Argon diffusion data support RATE’s 6,000-year helium age of the earth
Here I present a new analysis of old (1986) argon retention data from the same borehole that provided helium retention data for the Radioisotopes and the Age of the Earth (RATE) research initiative.1 The deepest part (4.56 km) of the borehole was hot enough to cause more than a 20% loss of radioactivity-generated argon-40 from feldspar in the granitic basement rock, conventionally dated to be 1.5 Ga old. Data and equations from the 1986 article show that at the present temperature (313°C) at that depth, it would take only 5,100 (+3,800/-2,100) years for the feldspar to lose that much argon. This supports the 6,000 (± 2,000) year helium diffusion age that RATE found for zircons in the same borehole.
Old article interprets argon data oddly
In a recent letter to this journal,2 Gary Loechelt, a critic of the RATE helium project, focused my attention on a paper about past temperatures in the borehole (figure 1) that provided the helium data we used. In 1986 the Journal of Geophysical Research published the article,3 by T. Mark Harrison, Paul Morgan, and David D. Blackwell, three geoscientists at three U.S. universities. It was one of three articles I had cited about the temperature issue. Readers can see my detailed review of all three articles in my recent letter replying to Loechelt.4 As I focused on the 1986 article, I saw that it appeared to ignore the heat that a nearby volcano would have provided to the borehole during the alleged one million years (1.04 Ma) since its last ash eruption. Instead, its authors thought (along with Loechelt) that the temperatures in the borehole were relatively low, e.g. at 2.9 km depth falling below 130°C 870 Ma ago and reaching 87°C more than a million years ago. Then only twenty thousand years ago, they claimed, the temperatures rose dramatically, by more than 100°C, up to the high values observed today.
This seemed quite odd to me, especially since a 1978 study5 by the authors’ Los Alamos colleagues showed that the nearby volcano would heat the borehole up to within 50°C of today’s temperatures, maintaining that high temperature for (allegedly) the last 0.8 Ma. The temperature would have been a lot more if the magma body causing the volcano had been somewhat closer to the borehole than they assumed in that model. Confirming the latter, a 1989 study6 of fluid inclusions in the rock gave data (not theory) that past temperatures in the borehole had peaked at levels about 50°C higher than today’s levels. By conventional uniformitarian dating, the peak would have been about 0.9 Ma ago. I would have thought that Harrison et al. would be quite aware of the possibility of such heating from the volcano. So why did they want the borehole to be relatively cool (e.g. 87°C at a depth of 2.9 km) until very recently? Why did they ignore the volcano?
I will show below that it was probably because they knew borehole minerals could not have retained the observed large percentages of argon for hundreds of millennia at anywhere near today’s high borehole temperatures. Much more argon would have diffused out of the minerals. Here I will show that their argon diffusion data favor an age of only 5,100 (+3,800/-2,100) years. That strongly supports the helium diffusion age RATE found for zircons in the same borehole, 6,000 (± 2,000) years.7
Experimenters measured leak rates of argon in feldspar from GT-2
The deep Precambrian granitic ‘basement’ rock from borehole GT-2 contains not only zircons, but also a potassium-bearing feldspar called microcline (K Al Si3 O8, figure 2). The potassium is mostly the stable isotope 39K, but as with all natural potassium, about 0.01% of it is the radioactive isotope 40K. The latter decays (with a present half-life of 1.25 Ga) into two daughter atoms, one of which is the stable argon isotope 40Ar. So if a researcher finds out how much potassium is in the feldspar, he can use the 40Ar in it to try to estimate the age of the mineral.
Harrison et al. took samples of feldspar from five depths (table 1) in the borehole. Then they put them into a nuclear reactor for a calibrated length of time. The neutrons in the reactor convert some of the stable 39K into 39Ar. The latter is not stable, but its 269-year half-life is long enough to allow researchers to use it to estimate the amount of 39K in the sample. Comparing that with the 40Ar in the sample is the basis of the ‘argon-argon’ variety of potassium-argon dating.8,9
Then, in a vacuum chamber, they heated each sample in 50°C steps and measured how much of each argon isotope was released during each step. That gives the diffusivity D (‘leakiness’) of argon moving through and out of the Feldspar at that temperature. More specifically, the rate of outgassing (fraction of the eventual total lost per unit time) gives values of D/a2 directly as a ratio, where a is the average radius of the crystals (or ‘diffusion half width’, which the authors symbolized with an l). Harrison and his co-workers fit the values of D/a2 to the following equation:
where R is the gas constant (1.986 calories per mole-Kelvin), T is the absolute temperature in Kelvin, D0 is the ‘frequency factor’, and E is the ‘activation energy’. The last two parameters are constant with temperature for any given sample, but are often different for samples from different locations. Here the authors got one set of values of D0/a2 and E for depths 1, 2, and 3, and a different set of values for depths 4 and 5. I’ve shown both sets of values in table 1.
