It once led to their romance; years later, it still dominates their thoughts and fills their conversations.
It brought Rebecca, an Orthodox Jew, to the Catholic Church; it led John to suspend himself from a two-metre-tall cross to study how blood might have stained the cloth.
Together, the two have committed to memory every crease, scorch mark and unexplained stain in their years-long pursuit of the mystery: is the Shroud of Turin, which allegedly bears the image of a crucifixion victim, the burial cloth of Jesus? In 1988, science seemed to put that question to rest.
Radiocarbon dating by three laboratories showed that the shroud originated in the Middle Ages, leaving the "shroud crowd" reeling. Shroud sceptics responded: "We told you so." The Catholic Church admitted that it could not be authentic.
But John Jackson, one of the shroud's most prominent researchers, was among those who insisted that the results made no sense. Too much else about the shroud, they said, including characteristics of the cloth and details in the image, suggested that it was much older.
Twenty years later, Dr Jackson, 62, is getting his chance to challenge the radiocarbon dating. Oxford University, which took part in the original radiocarbon testing, has agreed to work with him in reconsidering the age of the shroud.
If the challenge is successful, Dr Jackson hopes to be allowed to re-examine the shroud, which is owned by the Vatican and stored in a protective chamber in Turin, Italy.
Dr Jackson, a physicist who teaches at the University of Colorado, hypothesises that contamination of the cloth by elevated levels of carbon monoxide skewed the 1988 carbon-14 dating by 1300 years. "It's the radiocarbon date that, to our minds, is like a square peg in a round hole."
On that point, Christopher Ramsey, head of the Oxford Radiocarbon Accelerator Unit, seems to agree. "There is a lot of other evidence that suggests to many that the shroud is older than the radiocarbon dates allow, and so further research is certainly needed," he said.
Steven Schafersman, a geologist who maintains a sceptical website about the shroud, dismisses the effort as one that's bound to fail.
"He's had other ideas, but they've all been shot down, and this one will be shot down too," he said of Dr Jackson.
But others are challenging the radiocarbon date. At a conference sponsored by the Shroud Science Group at Ohio State University last weekend, the Los Alamos National Laboratory presented findings that the 1988 test results were flawed because the samples tested came from a portion of cloth that may have been added to the shroud during medieval repairs.
The shroud's historical record dates back to 1349, when a French knight wrote to the Pope of his possession of a cloth he described as the burial shroud of Christ. In 1978, a team of scientists led by Dr Jackson conducted a series of tests, including X-rays and chemical analyses. They concluded that the shroud was not painted, dyed or stained and that the bloodstains were real. But those findings did little to quell the controversy.
Many believe that Jesus imprinted his image on his burial cloth during his resurrection, and others think that the shroud is the authentic burial cloth but that the image was formed by natural processes. Sceptics maintain that the shroud is a forgery created by a medieval artist seeking to display it to relic-hungry pilgrims.
The debate is often bitter. In this world, Dr Jackson, a devout Catholic and former military scientist who has been transfixed by the shroud since he first saw its image when he was 13, has long been a central figure.
His faith isn't incompatible with his scientific training, he said.
"How I think about the shroud comes from the shroud. It's not, 'Gee, I'm a Christian, so I'll force it to be what I want it to be.' That's not scientific logic."
His wife, Rebecca Jackson, now 60, was 34 when she impulsively decided to enlist in the army. She converted to Christianity, a religion she said began to appeal to her as a teenager.
In 1990, she was watching a documentary on the shroud. She tracked down Dr Jackson and their shared interest in the shroud led to a relationship and her religious conversion followed.
Together, they give speeches worldwide and run the Turin Shroud Centre of Colorado, where they conduct research funded mostly by donations.
Dr Jackson has conducted research on the shroud's creases, image formation and how blood flows from a crucified body, which he studied by suspending his own body from a cross.
Keith Propp, 55, has worked with Dr Jackson for 23 years.
"It's like we're on an archaeological expedition that's not finished. I'm not sure we'll ever be truly finished," he said. "A lot of the pleasure is in the journey itself."
Shrouded in controversy and mystery — the arguments on both sides
■ A 1978 research team found the shroud was not painted, stained or dyed and concluded the bloodstains were real.
■ The cloth appears to be an authentic burial cloth that conforms to first-century Jewish customs.
■ Crease marks suggest it may be the same shroud exhibited in Constantinople in the early 1200s.
■ A Hungarian manuscript written in the 1190s contains illustrations of a shroud similar to the Turin shroud, including distinct burn holes.
■ The man in the image has crucifixion wounds on the wrists, which is historically accurate.
■ Radiocarbon dating by three separate labs placed the creation of the shroud between 1260 and 1390.
■ A chain of custody dates the shroud to the 1300s in France, a time frame matching the radiocarbon dating.
■ Relic viewing was a lucrative business in the Middle Ages, and pilgrims would have paid to view Christ's "burial cloth".
■ Medieval artists could have created the shroud by painting a model with red ochre and wrapping him in linen.
■ Particles of paint found on the shroud suggest paint was used to form the image.
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