"What kind of experiment?"
"Well, sort of like in QM, when you take an ensemble of identical, identically prepared systems. What you'd need to do is clone a bunch of people, and set up each of their clones in identical situations in identical environments. Then observe them and see if, and how, they differ."
"So you want to know if this is theoretically possible?"
"Now let's just examine your requirements here, starting with 'identical environments'. If you want any kind of outdoors in your environments, they'd have to be at the same latitude, and longitude, for that matter, so they'd have to be on different planets. They'd have to have the same weather, though, so they'd have to be on planets that had exactly the same effects on them--same sun, same moons, same other planets in systems. And, hell, you'd probably want them to have the same sky, too, so they'd have to have identical arrangements of stars around them. Though you could argue that would have no effect.
"So it'd be easier to keep them indoors all the time. So then you'd just have to prepare a bunch of identical internal environments. It might just be theoretically possible to keep them all the same temperature, say, in spite of wild variance outdoors, so they wouldn't have to be at the same latitude. Lighting could be done all artificially as well. Of course, you'd have to find some way of making sure that any failures of equipment would happen at the same time, or at least have the same effects. Again, in theory, it might be possible.
"'Identical situation' might be possible too, if by that you mean the arrangement of your various identical sets of people.
"But I doubt that by cloning you could get identical people. Even starting with the same batch of cells, there would be inevitable errors in redivision, which would not be very deterministic. They'd have some differences, subtle perhaps, but enough to make them non- identical, and make any evidence of lack of determinism suspect."
"So you don't think that, in theory, it's possible?"
"Why don't you just stick to separating twins at birth?"
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The Den of Ubiquity/ Aaron V. Humphrey / firstname.lastname@example.org