THE PENTATEUCH AND JOSHUA
[Part 2]
If potassium/argon dating is actually slightly in favor of the creationist position, perhaps we should re-examine the other dating methods to see if they really do dovetail with evolutionary theory as well as it is claimed. So we turn again to Geyh and Schleicher and look at those 75 other methods. Some of them, such as ^{138}La/^{138}Ce, ^{176}Lu/^{176}Ha, and ^{207}Pb/^{206}Pb, are used only for Precambrian material, and thus are irrelevant for dating life. They may be valid, or they may be invalid, but it doesn’t really matter for our purposes. Some, such as ^{3}H, ^{210}Pb, and ^{228}Th excess/^{232}Th, are used only for recent (< 3000 year old) samples, and thus again irrelevant for the question at hand. Some are considered highly experimental, such as the ^{10}Be/^{36}Cl method (if evolutionists do not have confidence in a method or its assumptions, it would seem difficult to use it to disprove a creationist time scale). Some are essentially variations on other methods, such as the ^{39}Ar/^{40}Ar method.^{41}
^{41}Which is a variation on ^{40}K/^{40}Ar dating and subject to the same criticisms. The only apparent advantage of the ^{39}Ar/^{40}Ar method, the plateau effect, is not always present, and it is sometimes grossly wrong by anyone’s standards when it is present. See Ashkenadze et al. in note 31. |
The krypton / krypton method utilizes the fact that ^{238}U spontaneously fissions at a very slow rate, producing krypton in some fission events. This krypton from spontaneous fission is compared to the krypton produced by the neutron-induced fission of ^{235}U, which is used in this method to measure the ^{235}U concentration. Because there is a constant ratio of ^{235} to ^{238}U, the concentration of ^{238}U is known if the concentration of ^{235}U has been determined. The resetting of the krypton/krypton clock requires elimination of all previously accumulated or acquired krypton. Krypton is a noble gas like argon. Since krypton atoms have a larger radius than argon, they are more easily trapped by minerals, and would be less likely to be eliminated than argon. As another parallel with potassium/argon dating, we find it suggested that krypton is lost, to account for younger ages than the “real” (evolutionary) age.^{42}
^{42}For example, Geyh and Schleicher, p. 151. |
^{43}An additional complication is that the samples are irradiated with neutrons, and since the neutron flux (amount of neutrons of the proper energy passing through a given area) is hard to measure, sometimes the krypton ratios are compared with those of a rock of “known” age. This procedure is justified if the reference rock is dated with either the krypton/krypton method or another reliable method, but if it is dated by the potassium/argon method, our discussion above makes the date obtained worthless as evidence for the evolutionary time scale. |
The uranium/xenon method and its derivative, the xenon/xenon method, use xenon produced by spontaneous ^{238}U fission. In the uranium/xenon method the uranium (and therefore the ^{238}U) is measured directly. In the xenon/xenon method the uranium is measured by measuring the fission products of ^{235}U, analogous to the krypton/krypton method. The clock for these methods is reset when all the xenon is driven off. Xenon is another noble gas, with atoms larger than krypton and therefore larger than argon. Again there is reference to the loss of xenon,^{44}
^{44}For example, Geyh and Schleicher, p. 153. |
^{45}For the xenon/xenon method, the same method of comparing the rock to be dated with a rock of “known” age is used as was used for the krypton/krypton method. Again this makes the method dependent not only on the hypothesis of zero xenon initially, but also on the accuracy of the date of the “known” age rock. |
The uranium/helium method depends on the fact that for each ^{238}U that decays to lead 8 ^{4}He atoms are produced. This is complicated by the fact that uranium commonly contains ^{235}U (producing 7 ^{4}He atoms), ^{234}U (a decay product of 238U producing 7 ^{4}He atoms), and ^{232}Th (thorium, producing 6 ^{4}He atoms). Thus if one knows the composition and amount of uranium and thorium present at the beginning, has a closed system (no U or Th moving in or out and especially no He moving in or out), and knows the amount of ^{4}He present at the beginning, one can estimate the time. It turns out that one cannot calculate the time straightforwardly, but one can find it graphically. Again we read of the loss of helium,^{46}
^{46}Geyh and Schleicher, pp. 248,250. |
^{47}Damon and Kulp, see note 40, and Noble and Naughton, see note 22. |
Terrestrial ages of meteorites in our age range are primarily found using ^{53}Mn, ^{36}C1, ^{81}Kr, and ^{129}I, and possibly thermoluminescence. These ages may be considered under the respective methods and need not be considered independently.
The nitrogen or collagen content of bones is a very rough method. It has nearly 2 orders of magnitude of demonstrated spread, and is influenced by such factors as temperature, moisture, pH, and bacterial environment. It is not nearly reliable enough to be of much use in differentiating between evolutionary deposits and Flood deposits.
Rubidium/strontium dating. We will now discuss the first method on our revised list. The ^{87}Rb/^{87}Sr method is dependent on the observation that rubidium is widely distributed with potassium (which it closely resembles chemically), and that about 1/4 (27.8346%) of the rubidium is ^{87}Rb, which is radioactive and decays by electron emission to ^{87}Sr. Its decay constant is 1.42 10^{-11}/year, which corresponds to a half life of 4.88 10^{10} years. This would make an excellent dating method if all the ^{87}Sr were eliminated at time zero. Unfortunately it is not, and so instead it is assumed that at time zero all the strontium is thoroughly mixed so that the strontium isotopes are homogeneously distributed. Strontium has three other isotopes ^{84}Sr, ^{86}Sr, and ^{88}Sr, which are present in constant ratios relative to each other.^{48}
^{48}48 So that ^{84}Sr/^{86}Sr = 0.056584 and ^{86}Sr/^{88}Sr = 0.1194, which gives percentages in usual rock of 82.52% ^{88}Sr, 7.00% ^{87}Sr, 9.86% ^{86}Sr, and 0.56% ^{84}Sr. The percentage of ^{87}Sr varies between 6.9% and 7.4%+, depending apparently on the past and/or present rubidium content of the rock. |
^{49}One could use the ^{87}Sr/^{88}Sr ratio or the ^{87}Sr/^{84}Sr ratio but the ^{87}Sr/^{86}Sr ratio is closer to 1, easier to work with, and the traditional one. |
