So Hey guys!!This drama is getting more and more interesting and hence I'm creating this discussion so that we all can share our theories about the plot here.
Here I'll be referring to the world in which seo Kyung dies as "World A" and the other as "World B" to avoid confusion.
So after 5 episodes in, I'm slowly getting an Idea about who would be the killer. And my choice is the Seo kyung's stepbrother in world B. Because all this started with the murder of their father which could have also been committed by him in world B. Also while he and do won got into a fight at care center, he said that "I killed them" which seems to point at his other version.
Plus we see that in EP 5 in train, the killer limps which also matches with the stepbrother.
And as to why the murders never happened in world A I'm not yet sure but I think it has something to do with do won of World A and also because the stepbrother became mentally disabled.