The authors’ report of the argon diffusivities leaves something to be desired for my purpose of determining age. They show (in figure 3) only the diffusivity data for depths 1, 2, and 3, not for depths 4 and 5. They report error bars for the former set but not for the latter, saying only that the parameters of eq. (1) for the two deeper samples are “~ 8,000 s-1” and “~ 44 kcal mol-1”. That suggests the fit, normally to a straight line on a plot of ln(D/a2) versus 1/T, was not too good for samples 4 and 5. Perhaps that is because the slope of the fit starts to decrease at lower temperatures. Such a decrease is very common in naturally-occurring minerals.10 In support of that idea, their figure 3 does not show any diffusion data at lower temperatures, showing only a straight-line fit from 700°C down to 400°C. Therefore the values of D/a2 in table 1 for the three shallowest depths, being extrapolated beyond the data down to rather low temperatures, are probably lower than the real numbers. However, it turns out that I only need data for the fifth sample, at 313°C. That is not far below the low end of the temperature range of the fitted data, so the extrapolated value in the table should be good enough.
Feldspar from hottest parts of borehole lost some argon
In the laboratory, the first argon emerging from a sample comes from the outermost parts of the crystals. Argon emerging later comes from deeper within the crystals. The 39Ar, having been produced in the reactor from 39K, is uniformly distributed throughout the crystals. But the 40Ar comes from 40K decaying in situ over a long time. If any 40Ar has leaked out of the crystals in situ, it will have come from the outer parts first. So any diffusion taking place down in the hot rock will leave the outer parts of the feldspar crystals depleted in 40Ar.
Harrison et al. examined this issue by plotting ‘age spectra’ in their figure 2. Their graph showed, for each of the five samples, the 40Ar-based ‘age’ on the vertical axis and the percent (of the eventual total) 39Ar released on the horizontal axis. My figure 3 reproduces the curve for the deepest sample, number 5, adding the shading and annotation. The ‘age’ values of course depend on the assumption that nuclear decay rates have always been at their present slow rates. The peak of 1,160 Ma shows that over ‘one billion years’ worth’ of 40K to 40Ar decay occurred in situ. RATE hypothesized that occurred during several episodes of accelerated nuclear decay in the past, the more recent one being during the year of the Genesis Flood. We also hypothesized an accelerated cooling mechanism that would get rid of much of the resulting radiogenic heat.11
Figure 2 by Harrison et al. shows that the curves for samples 1, 2, and 3 rose almost immediately to their maximum value. They estimated that sample 3 had lost less than 2% of its 40Ar, and that samples 1 and 2 lost even less than that. Sample 4 showed a somewhat slower rise, representing a nominal 5% loss. But the authors thought that value was small enough to have been greatly perturbed by other factors:
“The combination of the small amount of 40Ar* [asterisk indicates radiogenic] together with some absorbed excess 40Ar … results in poor resolution of the outgassing event.”
However, the authors have more confidence in the estimate of the losses from the fifth sample (the one I show in my figure 3 above):
“This sample has apparently lost about 20% 40Ar* in response to the recently elevated temperatures.”
My figure 3 shows why I think ‘20%’ is a slight underestimate of the argon loss. The ratio of the areas in the lightly-shaded and dark-shaded regions should give the ratio of 40Ar lost to 40Ar retained. The intersection of the dashed ‘1/2 Max’ line with the dotted curve should specify the area ratio fairly well. The intersection occurs at 25%, not 20%. The 0.2 Max and 0.8 Max horizontal lines (not shown here) intersect the dotted curve at 19% and 33%. I will use these values below to estimate an error range for the age. I’ve included my estimated 25% loss as a fraction in the bottom of the right-hand column of table 1. I put the losses Harrison et al. estimated in the other rows of the column. I’ve put parentheses around the less accurate values.