1. The radioactive decay constant of rubidium has been invariant.
2. The strontium isotopes were evenly distributed at time t.
3. No net rubidium migration has occurred since time t.
4. No net migration of strontium isotopes has occurred since time t.
5. We can accurately measure the ^{87}Rb/^{86}Sr and ^{87}Sr/^{86}Sr ratios in a given set of minerals.
If these assumptions are correct, we will find our plot giving a straight line:^{50}
^{50}The derivation of the formula is as follows: | |
^{87}Rb = ^{87}Rb_{0} e^{-kt}; ^{87}Rb_{0} = ^{87}Rb e^{kt} | Assumptions 1,3 |
^{87}Sr* + ^{87}Rb = ^{87}Rb_{0}; ^{87}Sr* = ^{87}Rb_{0} – ^{87}Rb = ^{87}Rb e^{kt} – ^{87}Rb = ^{87}Rb (e^{kt} – 1) | Decay products |
^{87}Sr = ^{87}Sr_{0} + ^{87}Sr* = ^{87}Sr_{0} + ^{87}Rb (e^{kt} – 1) | Assumption 4 |
^{87}Sr/^{86}Sr = (^{87}Sr/^{86}Sr)_{0} + ^{87}Rb/^{86}Sr (e^{kt} – 1) | Assumption 2 |
By assumption 5 we can measure the appropriate ratios. |
Note that where the line crosses the zero line for the ^{87}Rb/^{86}Sr ratio gives the original ^{87}Sr/^{86}Sr ratio. Any strontium that originally had no rubidium with it would have to have that ^{87}Sr/^{86}Sr ratio still. Even if there is no such sample, we can predict its composition using our straight line. The apparent age is found by taking the slope,^{51}
^{51}Which is the change in the ^{87}Sr/^{86} ratio divided by the change in the ^{87}Rb/^{86} ratio. |
We now turn to how these dates are used in practice. The first paragraph of Faure (whose area of expertise is strontium geochemistry) dealing with experimental results is a shock:
Igneous rocks of granitic composition may contain both mica minerals and K-feldspar, all of which can be dated by the Rb-Sr method. Ideally, all minerals of an igneous rock should indicate the same date which can then be regarded as the age of the rock. When mineral dates obtained from one rock specimen or from a suite of cogenetic igneous rocks are in agreement, they are said to be “concordant.” Unfortunately, “discordance” of mineral dates is more common than “concordance.” The reason is that the constituent minerals of a rock may gain or lose radiogenic ^{87}Sr as a result of [142] reheating during regional or contact metamorphism after crystallization from a magma. In such cases, the mineral dates generally are not reliable indicators of the age of the rock. We must therefore turn to the rocks themselves if we want to determine their ages. ^{52}
^{52}Faure, pp. 120-1. |
^{53}Faure, p. 124. |
^{54}In fact, the evidence was contrary in 1967, according to Hanson GN, Gast PW: “Kinetic studies in contact metamorphic zones.” Geochim et Cosmochim Acta 1967;31:1119-53. On p. 1120 Hanson and Gast state, “It is significant that no one has so far been able to thermally induce radiogenic strontium-87 to leave its host mineral in quantities commensurate to the loss of argon under geologically reasonable conditions even though it is not uncommon to find biotites in nature which have lost both radiogenic argon-40 and strontium-87 due to a thermal event.” I have not seen any data which would challenge their conclusion. |
^{55}Faure, pp. 127-8. |
^{56}Faure, p. 128, italics his. |
^{57}P. 84, citing Burwash RA, Krupicka J, Basu AR, Wagner PA: “Resetting of Nd and Sr whole-rock isochrons from polymetamorphic granulites, northeastern Alberta.” Canad J Earth Sci 1985;22:992-1000. |
^{58}Geyh and Schleicher p. 87, citing Schleicher H, Lippolt HJ, Raczek I: “Rb-Sr systematics of Permian volcanites in the Schwartzwald (SW Germany). Part II: Age of eruption and the mechanism of Rb-Sr whole rock age distortions.” Contrib Mineral Petrol 1983;84:251-91. Note that “The Rb-Sr system in these rocks is often disturbed in such a way that the linearity of the sample points is retained in the isochron graph, thus producing apparent isochrons with reduced age values (“rotated isochrons”, ...)”. |
^{59}Geyh and Schleicher, p. 85. |
^{60}Faure, p. 130, citing Clauer N: “A new approach to Rb-Sr dating of sedimentary rocks.” In Jager E, Hunziker JC (eds): Lectures in Isotope Geology. Berlin: Springer-Verlag, 1979, pp. 30-51; Clauer N: “Rb-Sr and K-Ar dating of Precambrian clays and glauconies.” Precambrian Res 1981;15:331-52; and Bonhomme MG: “The use of Rb-Sr and K-Ar dating methods as a stratigraphic tool applied to sedimentary rocks and minerals.” Precambrian Res 1982;1S:5-25. |
But there is evidence against this proposed migration. For example, pyroclastic rocks can be dated “only by their phenocryst minerals (e.g., biotite, muscovite, sanidine). This is a proven procedure for assigning radiometric ages . . .”^{59} Notice that tuffs do not equilibrate the strontium in their phenocrysts after deposition. Here, strontium apparently does not migrate even in minerals. In fact, sedimentary rocks, deposited under water, do not homogenize their strontium if the grain size, at least of illite clay, is 2 microns or larger.^{60} If strontium doesn’t migrate enough to equilibrate in aqueous suspension except possibly with small grain size, why should it have migrated enough to equilibrate across macroscopic collections of whole rock, some of which are presumably much more coarse-grained? (If the strontium moves at all, it has to equilibrate or else it would take incredible luck to avoid ruining the straight line of the isochron.)
Why strontium should easily migrate is not obvious to me anyway. Strontium is doubly charged in minerals, and is poorly soluble in water; generally much less so than (singly charged) potassium or rubidium. Theoretically it should be hard to get strontium to migrate. In fact, one might ask, if argon (a neutral gas) has been retained in a mineral (so that the potassium/argon [144] age is believable by an evolutionist), why should strontium ions migrate to reduce the rubidium/strontium age?
