The way I see it is this. This is speculation based off of quantum theory.
When the atomic bomb exploded. The world split off into 2 paradoxical time lines. But, they are indeed connected. Hence why they are getting flashes of memory going back to the island. Now remember, we've seen them time hoping back and forth throughout lost. And we've even seen them go back in time.
Faraday never became a scientist, therefore he continued his musical career. But he can remember his scientific studies because the lives are intertwined with those on the island. Just how jack had to ask about his appendix scar, almost like how Desmond now can consciously control both time lines.
There are others like Daniel's mom who know what is going on. But, they are not ordinary people. If you remember correctly, Eloise was also intruding on Desmond's time hoping previously when he wanted to buy a ring for Penny.
I'm sorry I'm ranting I'll stop for now and give this some time. Maybe I can be more coherent later.
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