Reckoning the argon diffusion age
Harrison et al. give an approximation,12 their eq. (1) relates the heating time t and the fractional loss f to the value of D/a2 at a particular temperature:
Turning this around gives the time t it would take at constant temperature to get a loss f:
Harrison et al. give an expanded form of this equation, their eq. (2), but it contains a typographical error (right-hand bracket in wrong place). I’ve included the resulting ages in the last column of table 1.
The only age that is relatively accurate is that of sample 5. Assuming that the 0.2 Max and 0.8 Max points (not shown) on the dotted curve of my figure 3 cover a range of error larger than all the other errors, we can assign the borehole an argon diffusion age of
After their eq. (2), Harrison et al. list similar results: “Results of these calculations yield maximum estimates of peak heating duration of between 3 and 60 ka. This dispersion is in part due to the near negligible, and therefore difficult to assume, 40Ar* loss from the four shallowest samples and the exponential dependence of temperature on heating duration.”
Since their assumed ‘transient’ heating episode lasts until the present, the ‘heating durations’ above are really age estimates. Their 3 ka age (the result one gets for f = 0.2 on the fifth sample) is the same as the lower limit of my estimate. Their highest age, 60 ka, differs somewhat from my 44 ka calculation for the fourth sample, perhaps because they were able to use non-curve-fit values and error bars for D/a2. But it is noteworthy that they did not include the fifth sample, the deepest one, in their caveat about the argon loss estimates. So we can take the loss for that sample, and consequently its age, as better-founded.
Taking the temperature as constant at about 313°C during most of the diffusion history of the sample is a good approximation, from either the uniformitarian or creation viewpoint. That is because the rock is dry, preventing water or other fluids from carrying heat by convection. That leaves only heat conduction to change the temperature. Since heat conduction is very slow in rock,13 the temperature should remain roughly constant for thousands of years. According to the two RATE hypotheses, accelerated nuclear decay and accelerated cooling during and a little after the year of the Genesis Flood, the rock temperature should have changed very little in the more than 4,300 years (Hebrew Bible chronology) that have elapsed since the Flood ended. So there is every reason to believe that the argon age is roughly correct—that the deep Precambrian ‘basement’ rock is thousands, not billions, of years old.
It is clear that the shortness of the argon age (relative to a million years, and certainly to a billion years) is the reason why Harrison et al. could not tolerate the idea that the volcano heated the borehole at any time earlier than about 20,000 years ago. (Even 20 millennia seems large in light of my diffusion age of only 5100 years.) With their low temperatures during the (alleged) 1.5 Ga before that, the argon losses would have been large even for the shallower samples.14 Yet if one grants the uniformitarian age of the nearby volcano, about 1 Ma, it would have heated the site more than enough15 to cause much greater losses just during that (alleged) megayear.16 In other words, the observed high argon retention conflicts severely with the uniformitarian-assumed long ages. These data say that the feldspar generated over a billion years’ worth of 40Ar, and then retained it, during a period of time that began only thousands of years ago. The argon data thus support accelerated nuclear decay, RATE’s young helium age, and the biblical youth of the world.
- Wieland, C., RATE group reveals exciting breakthroughs, 21 August 2003, news feature on Creation Ministries International website at creation.com/rate-group-reveals-exciting-breakthroughs. Also see various resources on the Institute for Creation Research website at www.icr.org/rate. Return to text.
- Loechelt, G., Critics of helium evidence for a young world now seem silent? Journal of Creation 24(3):34–35, December 2010. Return to text.
- Harrison, T.M., Morgan, P., and Blackwell, D.D., Constraints on the age of heating at the Fenton Hill site, Valles Caldera, New Mexico, Journal of Geophysical Research 91(B2):1899–1908, 10 February 1986. Return to text.
- Humphreys, R., Humphreys replies, Journal of Creation 24(3):35–39, December 2010. Return to text.
- Kolstad, C.D. and McGetchin, T.R., Thermal evolution models for the Valles Caldera with reference to a hot-dry-rock geothermal experiment, Journal of Volcanology and Geothermal Research 3:197–218, 1978. Return to text.
- Sasada, M., Fluid inclusion evidence for recent temperature increases at Fenton Hill hot dry rock test site west of the Valles Caldera, New Mexico, USA, Journal of Volcanology and Geothermal Research 36:257–266, 1989. Return to text.
