recognized that the same straight-line plot as the isochron can be achieved if the original melt were a mixture of two original homogenized pools.[12] Figure 1. may also be used to illustrate this case. If points a and c are the compositions of the two original pools that partially merged to form the melt, any sample from the melt will occupy a place on a straight line between them, such as point b. No sample will be found above a or below c. Such a "mixing line" has no time significance, and the textbook warns to be wary of accepting such mixing as a true isochron.
Faure's text also proposes a test for mixing. [13] If a plot of ⁸⁷Sr-⁸⁶Sr vs 1/Sr (the concentration of strontium) shows a linear relationship, then mixing is indicated. A brief study conducted in 1981 showed a high degree of correlation to this mixing test in the isochrons being published.[3] A subsequent public dialog between Dalrymple[6] and Arndts & Overn [4] concluded that although the mixing test is strongly indicative of mixing, there are circumstances under which mixing would not be detected by such a test, and others wherein the test could give a false indication of mixing. The caution for the geochronologist would be to suspect any isochron, since there is no way to rule out mixing.
It is now clear, however, that there is at least one positive test for mixing. It is the whole-rock isochron itself. If the whole rock yields samples that give a linear plot, whether the slope is positive or negative, or whether the slope signifies an age that fits a preconceived model or not, there is no other known mechanism outside of mixing to which the data may be rationally ascribed.
Discussion
Mixing is an unfortunate misnomer that has become popular for describing rocks formed from two or more original melts, or from a melt becoming contaminated by isolated incorporation of local rock. Understand it to mean partial mixing, with resulting heterogeneity. Complete mixing would result in homogeneity, and would give only a single point to plot. No curve of any kind, nor even a scattering of points would occur.
This homogeneity is the assumed starting point in the history of the rock being dated. It then solidifies. But now, years later, we dig up 6 adjacent meter cubes of the rock, and discover that the normalized ratio of the parent (and incidentally of the daughter) is different in each cube, sufficient to plot as an "isochron". How can we rationally accept the assumed initial homogeneity? We can not.
What is needed but missing in the whole rock isochron is a mechanism to establish initial homogeneity, and then to extract heterogeneous samples. The mineral crystals do the job in an elegant way. Each type accepts a different level of contamination of the parent isotope, chemically determined. One cannot rationally extend this process back to the whole rock. It has been tried, but there is a fallacy . [5,20]
As we stated in 1986: [5]
The whole-rock isochron is justified on the basis that migration of the isotopes in a metamorphic event may be confined to distances of perhaps 1 cm. This is much larger than the average crystal size. Thus the original constituents of each crystal will lie nearby. By taking samples of 100-cm dimensions, one could assure that the entire content of the original crystals are well represented by the sample, with very small error. However, this matrix is the original melt that was theorized to be homogeneous. The ability to find differences in the rubidium content among the samples violates the assumption of original homogeneity. Original inhomogeneity is the only possible explanation: in other words, mixing.
This method of justifying the whole-rock isochron on the basis of the mineral is logically unsound. Within the larger matrix the tiny crystals may incorporate discrete trace elements and return them over time. But they are powerless to alter the composition of the whole-rock matrix.
It is claimed that fractional crystallization of magmas and separation of crystals from the remaining liquid result in suites of comagmatic rocks of differing composition. [10]. This may be true, but there is no experimental evidence that this can generally be applied to trace elements that are foreign to the crystals. Add the fact that trace elements are not securely held by crystals until temperatures are well below the melting points, and this postulate falls far short of explaining the variation in rubidium in whole-rock isochrons. Mixing is much preferred, particularly when it is noted that many data sets have negative slope, where mixing is always the accepted explanation. Often the negative-slope data pertain to large formations that particularly fit the hypothesis of slow cooling from a melt. [15,18]
In the case of the mineral isochrons the scheme postulates an initial homogeneous melt, represented by a single point on the diagram. As the crystals form, their differential solubility will move their individual points on the diagram horizontally , different distances. (Only horizontally, since the vertical is a ratio of two isotopes of the same element). The large volume of whole-rock isochrons, however, shows the general case to be an initial heterogeneous melt represented by the kind of diagram published as an isochron, and which we conclude is actually a mixing line. Any point in the melt can be represented as a point on the straight line. When mineral crystals form, each crystal will move its point off the straight line in one or the other horizontal directions. The result is a scattering of the points. The geochronologist discards it as one of the following:
A three or more part mixture,
Subsequent metamorphosis,
Not a closed system: In this case he recognizes that crystals really cannot be expected to be a closed system. They tend to continue to reject contaminants long after formation, the mobilities of foreign elements in crystals being a whole school of scientific study. The retention of trace elements in crystals is so inadequate that it has been possible to construct "Isochrons" from various parts of the same crystal.[17] It is common that when the mineral isochron fails, the geochronologist then produces a whole-rock isochron from the same formation.
The ability to obtain a whole-rock diagram, straight-line or not, can be considered proof that the data represent a "mixing line" rather than an "isochron". If mixing has not occurred, and the system has remained closed, then the whole-rock data must all lie on a single point. In fact, even if the whole-rock data show scatter, either mixing is indicated -- but of a complex nature, with more than two components -- or there have been subsequent alterations described as the system being open, or both.
