The biggest reason it's come back to light is because of the Vatican, and the Pope's mention of it in L'Osservatore Romano, the Vatican newspaper. Otherwise it is ridiculous and greatly immature of newspapers to suggest there is 'new evidence', there isn't. Il Mistero della Sindone is largely recycled sindonology studies from 1978 as part of the Shroud of Turin Research Project "STURP", apart from the fact that these new experiments didn't attempt to date it.
There are still a number of problems the experiment fails to address. Namely, the historicity of its cloth. Whilst sindonologists claim herringbone weaving existed prior to the alleged Jesus, there is no hard historical evidence for it until 1,300 CE. It also fails to analyze the 'blood stains' which were found by Walter McCrone to be vermilion tempera and red ochre paint. A later examination by STURP claimed it to be blood, however the report was severely lacking any analytical detail and the two researchers were not biologists, chemists, or pigment experts. It also fails to analyze the lack of cloth distortion that you would expect from wraparound. Further problems with the historicity of the blood stains is that they just don't fit in with Jewish burial.
One more suitable hypothesis is that the cloth was perhaps created by Leonardo da Vinci, arts consultant Lillian Schwartz of the School of Visual Arts made a computer generated comparison of the Shroud of Turin face with the reconstructed face of Leonardo da Vinci, and they matched. It would also explain the complex paint mixture on the shroud. Luigi Garlaschelli made a fake shroud in which he wrapped a cloth around his face, covered it in clear pigment, then baked it in an oven - it gave the cloth the same appearance. One possible method for the 'original'.
Furthermore, even if it does turn out to be real — highly unlikely — it does not prove it was of the exact same time frame. And regardless, it doesn't prove it was Jesus just because of the alleged crucifixion — which it does not conclusively prove. The fact is, crucifixion was a common execution by both the Romans and the Carthaginians over nearly 900 years. And even by the very unlikely off-chance it proves it was Jesus (Not sure how scientists would go about this...) then it still doesn't prove any form of divinity.
I would love for conclusive evidence of the Shroud of Turin to date back to this time period, I like to have my beliefs (or lack of) challenged. Unfortunately the recent 'new' studies just aren't conclusive enough.
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But the video doesn't disprove it. It largely revolves around the studies conducted by John P. Jackson, whose methods have been largely criticized, even amongst sindonologists of STURP. His suggested methods of the image being formed by radiation contradict the laws of physics. Furthermore his optics study that states it 'could not be a copy' is widely critisized again, not just for lacking in standard scientific methedology (that is, empiric testing that can be falsified and fails to follow occam's razor), but for the fact it's wrong, almost to the point that it's laughable. Emanuela Marinelli who also believes it to be that of Jesus, also criticized Jackson's study, and found in his own that their is some level of superimpostion of imagery, and that the image is not compatible with having been wrapped around a person. I suggest you actually read the studies which you will find on Academia.edu, JSTOR, and library of digital and scientific imagery, rather than supplying YouTube links with 'studies' based almost entirely on conjecture. Even the Vatican for all its praise of it, wont claim authenticity of it.