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Does anyone know the name of this book (might be a series)?

  • Planets are colonized by people having copies of themselves beamed to the planet. A person walks into a booth on earth for a few minutes and then goes about their life. On the other planet a copy walks out with all the memories of the original.

  • The story line was about how the lives evolve differently and the same limited number of people keep bumping into "themselves." I think I read it in the 70's but think it is older.

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Possibly the 'Cuckoo' series Farthest Star (1975) and Wall Around A Star (1983). People are 'beamed' to first, a starship approaching the mysterious object Cuckoo, and later to a station orbiting Cuckoo. The original people, as you described, step out of the booth and go about their business.

From the wikipedia article linked above:

The series explores several themes. The most used is the notion of an interstellar teleporter that leaves the original being behind and sends only a duplicate. When a person is duplicated, the original can just pass out of the machine without a second thought. However the duplicate arrives at the destination with the same state of mind as the original, and thus is shocked to realize that he or she is now stranded far from home. Another is the fact that the copies can be 'edited' at destination.

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