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Radiometric dating falsely assumes rates are constant (Talk.Origins)
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- Radiometric dating assumes radioisotope decay rates are constant, but this assumption is not supported. All processes in nature vary according to different factors, and we should not expect radioactivity to be different.
Morris, Henry M., 1974. Scientific Creationism, Green Forest, AR: Master Books, p. 139.
The first thing that needs to be noted is that the wording of this claim is not found in Morris' book. This is Talk Origins' interpretation of his actual comments.
Second, Morris' book predates all but one of Talk Origins' references. So the most the response can do is prove it to be out of date. To some degree it is out of date since considerable research has been done on both sides since 1974. The above claim is out date in the sense that it assumes that natural fluctuations affect decay rates. Accelerated decay is now associated with two Biblical events, Creation and the Flood, and both events are literally acts of God.
There are also reasons, Biblical and scientific, to associate both events with rapid space expansion and time dilation. Time dilation would convert the normal expansion of space to a local rapid expansion. Some models for accelerated decay would be triggered by a rapid expansion of space.
(Talk Origins quotes in blue)
1. The constancy of radioactive decay is not an assumption, but is supported by evidence.
The fact that there is some supporting evidence for an assumption only increases the reasonableness of the assumption, but in this case it is still an assumption .
This is particularly the case given recent evidence for accelerated decay in the form of helium diffusion rates in zircon crystals. It turns out that the diffusion rate is about 10,000 times too fast for an old Earth, but it fits one or more bursts of accelerated decay in the past 4000 to 8000 years perfectly.
Reference: Radioisotopes and the Age of the Earth
First of all, this only shows that decay rates are not varying right now. It says nothing about past events.
Second, the reference is out of date. More recent experiments have shown some degree of accelerated decay in both Alpha and Beta decay. In the case of Beta decay the factor is a billion fold.
All these do is suggest that the accelerated decay event was a local phenomenon. Some possible causes of accelerated decay can be local only.
The fine structure constant  is defined as:
None of the constants that define the fine structure constant are likely candidates for variability during an accelerated decay event. They affect too many other physical properties. Furthermore while the fine structure constant affects neuron capture rates, it is not the only factor that does so. This would be particularly true inside a fission reactor.
Furthermore, Talk.Origin's is only telling one side of the story. Chaffin showed that though the change in well depth is very small (not nonexistent as Talk.Origin puts it). Chaffin states that, "even these small variations could allow the U-238 half-life to vary by more than one order of magnitude." (Chaffin. The Oklo Constraints on Alpha-Decay Half-Lives. "American Physical Society", The 70th Annual Meeting of the Southeastern Section, November 6-8, 2003, Wilmington, North Carolina)
So the Oklo reactor is actually PROOF of accelerated decay. Another factor that Talk.Origin's failed to mention is that the Big Bang theory PREDICTS changes in the fine structure constant. So this should be considered evidence against it. 
2. Radioactive decay at a rate fast enough to permit a young earth would have produced enough heat to melt the earth.
True, unless there was a mechanism to get rid of the heat. Fortunately General Relativity provides just such a mechanism, in the expansion of space. The expansion of space causes galactic red shift and it has a tendency to cool things off. If Earth was experiencing a rapid expansion of space during an accelerated decay event it would remove the excess heat quite effectively. A local rapid expansion could result from time dilation.
3. Different radioisotopes decay in different ways. It is unlikely that a variable rate would affect all the different mechanisms in the same way and to the same extent.
Assuming that it is necessary that all decay methods change to the same extent, both proposed periods of accelerated decay are thought to have occurred during Creation and the Flood, and as such they were acts of God—literally. So the likelihood of it occurring naturally is irrelevant.
This is highly debatable. There are numerous examples of inconsistent dates.
Reference: Radioactive Dating Explained - Part 2
Reference: The Unreliability of Radiometric Dating
Reference: Potassium-Argon and Argon-Argon Dating
Reference: RADIOISOTOPES IN THE DIABASE SILL ...
Furthermore a study of a survey of radiometric dates from Alaska showed no statistical tendency towards agreement.
Here is a chart of dating data from The Alaska Division of Geological & Geophysical Surveys . The data was collected from various locations scattered over Alaska. The report containing the charts called Radiometric dates from Alaska - a 1975 compilation  is simply a chart of data with no interpretation beyond the date calculations.
Now 62% of the locations had only one date and so there was nothing to compare the dates to. Another 35% were remeasured by the same method and therefore they only show the isotopic consistency of the rock. Only 3% of the locations had dates by different methods.
The result is that after evaluating the radiometric dates from 509 locations scattered over Alaska, there is no statistical indication of a trend favoring concordance. Yes, this is based on only 14 samples, but that shows how seldom more than one dating method is used ( or reported ) in radiometric dating.
Scientist can’t even agree on a calibration curve for radiocarbon. You can’t say dates are consistent if you don’t have anything to make it consistent to. []
Actually such agreement only goes back to about 1000 B.C;. prior to that there starts to be significant disagreement. Furthermore all three other dating methods are used for calibrating at least radiocarbon dating, removing them as independent tests. It's amazing how consistent measurements can be when one is used to calibrate the other.
Reference: Encyclopedia: Radiocarbon dating
4. The half-lives of radioisotopes can be predicted from first principles through quantum mechanics. Any variation would have to come from changes to fundamental constants. According to the calculations that accurately predict half-lives, any change in fundamental constants would affect decay rates of different elements disproportionally, even when the elements decay by the same mechanism.
First of all this article deals only with Alpha decay. With Beta decay a variation in mass of the weak nuclear force's transmission particle would affect all beta decay rates proportionally.
Reference: Radioisotopes and the Age of the Earth
Furthermore, even with alpha decay there are factors that could change all alpha decay rates proportionally.