You know how at some point in the 50s the timeline split into our world and the FO world? What caused this? And was there another version of us and our heirs in the other timeline?

Its never been said. I dont think it was a dramatic difference. (I mean as Difference as in lsomeone not being born, or an attack or something like that)

Personaly I go with the transistor not being developed as the key defining point, at least as far as technology is concerned; but there isnt a specific key division point given.

As for whether there is another version of you... It would depend on how the changes effected your parents, and their parents ability to "Find" each other given the differences

I don't think there had to be a cause for the split. It's not an alternate timeline created from the perspective of "what would the world look like if we changed this and that from our own timeline", but from the one of "how did the people in the 1950s imagine the future would look like".

I'm actually quite interested in this. I'm also curious to know if things would be different in terms of the war and such if something less significant was changed to cause the timeline split. Perhaps everything could have evolved into what they are today and further on instead of the "stuck in the 50s" type technology but the events stayed the same (the war, bombs, fallout, etc).

Personally I am not a fan of the 50s architecture or it's supposed evolution into a more "advanced" state. I'd prefer an alternate reality where things were like now or what it will be like for us in 2077 (though it will always be stylized depending on what time period you live in). I would not be opposed to changing Fallout's history for my game to what I prefer though, perhaps by modding the hell out of it.

The "split" is somewhat hard to place, due to there being no real explanation for the fact that the 50s never really seemed to end and because science doesn't really work the same way in our world as it does in the Fallout world, IE: The affects of radiation on animals.

One major split that could be the cause of most of is that in the Fallout World, the Cold War didn't end. It continued on and on increasing the Government and Military's level of aggression and causing the general paranoia of the 50s era to continue, along with the "everything is peachy keen, nothing to worry about" feeling given off by 50s media, which leads to things like the Happy thumbs up that Vault boy gives while explaining what to do when the world is consumed in nuclear Holocaust.

The best i can tell the spilt happened when SCIENCE! won over regular science. Alot of stuff in fallout is 50's scifi because that weird scifi SCIENCE! actually worked. And the microchip was never developed.

I think that is probably close to the truth, when creating the world for Fallout I don't think the designers asked themselves "What would the world be like if [insert event here] went differently?" It's more like "What would the world look like if the future ended up how people in the 1950s might have envisioned it, and then got blown up by nuclear war?" That also explains why science even works differently, or should I say "Science!"?

Therefore, the split is not caused by a specific, definite event, things as a whole just worked out a bit differently from in real life.