According to the video, the carbon dating took was invalided.
Another argument against the results of the radiocarbon tests was made in a study by Anna Arnoldi of the University of Milan and Raymond Rogers, retired Fellow of the University of California Los Alamos National Laboratory. By ultraviolet photography and spectral analysis they determined that the area of the shroud chosen for the test samples differs chemically from the rest of the cloth. They cite the presence of Madder root dye and aluminium oxide mordant (a dye-fixing agent) specifically in that corner of the shroud and conclude that this part of the cloth was mended at some point in its history. Plainly, repairs would have utilized materials produced at or slightly before the time of repair, carrying a higher concentration of carbon than the original artefact.
A 2000 study by Joseph Marino and Sue Benford, based on x-ray analysis of the sample sites, shows a probable seam from a repair attempt running diagonally through the area from which the sample was taken. These researchers conclude that the samples tested by the three labs were more or less contaminated by this repair attempt. They further note that the results of the three labs show an angular skewing corresponding to the diagonal seam: the first sample in Arizona dated to 1238, the second to 1430, with the Oxford and Swiss results falling in between. They add that the variance of the C-14 results of the three labs falls outside the bounds of the Pearson’s chi-square test, so that some additional explanation should be sought for the discrepancy.
Microchemical tests also find traces of vanillin in the same area, unlike the rest of the cloth. Vanillin is produced by the thermal decomposition of lignin, a complex polymer and constituent of flax. This chemical is routinely found in medieval materials but not in older cloths, as it diminishes with time. The wrappings of the Dead Sea scrolls, for instance, do not test positive for vanillin.
Raymond Rogers’ January 20, 2005 paper in the peer-reviewed scientific journal Thermochimica Acta provides apparently conclusive chemical evidence that the sample cut from the Shroud in 1988 was not valid. Also in the paper, his determination of the kinetics of vanillin loss suggests the shroud is between 1,300 and 3,000 years old.
This aspect of the controversy can likely only be settled by more radiocarbon tests, which, as noted, the Holy See does not presently allow, citing sacrilegious damage to the relic. In his 2005 paper, Rogers suggests that elemental carbon in pieces of charred material removed during the restoration in 2002 could be used to date the shroud if cleansed using concentrated nitric acid.