Carbon 14 Dating and the possible effect of "leaching"

The Carbon 14 "leaching" hypothesis:Some creationists have proposed that 14C is preferentially leached out of samples, thus resulting in a false old age of samples.Let's look at what the data says about this hypothesis (we'll also ignore the total idiocy of arguing that leaching accounts for the Lake Suigetsu data even though it covers a period of time in excess of any "Young Earth" scenario, and if we are not worried about a "Young Earth" scenario then there is no problem with 14C dating methods).First we'll use data from Lake Suigetsu. We could probably get the actual data from the sources, but this isn't necessary for our needs -- we can extract sufficient accuracy from this graph to show the concept is false:
{note: image originally from http://www.cio.phys.rug.nl/HTML-docs/Verslag/97/PE-04.htm,
image copied to a mirror site to cut down on bandwidth usage for the original site}The data from Lake Suigetsu is the small solid dots and it starts somewhere about 8000 or 9000 years ago according to the article "A 45.000 YEAR VARVE CHRONOLOGY FROM JAPAN"
by H. Kitagawa and J. van der Plicht.First lets match a straight line to the data points:

I've also highlighted the data from corals (purple circles) to show how they also fit the line. Note that this line covers and matches the line from the tree rings at the start of the diagram -- it has the same slope, so it correlates to that data as well.We'll use this line to extract some 'normalized' data and then see where a leaching hypothesis takes usFrom the line on this last image we see that it runs from the assumed zero point (at 0,0) to a 14C age of 38,000 years ago for an actual 45,000 years ago - based on the floating data match by Kitagawa and van der Plicht (a factor that we will eliminate from the process below)So the correlation of 14C to age is:
varve age = 14C age x 45/38 = 1.1842f(14C/12C)where f(14C/12C) is previously defined as
How Carbon-14 Dating Works | HowStuffWorks:
t = [ln(N_f/N_o)/(-0.693)]xt_1/2
where t is the computed age, t_1/2 is the half life (5715 years), N_f is the (final) ratio of 14C/12C atoms in the sample and N_o is the (original) ratio of 14C/12C atoms at the time of death.Using these two formulas we can calculate the 'normalized' proportions of 14C/12C for samples at different base ages per the above graph:The 14C age formula above rearranged becomes
-0.693*t_14C/5715 = ln(N_f/N_o)
or
(N_f/N_o) = e^{^(-0.693*t_14C/5715)}Substituting (varve age * 38/45) for t_14C and working out all the constants we get:
(N_f/N_o) = e^{^(-0.693*(38 varve age/45)/5715)}
or
(N_f/N_o) = 1/e^{^(varve age/9766)}And this gives us a table of data that we can use to represent the Lake Suigetsu floating data:

Varve	 Nf/No
Age	 Ratio
-----	------
0	1.0000
8000	0.4408
10000	0.3592
12000	0.2927
14000	0.2385
16000	0.1943
18000	0.1583
20000	0.1290
22000	0.1051
24000	0.0856
26000	0.0698
28000	0.0569
30000	0.0463

Next we'll remove the uncertainty of the floating start of the data by starting ours at the 8000 years ago and using deltas from that time and compare those to the actual N_f/N_o values:

  Time    Actual
Interval   Nf/No
--------  --------
0	0.4408
2000	0.3592
4000	0.2927
6000	0.2385
8000	0.1943
10000	0.1583
12000	0.1290
14000	0.1051
16000	0.0856
18000	0.0698
20000	0.0569
22000	0.0463

And when we graph this data we get the following:

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Graph of actual 14C content versus actual time intervals from time "X"In excel I can model a "trendline" through the data points and I can also have it tell me what the function is and what the "R^{^2}" value is (a measure of the accuracy of the trendline formula in matching the actual points -- 1.0 means an exact match at every point).When I do this for polynomial trendlines I can approach 1.0 with a function like (this uses 6 constants and has an R^{^2} value of 0.999999994)When I do this for an exponential trendline I get: (which uses 2 constants and has a perfect match -- to data assuming (1) an 8000 year gap and (2) an exponential function)Now the fun begins. We know there is an offset at the beginning of the data, but we don't know how big it is eh?What we can do is model it a different initial time (t_i) and see what effect this has on the curve.

If I set the t_i at 2000 years ago I get:

y = 0.5409744643e-0.0001023972x
R2 = 1.0000000000

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If I set the t_i at 4,000 years ago I get:

y = 0.6639231983e-0.0001023972x
R2 = 1.0000000000

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If I set the t_i at 6,000 years ago I get:

y = 0.8148148245e-0.0001023972x
R2 = 1.0000000000

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If I set the t_i at 8,000 years ago I get:

y = 1.0000000000e-0.0001023972x
R2 = 1.0000000000

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If I set the t_i at 10,000 years ago I get:

y = 1.2272727126e-0.0001023972x
R2 = 1.0000000000

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If I set the t_i at 12,000 years ago I get:

y = 1.5061983111e-0.0001023972x
R2 = 1.0000000000

In each case I get a 100% match to the points on the curve, the formula is of the form:
y = Ae^{^(Bx)}
Where y = N_f/N_o, x = time and A and B are constants.In each case I get B = -0.0001023972 which means I can write the general formula as
y = Ae^{^(-0.0001023972x)}
or
N_f/N_o = Ae^{^(-0.0001023972t)}
or
N_f/N_o = A/e^{^(t/9766)}
You will also note that A = 1.0 for t_i = 8000 years (no surprise as this becomes the formula used to generate the data points).The important point though, is that for any {delta t} you pick it doesn't matter what the real formula starting date is, the amount of change in N_f/N_o over that time period is perfectly modeled by the decay rate of 14C -- here carried out to 10 decimal places -- and only the decay rate of 14C.There is no "room" for 14C to preferentially leach out of the objects compared to 12C without affecting this data, therefore there is absolutely no significant effect of preferential leaching on the objects over the whole period of the data.If preferential leaching of 14C does not occur over 29,100 years it is not going to have occurred over a period shorter than that. Preferential leaching is falsified as a hypothesis.One can quibble about the accuracy of the starting date used, but the fact remains that 14C dating {predicts\measures\confirms}the same time periods as are found by counting the annual layers.Now remember that N_f is the (final) ratio of 14C/12C atoms in the sample and N_o is the (original) ratio of 14C/12C atoms at the time of death, and because 12C is stable (does not decay) this becomes:
N_f/N_o = (14C/12C)_f/(14C/12C)_o
and if the (14C/12C) ratios are expressed as a percentage, then the 12C's cancel (each set to 100 relative to the 14C content) and you end up with:
N_f/N_o = 14C_f/14C_oThe other option for leaching is that it affects both 14C and 12C the same way. If this is the case then the measurement of (14C/12C) removes this effect from the data, and the results then accurately {predict\measure\confirm} the dates of the organic objects.Conclusion: there is no measurable significant effect of leaching on the dates derived from 14C analysis. The hypothesis is falsified.Enjoy.(dates and dating)Edited by RAZD, : typotypicaltypos

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