- Humphreys, D.R., Young helium diffusion age of zircons supports Accelerated nuclear decay; in: Vardiman, L., Snelling, A.A. and Chaffin, E.F. (Eds.), Radioisotopes and the Age of the Earth: Results of a Young Earth Creationist Research Initiative, Institute for Creation Research, El Cajon, CA, and Creation Research Society, Chino Valley, AZ, ch. 2, pp. 25–100, 2005. Chapter 2 archived at http://www.icr.org/article/young-helium-diffusion-age-zircons/. Return to text.
- Faure, G., The 40Ar/39Ar method of dating; in: Principles of Isotope Geology, 2nd ed., John Wiley & Sons, New York, chap. 7, pp. 93–116, 1986. Return to text.
- Overman, R.L., Evaluation of the Ar/Ar dating process, Creation Research Society Quarterly 47(1):23–30, Summer 2010; Publicly archived at: www.creationresearch.org/crsq/articles/47/47_1/CRSQ Summer 2010 Overman.pdf. Return to text.
- Humphreys, ref. 7, pp. 3436. Note ‘defect line’ in fig. 5, p. 35, Erratum: on p. 34 of this reference, in my eq. (3), the second exponential should have a minus sign in his argument, as does the first exponential. Return to text.
- Humphreys, ref. 7, pp. 67–74. Return to text.
- Carslaw, H.S. and Jaeger, J.C., Conduction of Heat in Solids, 2nd ed., Clarendon Press, Oxford, England, section 3.3, p. 97, eq. 11, 1959. To get the Harrison et al. equation, replace 1–(vav/V0) by f, κ by D, l by a, and take the approximation for t small compared to a2/D. Return to text.
- Harrison et al., ref. 3, p. 1906, fig. 9, have the temperature at the bottom of the borehole, close to their conjectured heat source (therefore moving heat fast), rising by conduction less than an average of 0.01°C per year. Return to text.
- Humphreys, ref. 7, p. 50, eqs. 10–14. Use a=b, t = 1.5 Ga = 4.7 ´ 1016 s and D/a2 = 3.645 x 10-19 s-1. The latter value is an extrapolation of the diffusion parameters of sample 3 in table 1 down to the 87°C desired by Harrison et al. for that depth. This value of D/a2 is probably a severe underestimate in light of the usual crystal defects, which can raise diffusivities by several orders of magnitude at low temperatures (ref. 7, pp. 34–36). Even with the low temperature and the underestimated diffusivity, the loss during 1.5 Ga would be about 39%, an order of magnitude greater than the (less than) 2% observed at that depth. Return to text.
- Humphreys, ref. 4, p. 37, section titled “The best uniformitarian picture of temperature history”. Return to text.
- Humphreys, ref. 7, p. 50, eqs. 10–14. Use a=b, assume the deepest sample got no hotter than its present temperature of 313°C, and use the table 1 value of D/a2 = 3.1 × 10-13 s-1 with a time t = 1 Ma = 3.1 × 1013 s. Then the argon loss would be very close to 100%, leaving essentially no argon at all, a loss much greater than the observed loss of 25%. Return to text.
Graham D. said "I have also taken the time to check the sources, most of which are *hmm* creationist sources. Not reliable sources I might add."
First, this is a genetic fallacy; Graham is saying that the sources are not reliable simply because they are from creationists. Using the same logic, I could just as easily turn around and say that any claims made by evolutionist sources are not reliable either, since they are just as biased as creationists are.
Second, does Graham really think that evolutionists are going to publish data that supports a young earth? Not likely, because they are committed to their paradigm and have faith that they will find a way to explain away any of the evidences against the evolutionary paradigm.
I'm the friend of G.P.
I thought this was interesting when I thought it was about young earth, but got quite annoyed with it when I saw that that author thinks someone else's data shows a 6,000 age, provided we use data from sample 5 but not sample 4, and use some assumption (not described) to adjust a formula that is ~ from column 2.
The right side of the table is all imprecise, but the author says he will show a 6,000 result, and puts that in the title and summary.
It could have been about extra data not being published, but instead it overreaches in making claims supported by a single sample based on extra assumptions and conditions.