Has any legitimate isochron ever been formed? It is improbable. There is ample evidence for mixing. Any "isochron" could be mixing. There is no way to rule it out. All whole-rock "isochrons" are mixing, and they are approximately 90% of all published. Many of the remaining (mineral) "isochrons" have a whole-rock point located close enough to the straight line to discredit them. Why should we expect any of the others to be "true isochrons", since mixing has the strongest probability?
If one possesses a strong faith in the antiquity of the rocks, one could rationally expect that an occasional mineral isochron is legitimate. But it would also require the whole-rock diagram to be concentrated in a single point. (Neither a straight line or scattered). Often a whole rock point is put on a mineral diagram. That does not meet the criterion. Several whole-rock samples must be obtained, using the same techniques required for the whole-rock method. Their individual data points must be identical, i.e. superimposed on the diagram. At that point mixing would not have been ruled out, but all available tests requiring mixing would have been eliminated.
In the dialog with Dalrymple [4] it was noted that he is unwilling to defend the whole-rock isochron. In his latest book [7] on the age of the earth he has included a section that describes the elegant process with which crystals (minerals) give the necessary heterogeneity to make the system work. He also shows why the mineral isochron cannot be relied upon for dating, but does not state that conclusion. He carefully avoids describing the whole-rock method, which leads the casual reader to conclude that it is validated by the same processes as is the mineral method. Nothing could be farther from the case. Dalrymple has seen our initial critique of the whole- rock method, [5] and is obviously reluctant to forthrightly claim any scientific merit for it. He has clearly sidestepped the issue.
Dalrymple [7] does not depend directly on isochron dating of rocks to date the earth, but rather on the lead- isotope ratios. He must be commended for his carefully pointing out the many assumptions involved. However, he finally ignores them and claims that the age has been determined within a very narrow margin.
His ultimate method is to take the radiometric ages of lead ores (Circa 2.6-3.5 Ga) and correct to the beginning. Again I point out that the "isochrons" used to date the ores, as well as those of the meteorites, that add so much to Dalrymple's confidence in the method, are most probably mixing. Note tables 7.4 and 7.5, [Ref 7] which give many meteorite ages. Almost all are whole-rock.
Additionally note that with all his enthusiasm for the isochron, Dalrymple characterizes the method as a "first approximation" [8]
As has been pointed out many times before, all radiometric methods including the linear-plot techniques have been effectively "calibrated" to the fossil dates by selecting among the discordant data those that fit the accepted stratigraphic model. [16] Since the proponents of the isochrons don't take them at face value, others should by equally wary.
See also: "Still No Proof For Ancient Age -A Response" by W. M. Overn and Russell T. Arndts A technical analysis of "Isochrons" as defended by Dalrymple against creationist criticism, showing that despite mathematical sophistication, they are unreliable and are calibrated to "known ages" using the geologic column.
For Exciting New Work On Radiometric Dating Showing a Young Earth, Click HERE
BIBLIOGRAPHY
[1] Arndts, R. & Overn, W. 1981 "Pseudo Concordance in U-Pb Dating" Bible-Science Newsletter 19(2):1.
[2] Arndts, R. & Overn, W. 1981 "Isochrons" Bible-Science Newsletter 19(4):5-6.
[3] Arndts, R., Kramer, M. & Overn, W. 1981 "Proof of the Validity of the Mixing Model" Bible-Science Newsletter 19(8):1.
[4] Arndts, R. & Overn, W. Proceedings of 1985 Creation Conference North Coast Bible-Science Association, Cleveland, Ohio.
[5] Arndts, R. & Overn, W. 1986 "Radiometric Dating -- An unconvincing Art" Proceedings of the First International Conference on Creationism Vol 2, Creation Science Fellowship, Pittsburgh, Pennsylvania, pp 167- 173.
[6] Dalrymple, G. B. 1984 "How Old is the Earth? A Reply to {at}Scientific Creationism' " Proceedings of the 63rd Annual Meeting of the Pacific Division AAAS 1(3):84-86
[7] Dalrymple, G. B. 1992 The Age of the Earth
[8] Ibid p. 402.
[9] Faure, L. 1977 Principles of Isotope Geology John Wiley & Sons, Inc. New York, New York. p.78
[10] Ibid p. 79.
[11] Ibid p. 83-87.
[12] Ibid p. 97-105.
[13] Ibid p. 101.
[14] Jager, E. & Hunziker, J. C., eds, 1979 Lectures in Isotope Geology Springer-Verlaug, Berlin, Heidelberg and New York, p. 36
[15] Ibid p. 142-144
[16] Overn, W. 1986 "The Truth About Radiometric Dating" Proceedings of the First International Conference on Creationism Vol 1, Creation Science Fellowship, Pittsburgh, Pennsylvania, pp 101-104.
[17] Scharer, V. & Allegre, C. 1982 "Uranium - Lead System in Fragments of a Single Zircon Grain" Nature 295 (Feb.): 585
[18] Tilton, G. R. & Barreio, B. A. 1979 "Origin of Lead in Andean Calc-Alkaline Lavas, Southern Peru" Science 210, 1245-1247
[19] Woodmorappe, John 1979 "Radiometric Geochronology Reappraised" Creation Research Quarterly 16, 102-129
[20] York, D. & Farquhar, R. M. 1972 The Earth's Age and Geochronology Pergamon Press, New York, pp. 80 ff.