Monte Carlo method applied to the mechanical dating of the Turin Shroud

Alternative dating methods to radiocarbon have been recently developed to study the Turin Shroud (TS), the linen sheet that according to the tradition enveloped the dead body of Jesus Christ; among them, a mechanical one is based on the study of five mechanical parameters in reference to the breaking strength, the Young modulus and the loss factor. This method tests single TS linen fibers using a machine, built in for the purpose, capable to measure the stress-stain parameters during loading cycles. These parameters have been already shown to be dependent on the age of the linen under test, and a preliminary result has been obtained: the TS date is 400 A.D. ±400 years at 95% confidence level. A companion paper has combined this mechanical result with two chemical ones, coming from Raman and FT-IR spectra, and the combined result is 90 AD ±200 years at 95% confidence level, thus confirming the compatibility of the age of the TS with the period in which Jesus Crist lived in Palestine. As the evaluation of the uncertainty propagation is not simple in the case of the mechanical parameters, this paper tries to furnish a more reliable result applying the Monte Carlo method to the mechanical parameters directly measured. The obtained mechanical age of the TS of 279 A.D. ±216 years at 95% confidence level is compatible with the previous results, but with an uncertainty almost halved.