The explanations for low rubidium/strontium dates seem lame to me. In fact, there seems to be a certain apriorism in their interpretation. For dates that fit the evolutionary time scale, even if the “assumptions are probably not strictly satisfied by any of the common detrital minerals”, still, “useful information” is presumed to have been obtained.^{61}
^{61}Faure, p. 134. |
^{62}Faure, p. 123. |
^{63}Pp. 196-7. The four tests they give are: 1. Direct comparison with other radiometric ages, 2. Direct comparison with fossils, 3. Stratigraphic sequence, and 4. Inference. Note that all but the first test reduce to whether the date fits with the evolutionary time scale, and if the other radiometric methods are chosen on the basis of their “reliability” (how well those methods fit the evolutionary time scale), the first test also reduces to a fit with that scale. |
^{64}P. 131, italics his. Note the absence of the possibility that to within the limits of the measurement the strata were laid down contemporaneously. |
The more logical interpretation is that the rocks are not as old as the conventional ages would make them. But can one then explain those beautiful straight line “isochrons” from the standpoint of a short chronology? It turns out that one can. Suppose that instead of mixing our rock to homogenize the strontium isotopes, allowing the rock to crystallize with partial separation of rubidium from strontium, and then letting the rubidium decay in place, we let the rubidium decay in one rock before mixing it with a rock containing strontium but little or no rubidium. If we do not completely homogenize the two rocks, components will be[145] mixed in varying proportions, and the “mixing line” produced is mathematically indistinguishable from an isochron.^{65}
^{65}The mathematical derivation in the simplest case is as follows: In rock A let us suppose there is r rubidium-87 per gram, and s_{1} strontium-87 per gram. In rock B let us suppose there is s_{2} strontium-87 and t strontium-86 per gram. Then in a mixture of a proportion a of rock A and a proportion b of rock B (a + b = 1) there would be ar + as_{1} + bs_{2} + bt per gram. The ^{87}Sr/^{86}Sr ratio would be (as_{1} + bs_{2}) / bt and the ^{87}Rb/^{86}Sr ratio would be ar / bt. Thus for a given mixture ^{87}Sr/^{86}Sr = bs_{2}/bt + (s_{1}/r)(ar/bt) = (^{87}Sr/^{86}Sr)b + (^{87}Sr/^{87}Rb)a ^{87}Rb/^{86}Sr. Notice that the plot of ^{87}Sr/^{86}Sr versus ^{87}Rb/^{86}Sr is a straight line with intercept (^{87}Sr/^{86}Sr)b and slope (^{87}Sr/^{87}Rb)a, precisely analogous to the isochron plot shown above. A more complicated but analogous equation giving a straight line can be obtained for impure sources. Given rock A with r_{1} ^{87}Rb s_{1} ^{87}Sr, and t_{1} ^{86}Sr, and rock B with r_{2} ^{87}Rb, s_{2} ^{87}Sr, and t_{2} ^{86}Sr, we have in any given mixture ^{87}Rb/^{86}Sr = r/t = (ar_{1} + br_{2})/(at_{1} + bt_{2}) and ^{87}Sr/^{86}Sr s/t = (as_{1} + bs_{2})/(at_{1} + bt_{2}), assuming t_{1} > 0 and t_{2} > 0 (both rocks have some ordinary strontium) and a is the proportion of rock A and b is that of rock B (so a + b = 1). Then (assuming r_{1}/t_{1} ≠ r_{2}/t_{2}, that is, the two rocks do not have the same ratio of rubidium to ordinary strontium), s/t = (as_{1} + bs_{2}) (r_{1}t_{2} - r_{2}t_{1}) / [(at_{1} + bt_{2}) (r_{1}t_{2} - r_{2}t_{1})] = (ar_{1}s_{1}t_{2} - ar_{2}s_{1}t_{1} + br_{1}s_{2}t_{2} - br_{2}s_{2}t_{1}) / [(at_{1} + bt_{2}) (r_{1}t_{2} - r_{2}t_{1})] = (ar_{1}s_{2}t_{1} - ar_{2}s_{1}t_{1} + br_{1}s_{2}t_{2} - br_{2}s_{1}t_{2} + ar_{1}s_{1}t_{2} - ar_{1}s_{2}t_{1} + br_{2}s_{1}t_{2} -br_{2}s_{2}t_{1}) / [(at_{1} + bt_{2}) (r_{1}t_{2} - r_{2}t_{1})] = [(at_{1} + bt_{2}) (r_{1}s_{2} - r_{2}s_{1}) + (ar_{1} + br_{2}) (s_{1}t_{2} - s_{2}t_{1})] / [(at_{1} + bt_{2}) (r_{1}t_{2} - r_{2}t_{1})] = (r_{1}s_{2} - r_{2}s_{1})/(r_{1}t_{2} - r_{2}t_{1}) + [(ar_{1} + br_{2}) (s_{1}t_{2} - s_{2}t_{1})] / [(at_{1} + bt_{2}) (r_{1}t_{2} - r_{2}t_{1})] = (r_{1}s_{2} - r_{2}s_{1}) / (r_{1}t_{2} - r_{2}t_{1}) + (r/t) [(s_{1}t_{2} - s_{2}t_{1}) / (r_{1}t_{2} - r_{2}t_{1})], which again is a straight line. |
This way of explaining rubidium/strontium dates naturally accounts for systems like the theoretical example given in the figure on p. 85 of Geyh and Schleicher. Whole-rock dating gives a relatively unaltered mixing line. But if there was a certain amount of equilibration between the minerals in a single rock followed by re-separation of rubidium and strontium before it cooled, the slope of the mixing line could be reduced.