I get the impression that you only skimmed the article briefly before you dashed off a comment to G. P. and then to CMI. That's because the article explains all the reasoning and formulas you are "annoyed" about, more than adequately. But to make them clearer for you, I didn't use the argon loss fraction from sample 4 "(0.05)" because the researchers (Harrison et al. ) who measured it said it was unreliable, showing "poor resolution of the outgassing event." Did you read my quote from them just a few paragraphs above the table? Since the point was important to you, did you take the time to look up the Harrison reference?
I don't understand what "assumption (not described)" I'm supposed to have used to "adjust a formula ..." I didn't adjust any formula. My eq. ( 3 ) for the age comes directly (using high-school algebra) from Harrison's eq. ( 2 ). That and eq. (1), also from Harrison, are the only formulas I used, and I didn't "adjust" them. The rest of your sentence, "... that is ~ from column 2." Column 2 is the depth of the samples, so you couldn't possibly have meant what you typed. Did you mean to say "the second column from the right", i.e., the "Argon Loss" column, and the fifth row, for sample 5, namely "~0.25"? The paragraph right above the table explains in excruciating detail why I used 0.25 instead of Harrison's 0.20.
I think that if you had understood that paragraph, Figure 3, the argon-argon dating method, and Harrison's "age spectrum", all explained in the "Feldspar from hottest parts of borehole lost some argon" section, then you never would have made any of your criticisms. For example, you wouldn't have missed that my error range for the argon loss goes from 0.19 to 0.33, which includes Harrison's 0.20 and my 0.25. So you didn't understand the error range behind the "~" symbol you were annoyed about, and you didn't understand its basis. I can understand why you skipped that section, because, if you don't understand the "age spectrum" method, it requires considerable thought, and probably looking up some of the references. But what you skipped contained the answer to all your criticisms.
Last, all of this is making a mountain of criticism out of a molehill of things to gripe about. First, even if one accepts the "60,000 year" upper limit given by Harrison for the age of sample 4, it is still far short of 1.5 billion years, the alleged time the argon and helium had to accumulate and be retained in the borehole minerals. That's a major point, not to be overlooked. Second, my argon results are merely supplemental to my helium results. If you really want to judge this issue properly, you need to read the chapter linked in reference 7 of the article carefully. For your convenience, here is the correct link: http://www.icr.org/article/young-helium-diffusion-age-zircons/ .
Last, let's discuss your annoyance. I can understand why my terse reply to G. P., "study the article", might have further annoyed you. I apologize for being lazy and wanting you to do all the work of understanding. But why were you annoyed before that, by the article itself? Wouldn't you now agree that you jumped to the conclusion that I was being sloppy and dishonest simply because you didn't understand the "Feldspar from hottest parts of borehole lost some argon" section? It is indeed a universal tendency to make such assumptions. I do it myself all too often. But were you predisposed to make such an assumption because you didn't like the article's conclusion, that the earth is as young as the Bible says?
Wanting you to understand,
I noticed that you mentioned that this article was published in the Journal of Creation. Do you really expect me to take that seriously?
I've done a bit of research primarily on the internet, and noticed that the only websites praising this "research" are creationist websites. I've checked numerous legitimate journals and have found no such entries concerning this phenomenon except a couple, which ALL support a 4.55 billion year old earth.
I have also taken the time to check the sources, most of which are *hmm* creationist sources. Not reliable sources I might add.
I read from various science journals almost every day, and have not spotted a single entry regarding even the smallest possibility of a young earth. You guys really have not made the smallest dent (did I spell that right?) in established science.
Well Graham, I expect you to take the scientific data and reasoning in the article seriously. I notice that you show no sign of actually having thought about those things for yourself. It appears that, as I mentioned to several other people above who said similar things, you expect the secular science "establishment" to do your thinking for you. But, having once had the secular science point of view myself (as an atheist in the early years of my graduate studies), I know that (A) I wouldn't have been able to think clearly about evidence the Bible is true, and (B) I wouldn't have told you about such evidence. When the spiritual stakes are high---namely, determining whether the Bible is true and whether Jesus Christ really does have a claim upon your life---you cannot rely upon any other person to tell you what is true and what is not ... not even if they wear the robe of "scientist". I suggest that you investigate the claims of Jesus Christ in the Bible for yourself. But beware: that was a major link in the chain of events that God used to transform me from an atheist into one of His children. See also Creationism, Science and Peer Review.
