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A sizeable human population was separated from the rest of the Earth people for a long time, long enough for allopatric speciation to happen. They are no longer Homo sapiens and now have ZERO reproductive compatibility with the ordinary Earth human. At the separation time, this "away team" had access to all the knowledge and technology XXI century humanity have. Environment and population size was not an issue to their survival.

It is still undecided if this "other humanity" was separated in another dimension, planet or by another means, but there were absolutely no transmission of genetic material between Earth and the away team from the time of separation to the moment of this "first contact" in our story.

How long should these two human populations be separated for this speciation to happen?

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From this slide from a presentation about allopatric speciation, scientists performed a study involving 40 pairs of allopatric fishes and estimated it would take somewhere between 0.8 and 2.4 million years. Note that this is a very limited study and may not apply to Homo sapien. However, I would imagine humans surviving in an optimal or near-optimal environment, on both sides of the divide, to diverge slowly. If the environments differ greatly, speciation will likely occur faster. Half a million years seems like a good starting point.

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Well the Aborigines of Australia were separated from the rest by about 75,000 years with no issues what so ever.

So there are two things that can affect the time it takes to make major changes in the genome. The first is extremely different environment that needs to be adapted to.

The other would be gene manipulation. We are currently closing in on manipulating our genes to help us along. Chances are to really speed up the separation would require playing with the genes to push us in different directions. Using Frostfyre's numbers of 1-2 million years for normal I would guess with direct manipulation you are still talking 100,000-250,000 years. since we are talking about each whole species being unable to interbreed.

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Considering the timelines of the other answers, I might suggest that maybe one group of humans took the robot approach and uploaded their consciousnesses into metal bodies. That would certainly make interbreeding difficult, and on a much shorter timescale. Since you're looking at hundreds of thousands of years for the organic approach, and we're starting out with modern tech, I'd honestly think this technology would be invented by both sides long before important genetic differences developed, though ethical concerns may have stopped one side from making such a big evolutionary leap.

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