Is it realistic to believe that granitic intrusions, for example, do not mix completely? Apparently so. At least Geyh and Schleicher think so; “For example, there are indications that the condition of isotopic homogeniety of a magmatic body at time t_{0}, [146] prerequisite for isochron dating of magmatic rock, is not always fulfilled. But for the Rb/Sr system, for example, initial heterogeniety would place the determination of a whole-rock isochron age in doubt, if not make it impossible.”^{66}
^{66}Pp. 12-13. |
^{67}Geyh and Schleicher, p. 87. |
^{68}Contrary to the claim of Dalrymple, see note 9, p. 109. |
In fact, when faced with “isochron” lines that are grossly too old even by the evolutionary time scale, geochronologists have no trouble ascribing them to mixing lines. Several examples are given in Faure.^{69}
^{69}Pp. 145-7. His examples follow: Pleistocene to Recent (<1.6 million years old) lava with a Rb/Sr age of 773 million years (Bell K, Powell JL: “Strontium isotopic studies of alkalic rocks: The potassium-rich lavas of the Birunga and Toro-Ankole Regions, east and central Africa.” J Petrol 1969;1O:536-72); upper Miocene to Pliocene (5-9 million years old by K/Ar dating) lava with a Rb/Sr age of 31-39 million years (Dickinson DR, Dodson Mn, Gass IG, Rex DC: “Correlation of initial ^{87}Sr/^{86}Sr with Rb/Sr in some late Tertiary volcanic rocks of south Arabia.” Earth Planet Sci Lett 1969;6:84-90); Pliocene to Holocene (<5.3 million years old) lava giving Rb/Sr ages of 570 and 870 million years (the 570 million year “isochron” is apparently from <3000 year old lava. Leeman WP, Manton WI: “Strontium isotopic composition of basaltic lavas from the Snake River Plain, southern Idaho.” Earth Planet Sci Lett 1971;11:420-34); and Miocene to Holocene (<24 million years old) volcanic rock with a Rb/Sr age of 1.2 billion years (Duncan RA, Compston W: “Sr-isotopic evidence for an old mantle source region for French Polynesian vulcanism.” Geology 1976;4:728-32). An additional report has been made of Pliocene to Holocene (<5.3 million years old) lava with a Rb/Sr age of 1.5 billion years (Leeman WP: “Late Cenozoic alkali-rich basalt from the western Grand Canyon area, Utah and Arizona: Isotopic composition of strontium.” Bull Geol Soc Am 1974;85: 1691-6). |
^{70}For an example, see Dasch EJ, Green DH: “Strontium isotope geochemistry of lherzolite inclusions and host basaltic rocks, Victoria, Australia.” Am J Sci 1975;275:461-9. |
It may be pertinent to note that in order to completely reset [147] an isochron, strontium isotopes must completely homogenize, to the nearest part per 10,000 or so, without homogenizing rubidium, or at least with subsequent refractionation of rubidium. If one simply mixes rubidium along with strontium, one has a mixing line with the same slope as the original isochron. This would make it more difficult to assume re-equilibration.
What about the apparent order in rubidium/strontium dates? Some of it is more apparent than real, due to the biases we noted under potassium/argon dating. But there is a real order as well. This might be accounted for by more complete mixing of the starting components for mixing lines as the Flood went on, with flatter “isochrons” as a result. And what about the matching of rubidium/strontium dates with potassium/argon dates? Some of the dates do not match.^{71}
^{71}For example, see Odin GS (ed): Numerical Dating in Stratigraphy. Chinchester, UK: John Wiley and Sons, 1982. Chapter 12 (Keppens E, Pasteels P: “A comparison of rubidium-strontium and potassium-argon apparent ages on glauconies.” Pp. 225-44) is full of examples of disagreement, and also has examples where the two methods agree but both differ from the accepted age. One may argue that glauconies are not always reliable, but examples of “incorrect” dates from other minerals such as biotite and whole rock granite may be found in chapter 24 (De Souza HAF: “Age data from Scotland and the Carboniferous time scale.” Pp. 455-66), for example. Also see Lanphere MA, Wasserburg GJF, Albee AL, Tilton GR: “Redistribution of strontium and rubidium isotopes during metamorphism, World Beater Complex, Panamint Range, California.” In: Craig H, Miller SL, Wasserburg GJ (eds): Isotopic and Cosmic Chemistry. Amsterdam: North-Holland Publishing Company, 1964, pp. 269-320. This fascinating study also demonstrates whole-rock (separated by, in some cases, miles) dates 200 million years younger than the presumed age of the formation (1.8 billion years), as well as up to 50% disparity between potassium/argon and rubidium/strontium mineral ages, in spite of minimal to no mineralogical evidence of metamorphism at this time (presumably 115 million years ago). |
^{72}Pp. 160-1, citing Hart SR: “The petrology and isotopic-mineral age relations of a contact zone in the Front Range, Colorado.” J Geol 1964;72:493-525, and especially Hanson and Gast, see note 54. |
Is there some mineral or rock that one might reasonably assume had complete initial homogenization of its strontium isotopes so that we can get a minimum rubidium-strontium age for deposition? Yes, there is. Evaporite minerals would be expected to have had all their strontium either in solution or equilibrium with solution at the time of deposition. But evaporites turn out to be a real can of worms. For it is not certain whether so-called evaporites are actually formed by evaporation. It is certain that most of them are not formed by the evaporation of seawater.^{73}
^{73}See Hardie in note 37. |
^{74}See Baadsgaard in note 36. |
^{75}Lippolt HJ, Raczek I: “Rinneite-dating of episodic events in potash salt deposits.” J Geophys 1979;46:225-8 (Rinneite [NaK_{3}FeCl_{6}] of Permian [250-300 million years old] age gave dates of 30-85 million years old by “model age” [the initial ^{87}Sr/^{86}Sr was estimated] and another sample gave 20 million years by actual isochron, but carnallite [KCl.MgCl_{2}.6H_{2}O] found with the rinneite did not fall on the isochron, dating instead to 8.5 million years); Lippolt HJ, Raczek I: “Cretaceous Rb-Sr total rock ages of Permian salt rocks.” Naturwissenschaften 1979;66:422-3 (two samples of these Permian potassium minerals gave ages of 82 ± 1 and 96 ± 1 million years within 10 feet of each other on the same horizon); and Baadsgaard in note 36. |
^{76}The equation being ^{40}Ca/^{42}Ca = (^{40}Ca/^{42}Ca)_{0} + (^{40}K/^{42}Ca) 0.888 (e^{kt} – 1) for the isochron line. The equation can also use ^{44}Ca or some other isotope as its reference instead of ^{42}Ca. |
^{77}Some studies (for example, Wilhelm HG, Ackerman W: “Altersbestimmung nach der K-Ca-Methode an Sylvin des Oberen Zechsteines des Werragebietes.” Z Naturforsch 1972;27a:1256-9; and Heumann KG, Kubassek E, Schwabenbauer W, Stadler I: “Analytisches Verfahren zur K/Ca-Altersbestimmung geologischer Proben.” Fresenius Z Anal Chem 1979;297:35-43) use model ages instead of isochrons. Heumann et al. dated langbeinite (potassium magnesium sulfate) with a potassium/argon age of 147 million years and a rubidium/strontium age of 152 million years, to 154 million years (the geological age was not given). The sylvite of Wilhelm and Ackerman, with a geological age of 200 million years, dated 133 million and 40.5 million years. Wilhelm and Ackerman attributed this to metamorphosis and recrystallization, without citing any other evidence for these processes. It is fascinating to note Baadsgaard’s data (see note 36), especially on the Alwinsal Willowbrook core. With rubidium-strontium dating the sylvite gives 20-60 million years, and the carnallite gives 2-20 million years, whereas the potassium-calcium dates are 4-85 million years and 85-125 million years, respectively. Notice the reversal of the (apparent) relative ages (the conventional age is 350 million years and the potassium/argon age is 200 million years). |
^{78}The formula is 1^{143}Nd/^{144}Nd = (^{143}Nd/^{144}Nd)_{0} + (^{147}Sm/^{144}Nd) (e^{kt} – 1) |
^{79}For example, see Geyh and Schleicher, p. 103: “This example clearly shows the high resistence [sic] of the Sm-Nd system to metamorphic resetting.” |
The ^{147}Sm/^{143}Nd method depends on the decay of ^{147}Sm to ^{143}Nd by the ejection of an alpha particle, with a decay constant of 6.539 10^{-12} /year (and therefore a half life of 106 billion years). The isochron method is again used.^{78} The same criticisms apply to this method as to the rubidium/strontium method, but this method has the additional disadvantage for our purposes of being hard to reset by anyone’s standards.^{79} Finally, the long half-life of ^{147}Sm means that most samarium/neodymium dates are Precambrian. Samarium/neodymium dating can be safely ignored in the present discussion.
