Under Everett's interpretation I understand the key notion is that every quantum possibility is physically realized in its own universe, such that any one universe only contains any one physical realization stemming from the "same" parent measurement. I've also understood that it's popular to say that, under this interpretation, the physical world(s) branch out - creating a tree - based on every such possibility.
But, physically speaking, if we take this branching approach naively at face value - are we supposed to understand that from any given state where you have X possible outcomes, what is now 1 physically real world, turns into X physically real worlds (one for each possibility)?
I see this perpetuated all over the place - that X and Y possibilities exist in their own, physically distinct universes, and that this removes some problems in Copenhagen or simplifies some of them. But it's also very confusing, because if that is the case, how do we explain this cloning-the-universe-up-until-this-point into however many possibilities there were? Where does that energy come from? Not to mention - how is it possible to copy all the information of an entire universe in an instant (without violating a bunch of physical laws in the existing universe)?
So - is it really as simple as this answer says; "it is just mathematics"? So that when the many-worlds interpretation says that every possibility is physically realized, you'd think of it in the sense that is to some degree analogical to how you'd think of the electron physically realizing all its possible paths in the double-slit experiment?
Or does the interpretation claim that there are actually physically real and distinct worlds - universes - for each possible outcome? As in, there actually exists a space-time (even if it's inaccessible to us) that is identical to its twin space-time(s) with the only exception being the outcome of that particular measurement? If that is the case, how do proponents of the MWI resolve the problems I posed earlier about information-copying?