Earnestly in Christ,
Hi there, A friend of mine has made the following observations about your article - they are as follows:
-- Quote --
The web-page title is "Argon diffusion data support RATE’s 6,000-year helium age of the earth" and yet the data supposedly says "5,100 (+3,800/-2,100)" Which leads to an unconnected conclusion: "That strongly supports the helium diffusion age RATE found for zircons in the same borehole, 6,000 (± 2,000) years" Table 1 shows only Depth and Temp as definite figures for the two deepest samples. The original samplers are unsure what to do with the deeper data
But the writer decides that he only needs to consider the deepest sample "~8000", and carry through presumed calculations resulting in ~5100 in a range of 8900-3000. And because that results in "6,000 (± 2,000) years" he writes an article!
The second deepest sample results in (44,000) based on the data, but we should just discard this data as the item is in parentheses (indicating a large error). The whole right side of the author's Table 1 is in parentheses, except for the deepest sample.The author dismisses the sample at 3.58km depth, but relies on similar data at the deeper 4.56km depth to support his hypo-thesis."
-- end quote --
Do you have a response?
Yes, I have an answer for your friend: "Study the article!" Detailed answers to all his questions are there.
I am still wondering why you guys insist on only presenting such ideas as the one above to a lay audience. Surely you would rather present it to academia. I mean really, what do you have to lose? If you could prove a young earth, say to be a mere 6,000 years old, you would certainly win a Nobel prize, there is no doubt about it! You would have fame, fortune and glory. For once you would have other Nobel prize winners agreeing with you.
So why not pursue such a sought after prize? Some might refer to the Nobel prize as the holy grail of scientific relics. All you have to do is convince the scientific community that the world is 6,000 years old and it is yours! Not to mention countless souls will be saved!
Actually, the article first appeared in the Journal of Creation, which has a quite sophisticated technical readership and well-qualified technical reviewers. RATE presented the helium diffusion results and the results of two other projects at an American Geophysical Union (AGU) conference. You can read about our reception on this page http://www.icr.org/research/index/researchp_aguconference/ . The response was much better than we expected, and there were no show-stopping comments. We even found some clandestine creationists were among the AGU membership.
I notice that you apparently did not intellectually engage the technical evidence in my article. That is probably because you are expecting secular academia to do your thinking for you, and tell you if there is anything correct in creationist science. Unfortunately, as I found out when I was still a graduate student, that expectation is rather naive.
This is fantastic! I'll bet those Godless evolutionary scientists at Caltech; MIT and the US Geological Survey (to name but a few)will tremble when you present your results to them. Please be sure to let us know how they respond.
I'd expect the reponse of the Godless ones (not the believing ones at the same institutions) to be much like yours, Jeff. They, like you, are depending on the science "establishment" to tell them honestly if evidence for a young world exists. Also like you, many of the Godless ones (I've found from experience) would dismiss the evidence in my article without intellectually grappling with it.
The article provides an excellent example of how the long-agers have been caught with the pants down, so to speak. They have no explanation for the contradiction staring in front of their faces where on the one hand they are convinced the volcano is millions of years old if not a lot more yet the temperature of the surrounding underground region had to be a lot cooler throughout virtually all of that period compared to the recent past. Then there is the Argon diffusion rates. Such a contradiction and the Argon diffusion analysis is enough to discredit the old age theory single handed, let alone the mountain of other evidence.
I'm glad you understood the article so clearly, Jack. It assures me that the skeptics who replied without grappling with the techncal details ought to have understood it also. If I had only their responses to go by, I might wonder if I could have explained things better. I probably could have done so, but that is apparently not the reason they don't want to understand it.
Excellent piece. The accelerated nuclear decay rates in the past, mentioned here, seem equivalent to the Astro-Phyisicist's Cold Dark Matter: something cooked up to explain difficult phenomena. Have you a response to anyone who criticises the far-reaching universal effects of such accelerated decay rates on all matter?
Thanks, Graham. Yes, the RATE group has been answering that question for years, in essence as follows: (1) Study the other lines of evidence (besides helium diffusion) in the RATE technical book online at http://www.icr.org/rate2/. (2) Come up with an alternative hypothesis that explains all the data. If someone has difficulty doing (2), then perhaps he should consider accelerated decay and cooling as the most reasonable answer.