Uranium / Thorium/Lead methods. These are three interrelated methods that all depend on the decay of a long-lived isotope (^{238}U, half life 4.468 10^{9} years, ^{235}U, half life 7.038 10^{8} years, [150] and ^{232}Th, half life 1.4010 10^{10} years), through several steps, to lead. Each isotope listed above produces a different isotope of lead^{80}
^{80}Abbreviated Pb, from the Latin plumbum, from which we get the English word plumbing. |
^{81}This is because the methods under discussion are only used to date materials 1 million years old or older. The longest-lived intermediate is ^{234}U with a 245,000 year half life. The other mean lives added together are less than 120,000 years for any series. |
These are essentially isochron methods. One can assume an invariant decay constant, initial homogenization of lead, and no migration of uranium, thorium, any of their daughter products, or lead, and no removal of ^{235}U by neutron-induced fission. ^{82}
^{82}There is one place in Africa where this assumption is probably not true, the Oklo uranium deposit. About half the ^{235}U has probably been fissioned. |
^{83}The equations are: ^{206}Pb/^{204}Pb = (^{206}Pb/^{204}Pb)_{0} + (^{238}U/^{204}Pb) (e^{kt} – 1), where k 1.55125 10^{-10}/year, ^{207}Pb/^{204}Pb = (^{207}Pb/^{204}Pb)_{0} + (^{235}U/^{204}Pb) (e^{kt} – 1), where k = 9.8485 10^{-10}/year, and ^{208}Pb/^{204}Pb = (^{208}Pb/^{204}Pb)_{0} + (^{232}Th/^{204}Pb) (e^{kt} – 1), where k = 4.9475 10^{-11}/year. There is also a ^{207}Pb/^{206}Pb age which is obviously mathematically interrelated with the uranium/lead methods, and as noted above, is only considered valid on precambrian age material anyway, and will not be given separate consideration here. |
Two criticisms of these methods can be made. First, even concordant dates can be precisely duplicated by mixing lines, just as in rubidium/strontium dating. Concordance may suggest that a deposit was last separated into uranium (and thorium) and lead fractions at a given time, but it does not prove that the last time it was made into a hot slurry was that long ago. This is particularly true for whole-rock dating, but is true for mineral dating as [151] well, since zircon is especially resistant to melting.^{84}
Secondly, in practice “The ages obtained with the above equations are almost always discordant.”^{85} This would imply that almost none of the deposits which are dated by the uranium/thorium/lead methods have been undisturbed since the last time the uranium/thorium/lead clocks were completely reset. This would invalidate the dating methods unless there is some way of mathematically correcting for the age discrepancies. These considerations have led to the concordia method of uranium/lead dating. It is difficult to determine the relative movement of uranium and thorium into or out of a rock or mineral if movement has taken place after formation. Therefore, it is difficult to relate thorium/lead dating to uranium/lead dating in a specimen which is assumed to have been disturbed. But the two uranium isotopes should migrate together, as should the different lead isotopes, and so the ^{238}U/^{206}Pb age and the ^{235}U/^{207}Pb age can be related to each other. If we assume that the uranium in the sample was initially lead-free (or if we correct for primordial lead based either on the isotope ratios of nearby lead without uranium or on the use of isochron methods), the ^{238}U/^{206}Pb ratio will give an age and the ^{235}U/^{207}Pb ratio will give an age. Where the ratios give the same age is called the concordia line (this is not a straight line). If a sample has aged (for example, 3 billion years) and then loses lead^{86}
^{86}This movement of lead can occur in zircons exposed to seawater under high pressure and temperature in a relatively short time (up to 61% lead loss at 13 d in 2M NaCl at 1Mbar and 500° C) according to Pidgeon RT, O’Neil JR, Silver LT: “Uranium and lead isotopic stability in a metamict zircon under experimental hydrothermal conditions.” Science 1966; 154:1538-40. |
There is an elaborate discussion of discordia lines in both Geyh and Schleicher^{87}
^{87}Pp. 117-27. |
^{88}Pp. 291-9. |
^{89}Geyh and Schleicher, p. 121. See also p. 124: “A multi-stage history of detrital zircon or monazite can produce a pseudo-linear plot with intercepts between discrete metamorphic events, which are then without geological meaning.” What is a “pseudo-linear plot”? It would seem to be a linear plot which we do not like. In that case how do we know that an ordinary “linear plot” has geological meaning except that we want to believe it? Some examples of lower concordia ages which are not realistic from anyone’s perspective are given in Tilton GR: ‘Volume diffusion as a mechanism for discordant lead ages.” J Geophys Res 1960;65:2933-45. Another example is given in Kuovo O, Tilton GR: “Mineral ages from the Finnish Precambrian.” J Geol 1966;74:421-42. |
^{90}This problem has been felt so acutely that several diffusion models have been developed to explain “invalid” lower concordia dates. The most prominent of these have been the constant diffusion model (Tilton GR, see note 89) and the radiation damage-induced diffusion model (Wasserburg GJ: “Diffusion processes in lead-uranium systems.” J Geophys Res 1963;68:4823-46). However, these models would be expected to be universal, or at least universal given certain parameters, and there are multiple examples of discordia lines which cannot reasonably be made to fit diffusion models (See, for example, Catanzaro EJ: “The interpretation of zircon ages.” In Hamilton EI, Farquhar RM (eds): Radiometric Dating for Geologists. London: Interscience Publishers, 1968; and Ludwig KR, Stuckless JS: “Uranium-lead isotope systematics and apparent ages of zircons and other minerals in Precambrian granitic rocks, Granite Mountains, Wyoming.” Contrib Mineral Petrol 1978;65:243-54). But note that even if the diffusion model were correct, it would still invalidate lower concordia ages as representing real time. |
^{91}This solution to the problem was noted in Steiger RH, Wasserburg GJ: “Comparative U-Th-Pb systematics in 2.7 10^{9} yr plutons of different geologic histories.” Geochim Cosmochim Acta 1969;33:1213-32. The derivation is as follows: We will take two rocks, Rock 1 with P_{1} ^{206}Pb, U_{1} ^{238}U, Q_{1} ^{207}Pb, and V_{1} ^{235}U, and Rock 2 with P_{2} ^{206}Pb, U_{2} ^{238}U, Q_{2} ^{207}Pb, and V_{2} ^{235}U. We will define for any rock P/U = R and Q/V = S. The concordia plot is then R versus S, and the discordia line becomes R = aS + b. We note that for any rock U/V is a constant, so that U_{1}/V_{1} = U_{2}/V_{2} and U_{1}V_{2} = U_{2}V_{1}. We will assume that there is some uranium in both rocks, so that U_{1} > 0 < U_{2} (and V_{1} > 0 < V_{2}).
