It doesn't matter where the photons are. One can be in New Jersey, the other gone out for bagels in the Andromeda Galaxy. Once they are entangled,, distance is not a factor. Instantaneous, simultaneous, immediate.
The year is 1959 (ie, when the book was written), and an alien artifact has been found on the moon. No, it's not an alternate-history novel. The public doesn't know that the moon is reachable via matter transmitter. There are problems with the transmitter: The device doesn't move you; it duplicates you. For a short time, before differing experiences cause you to diverge, you and your duplicate are so similar (call it nineteen decimal places' similarity :) that you are telepathically linked. Then there are two of you. One goes home for supper; one remains on the moon.
The artifact? The artifact is *very* alien, incomprehensible. And people who enter it die. For practical purposes, it's a maze: If you do the right things at the right times, you can get through it. Mapping that maze, however, costs lives at both ends. The duplicates on the moon map out a bit more of the artifact before being killed -- and the telepathically linked originals on Earth are broken by the experience.
Edward Hawks, the developer of the matter transmitter, needs someone who can survive the experience. He turns to Al Barker -- an adventurer with a bit of a death wish -- and talks him into joining the project. Again and again Barker goes through the maze -- farther each time -- and dies.