As has been pointed out by others, modern material of approximately twice the mass as the Shroud samples would have to be added to the samples to bring authentic first-century linen up to radiocarbon dates of the fourteenth-century, and this would have been just too obvious to go unnoticed by so many independent investigators. . . .
http://www.freeinquiry.com/skeptic/shroud/as/schafersman.html
Schafersman, a geologist, not a C14 physicist, is close to correct. You would have to ADD an additional approximately 180% by weight to the Shroud material as a contaminant to bring the 1st Century date to 14th Century. Using Shafersman's "twice the mass" approximately two out of three parts of the sample would have to be contaminants. In other words ~66% of the tested material would have to be NEW material to skew 1st Century into the 14th. The amount mass of the original material in the combined sample would be a mere 33% of the total tested mass.
Such large percentages of added contaminants would stick out like a sore thumb. That is why the bio-plastic theory was a non-starter and why the soot from the 1352 fire is also a non-starter. Adding enough bio-plastic or soot contamination to skew the date would be obvious and easily seen.
That is the critique of ADDING contaminants to existing material. Original Material PLUS contaminant. Easily refuted.
However, that is not the model that the Benford/Marino Renaissance era patch theory postulates.
The real cause is REPLACING original material with contaminants. Contaminant REPLACING original material. Not so easily refuted.
In the Benford/Marino theory, original material is replaced, mass for mass, with newer material—with its much higher ratio of non-fissioned C14—in the C14 test sample. Observation of contamination is much harder because the contamination is camouflaged—masquerading as original material. When the test is done, it is performed on a mixture of materials that would have dated at approximately 1st Century and also 16th Century, and the results were erroneous 13-14th Century dates... a combination of the 1st Century dates of the older material and the 16th century dates of the newer material.
If you test what you think is 100% original material, and in reality 40-60% of it was replaced with newer material using a skillful art that replaces the missing original material with more modern material, you DON'T see the contaminating material because it looks exactly like the original.
When you replace the existing material with a more modern contaminant, the amount to needed to skew the date is far less. In fact, the amount then is around 50%... if 50% of the material is 16th Century, and 50% is 1st Century, then the ratios of much higher C14 in the newer material overwhelms the much smaller amount of C14 in the older material... The math works out to 1350 +/- 50 years.
Use some logic, Soliton.
Look how close the data are. Take a homogenous, pure sample that weighs 100 gms that is 1st Century. Test it. The reported date is 1st Century, give or take the degree of confidence. Now add 200 gms (200%, twice the amount of original material) of a modern contaminant, and do the test to the 300 gms of combined sample and contaminant. The percentage is 33.33% original material to 66.66% contaminant. The test reports a date of 1400AD give or take the degree of confidence. Wow. What a change. Its really close to what Shafersman's critique (and mine, I might add, and which I have told you numerous times already) of the contamination theories.
Now, let's cut away 66% of the cloth, leaving only 34 gms, and replace it with 66 gms brand new cloth and skillfully weave them together so that it is not obvious. We have left 34% original and added 66% new—it's not that different from adding contaminants to get the 33:66 ratio of before. Repeat the test. Wow. We get a reported date of 1400AD. Now cut out only 34% of the original, leaving 66 gms of older material, and replace that 34% with a patch of 34 gms new material. New ratio is 66:34 old:new. Repeat test... Oh, Wow, we get a date of 1200AD!
What is between those dates? The reported dates from the 1988 C14 tests.
Half of the 1988 sample is still available (the Riggi sample). If this invisible patch theory is to be tested, why not test this piece to see if it is original or new? This is typical of the shroud's history. People create pseudo-scientific explainations over and over until one sticks. The Riggi sample was examined after the c-14 tests. A "bioplastic film" was allegedly found, but there was NO mention of cotton or reweaving. The Vatican, seeing the risk of having this sample in the public domain scarfed it up and hid it away. The proauthentity guys tried everything and nothing stuck. They cried fraud and contamination. B&M, two of the greatest quacks out there, came up with the invisible patch theory. Gonella and Rogers colluded to make it so. There is no actual evidence for an invisible patch at the C-14 site. Skeptics are not allowed near the samples. The Riggi sample answers everything. Why not just release it for testing to non- STURP scientists?