In a given mixture with x amount of Rock 1 and (1–x) amount of Rock 2 we have |
^{92}Contrary to the claim of Dalrymple, see note 9, p. 119. |
^{93}Gentry RV, Christie WH, Smith DH, Emery JF, Reynolds SA, Walker R, Cristy SS, Gentry PA: “Radiohalos in coalified wood: New evidence relating to the time of uranium introduction and coalification.” Science 1976;194:315-8. |
Is a mixing line a believable mechanism for discordia lines? Certainly for whole-rock dating a mixing line makes sense (and much of the dating that is done is whole-rock dating). For collections of zircons extracted from whole rock it also makes sense. Even if the dating is done on individual zircon crystals it would make sense unless uranium is consistently incorporated into zircon without lead. This would seem to require the uranium to be incorporated one atom at a time as an integral part of the zircon crystal structure.
The only requirement left of a creationist theory would be to explain the trend of dates to roughly match evolutionary theory. A general trend from older dates in earlier (i. e., lower) rocks to younger dates in later rocks could be explained by the gradually more thorough melting and mixing of the minerals in question as the Flood progressed. And of course there is some natural selectivity in what is published.
However, before we leave uranium/lead dating, attention should be drawn to a fascinating set of observations published in 1976.^{93} Some uranium-rich water percolated through Mesozoic coal (conventional dates over 100 million years old), depositing uranium and its daughter products. From pleochroic haloes of ^{210}Po found in the coal it was reasonably shown that the uranium solution infiltrated the coal before coalification was com-[155]plete, and that coalification was completed roughly 1-10 years from the time polonium (and therefore probably uranium) deposition began.
The uranium did not deposit evenly. Instead, it formed small inclusions which had haloes, mostly without the outer, last-stage haloes. Uranium/lead ratios were measured in several of these inclusions. The ratios ranged from 2,230:1 to 27,300:1 and even higher (unmeasurable lead content). This would appear to give a date of less than 300,000 years—how much less is anyone’s guess. Movement of lead would seem to be unlikely when lead inclusions 50 microns away seemed intact, and it would take massive movement of uranium to explain these dates on an evolutionary basis.
To my knowledge the raw data has not been challenged. Attempts to explain the data by impugning the analytical methods would seem to apply equally to evolutionary dates. And since there is radiogenic lead in these samples not associated with uranium, the experimental results suggest that whole rock dating is not valid unless, as a minimum requirement, the lead can be demonstrated to be microscopically in the same place as the uranium.
Lead/alpha dating is just a watered-down and much less sophisticated version of uranium/thorium/lead dating. It is done by counting the alpha activity in the sample, measuring the lead content, and assuming no initial lead.^{94}
^{94}The lead/alpha method is nearly equivalent to the chemical lead method, which is obsolete. |
Uranium series disequilibrium methods: The uranium series disequilibrium methods include several methods which utilize the daughter products of ^{238}U and ^{235}U. The methods that concern us are the ^{230}Th/^{234}U method, the ^{231}Pa/^{235}U method, the ^{231}Pa/^{230}Th method, the ^{234}U/^{238}U method, the ^{230}Th_{excess} method, the ^{231}Pa_{excess} method, the ^{230}Th_{excess}/^{232}Th method, the ^{231}Pa_{excess}/^{230}Th_{excess} method, and the ^{226}Ra_{supported} and ^{226}Ra _{unsupported} methods. The principles for each of them are similar, so they will be considered together, starting with the best-documented. The reliability of these methods is currently assessed [156]on the basis of several criteria:
-The sample must have a uranium content of >10 ppb, >1 ppm is better.
-Terrestrial carbonates should have contained no ^{232}Th at the time of formation.
-Coral (aragonite, less than 1% calcite), mollusc shells, speleothem, and travertine should be compact, impervious to water, and may show no signs of weathering. They must have formed a closed system (Schwarcz 1980).
-There may be no signs of diagenetic recrystallization, which could have mobilized uranium or subsequent disintegration products (Geyh and Henning [sic] 1986). Thus, for example, primary aragonite samples (e.g., mollusc shells or coral) may not contain any calcite.
-The proportion of acid-insoluble residue must be <5% and the ^{230}Th/^{232}Th activity ratio of terrestrial carbonate should be >20.
-The ^{226}Ra/^{230}Th and ^{234}U/^{238}U activity ratios of marine samples older than 70 ka should be in the range of 1.0 ± 0.1 and 1.14 ± 0.02, respectively.
-The radiometric age should be consistent with the stratigraphic data.
