When Admiral Nelson lost his arm in battle in 1797, he gained a new faith in the afterlife: The admiral could feel the muscles in his missing limb move so convincingly that he was certain his arm had become a ghost.

Two centuries later, phantom limb syndrome remains one of the most mysterious medical conditions on record. Experienced by the majority of amputees, the sensations it brings are vivid and precise: a too-tight wedding ring, a dribble of scalding water, a stiff joint. Somehow—and there is still no consensus as to exactly how—amputation causes a rewiring of nerve pathways to the brain, generating feelings where there should be none.

For many people, these ghostly appendages are physically painful and emotionally upsetting—a constant reminder of traumas best forgotten. B...