-Dates obtained using different methods, e.g., ^{230}Th/^{234}U (Sect. 6.3.1), ^{231}Pa/^{235}U (Sect. 6.3.2), ^{230}Th-excess (Sect. 6.3.5), ^{231}Pa-excess (Sect. 6.3.6), U/He (Sect. 6.3.14), and ^{14}C (Sect. 6.2.1), should agree.If even one of these criteria is not fulfilled, the results cannot be expected to be reliable.^{95}
^{95} Geyh and Schleicher, p. 213, citing Thurber DL, Broecker WS, Blanchard RL, Potratz HA: “Uranium-series ages of Pacific Atoll coral.” Science 1965;149:55-S. |
^{96}That it is intended to be applied this way can be inferred from Geyh and Schleicher, p. 222. Discussing methods for the “correction” of data, and noting their limitations, the authors state, “However, as none of these methods is entirely satisfactory, samples should be selected that will yield reliable ages with a high probability.” Reliable in what way? Giving the desired ages, or theoretically uncomplicated? If the former, then gross bias is introduced. |
^{97} Bard E, Hamelin B, Fairbanks RG, Zindler A: “Calibration of the 14C timescale over the past 30,000 years using mass spectrometric U-Th ages from Barbados corals.” Nature 1990;345:405-10. It should perhaps be noted that they cited disagreements between the presumed original 14C/C ratios of previously dated varved sediments, U-Th dating, and ice cores of up to 100% (p. 406). |
^{98}Because of this bias, the situation is a little like arguing that the economy in a Marxist country is doing well because the news reports are always good. If one believes in Marxism then they are reassuring evidence. But if one is trying to decide whether Marxist doctrine is correct, then the systematic bias makes the data unimpressive. This analogy should not be pushed too far. There is a major difference between scientific and Marxist reports. Science values truth, honesty, and trustworthiness, whereas Marxism is quite willing to dispense with them if it suits its purposes. Thus, although science has its Piltdown men, their perpetrators are disapproved even by evolutionists. Most of the time one can at least trust the raw data, whereas this is not true at all for Marxist propaganda. Reports of violent students at Tiannenmen Square are quite likely to be simply fabricated. |
But on to the methods themselves. They are dependent on having known initial amounts (or concentrations) of a parent and a corresponding daughter nuclide (or two independent nuclides) which have presumably been immobilized in the past, and measuring the state of progression of the relevant nuclides toward equilibrium.
The ^{230}Th/234U method, considered the most reliable, starts by assuming that no ^{230}Th is found in a sample at the time of closure of the system. The ^{234}U initially in the system decays to ^{230}Th with a half life of 248,000 years. The ^{230}Th itself decays with a half life of 75,200 years. With appropriate measurements of the ^{238}U/^{234}U and ^{230}Th/^{234}U ratios, a formula relating the age and the above ratios may be derived.^{99}
^{99}The equation is (the brackets indicate alpha activity ratios rather than atomic ratios). One is tempted to think that for practical purposes the alpha activity of ^{234}U should be equal to that of ^{238}U. However, it turns out that the uranium in water is relatively enriched in ^{234}U, so that in groundwater the decay of ^{234}U is greater than that of ^{234}U by a factor of as much as 10 or more. Seawater today usually has an activity ratio of 1.15. If it were not for this the equation would be much simpler. |
The method depends on four assumptions:
1. The decay constants have been invariant.
2. The initial ^{230}Th concentration was zero
3. There has been no net migration of ^{238}U, ^{234}Th, ^{234}Pa, or ^{234}U.
4. There has been no net migration of ^{230}Th.
For the purposes of our discussion we will grant assumption 1. The chief complaint of evolutionists concerns the acquisition of uranium by the specimen. If additional uranium is introduced, the radiometric ages will be too low. This apparently happens quite commonly.^{100}
Perhaps most devastating for the validity of the dating method, one can have “unknown, non-zero initial specific activities of the ^{230}Th in samples taken from different cores.”^{104} If one cannot be assured of initially zero ^{230}Th activity, the basis of the method falls apart. Apparently this initial ^{230}Th is felt to come partly from seawater and partly from terrestrial detrital particles. Of course the concentration of the latter would be expected to have been much higher during and shortly after a Flood, almost ex hypothesis. Therefore the method would appear to be theoretically incapable of proving the validity of the evolutionary time scale (by the same token, it would be very unlikely that it could prove a creationist time scale). We might conclude by saying that ^{230}Th/^{234}U dating is not very helpful in our quest. The significance of ^{230}Th/^{234}U ages is greatly limited.
The ^{231}Pa/235U method is closely analogous to the ^{230}Th/^{234}U method. It uses the assumption that ^{235}U is transported into a material without any ^{231}Pa. The ^{235}U then decays (via short-lived ^{231}Th) to ^{231}Pa.^{105}
^{105}The formula for ^{231}Pa activity is closely approximated by [^{231}Pa/^{235}U] = 1 – e^{-kt}, where k is the decay constant of protactinium-231, 2.021 10^{-5}/year, corresponding to a half life of 34,300 years. |
^{106}Geyh and Schleicher, p. 230. |
The ^{231}Pa/^{230}Th method utilizes a mathematical division of the equation for the ^{231}Pa/^{235}U method by the equation for the ^{230}Th/^{234}U method. It is not really an independent method, and does not need further consideration in this discussion.
The ^{234}U/^{238}U method is based on the observation that minerals formed in equilibrium with water contain an excess of ^{234}U with respect to ^{238}U (excess decays per minute, not excess at-[160]oms). This excess (or disequilibrium) is presumably because minerals containing uranium are damaged at the sites where ^{238}U has partially decayed, so the resultant ^{234}U is therefore more available for solution than undecayed ^{238}U. Seawater is enriched in ^{234}U compared to uranium ore, and groundwater is still more enriched. If one knows the original ^{234}U/^{238}U activity ratio one can closely approximate the time by t = ln ([^{234}U/^{238}U – 1]_{0} / [^{234}U/^{238}U – 1]) / k, where [^{234}U/^{238}U] is the activity ratio rather than the molar or weight ratio. However, without knowledge of [^{234}U/^{238}U]_{0}, time cannot be calculated. And there are no reliable estimates for this initial ratio.^{107}
^{107}See Geyh and Schleicher, p. 232: “The main problem in applying this method to the dating of terrestrial samples is the lack of exact knowledge of the initial ^{234}U/^{238}U activity ratio, which is known only for marine samples.” For marine samples, of course, a Flood might be expected to have had a major impact. And indeed there are evidences which could suggest that the initial ^{234}U/^{238}U activity ratio has varied. Ivanovich et al. in note 100 state on p. 410, “Furthermore, the ^{234}U/^{238}U activity ratios in modern marine shells are close to 1.15, the accepted value for oceanic water^{3} [Kaufmann et al. in note 100], whereas the uranium isotope activity ratios in fossil shells are commonly greater than 1.15 indicating assimilation and uptake of uranium isotopes at least partly from sources other than oceanic waters^{4,7}. [Veeh HH, Burnett WC: “Carbonate and phosphate sediments.” In Ivanovich M, Harmon RS (eds): Uranium Series Disequilibrium: Application to Enviornmmental Problems. Oxford: Clarendon press, 1982, pp. 459-80; and Rosholt JN: “Open System model for uranium-series dating of Pleistocene samples.” In: Radioactive dating methods and Low-level counting. Vienna: IAEA, 1967, pp. 299-3 11.]” The dating of corals by the ^{234}U/^{238}U and ^{230}Th/^{234}U methods appears to be the place in radiometric dating where the data are most consistently supportive of the evolutionary hypothesis. There are still minor glitches, such as the occasional inconsistency with ^{14}C dates, but the evolutionary time scale does explain the vast majority of the published data with simple and plausible assumptions (but see Bar-Matthews M, Wasserburg GJ, Chen JH: “Diagenesis of fossil coral skeletons: Correlation between trace elements, textures, and ^{234}U/^{238}U.” Geochim Cosmochim Acta 1993;57:257-76). So it is only fair to ask for a creationist model that will perform as well. A creationist model would have to start by saying that the ^{234}U/^{238}U ratio in seawater at the end of the Flood was close to 1.10, instead of the 1.15 ratio at present. With massive leaching of the continents and the input to the oceans of water with an average value of perhaps 1.5-4 (fairly typical of groundwater), the value of seawater would have risen fairly quickly to its present level and then moved little for the last several (4-20+ depending on the model) thousand years. The detrital content of the oceans, and therefore the thorium available for direct incorporation, would be decreasing during this time, giving decreasing ^{230}Th/^{234}U ratios and therefore decreasing”ages”. Thus it seems that if thorium can be incorporated directly into corals (and this should be tested as it has been in bone; see Rae and Hedges in note 100), there is a simple creationist model which can also explain the data. It is fascinating at this point to speculate concerning the two models. The creationist model suggests that Pleistocene corals near large land masses should be less reliable than mid-ocean corals, particularly having a ^{234}U/^{238}U ratio of greater than 1.15, while their ^{230}Th/^{234}U ratios should be higher than predicted by a straightforward evolutionary model. Furthermore, it suggests that there should be an unusual profile to pre-Flood corals. Their ^{234}U/^{238}U ratio should be less than 1.10, perhaps even approximating 1.00, which matches the evolutionary prediction of great apparent age, but their ^{230}Th content should be quite low, comparable with that of modern corals, giving ^{230}Th/^{234}U dates near zero. I have not yet run across any data in the literature which would appear to corroborate or refute these predictions. These predictions should be tested, but it is doubtful that any evolutionist would attempt to date Paleozoic or Mesozoic coral unless he considers a creationist model at least a possibility. |
^{108}Mean life? No supporting data are given by Geyh and Schleicher (p. 216). |
^{109}P. 236. An example of a sedimentary profile with a profile of excess ^{230}Th that is actually reversed can be found in Somayajulu BLK: “Analysis of the causes of variation of ^{10}Be in marine sediments.” Geochim Cosmochim Acta 1977;41:909-13. No other evidence is cited for the hypothesis that this is a disturbed sediment. |
The ^{230}Th_{excess} method is used to date ocean sediments and manganese nodules. It is based on the theory that in present-day oceans uranium (including ^{238}U and ^{234}U) stays in solution for approximately 250,000 years,^{108} whereas thorium is adsorbed onto plankton or sediment particles within decades. The excess thorium decays away by the equation
ln ([^{230}Th_{excess}]_{0} / [^{230}Th_{excess}]) = kt.
If the sediment is deposited at a constant rate, and the [^{230}Th_{excess}] is constant, then
ln [^{230}Th_{excess}] = ln [^{230}Th_{excess}]_{0} – kd/r,
where d is the depth and r is the sedimentation rate or the manganese nodule growth rate. Of course, the sedimentation rate and the thorium content of the oceans would be expected to have been greater in the past if a Flood occurred, making it difficult to make a straightforward interpretation of results. But an evolutionary interpretation is difficult also, as noted by Geyh and Schleicher:^{109} “The application of this method to pelagic sediments has been successful [has given the expected dates] in only a few cases because A_{0} [the initial excess thorium specific activity] apparently often changes with the rate of sedimentation . . .”. “In manganese nodules, in addition to changes in A_{0}, ^{230}Th can migrate by diffusion . . . causing apparent ages that are too small by up to a factor of 3.” So the ^{230}Th_{excess} method must be classified among [162] the methods which do not aid in choosing between evolutionary and creationist time scales.
The ^{231}Pa_{excess} method is very similar to the 230Th_{excess} method, and suffers from the additional drawback that ^{231}Pa is more soluble in water. It need not be further considered here.
The ^{230}Th_{excess}/^{232}Th method is similar to the ^{230}Th_{excess} method, but attempts to compensate for the variability of ^{230}Th concentration during sedimentation using the assumption that the input of ^{230}Th correlates “with the input of detrital ^{232}Th, which, of course, is not always the case.”^{110}
^{110}Geyh and Schleicher, p. 238. |
The ^{231}Pa_{excess}/^{230}Th_{excess} method assumes that all the ^{230}Th excess and all the ^{231}Pa excess in ocean sediments came from precipitation out of seawater with ^{234}U, ^{235}U, and ^{238}U in present-day concentrations. The method is not as clear-cut as one might wish.^{111}
^{111}Geyh and Schleicher, p. 240. |
The ^{226}Ra_{supported} and ^{226}Ra_{unsupported} methods are “only of historical significance with respect to.. . application for oceanographic studies.”^{112}
^{112}Geyh and Schleicher, p. 243. |