And if the MWI is true, those boundary conditions are already going to include a huge number of terms in a vast superposition, based on what happened in the entire past light cone up to that point and all of the possible quantum branch points that occurred. So there doesn't need to be any "world splitting" in the lab itself to have multiple worlds according to the MWI; multiple worlds are already included in the lab's boundary conditions. For example, if you are going to claim that there is a world in which @DrChinese is the US president, that doesn't mean we had to do something in the lab to switch timelines to that one.to determine what happens in the lab we only need the boundary conditions defined on the lab.
But the question is, which multiple worlds are already included in the lab's boundary conditions? Is there a world included in those boundary conditions in which @DrChinese is the US president? Supposing that there is some world in which @DrChinese is the US president, how many other things are different in that world as compared to this one? Is there even a lab in the same place at the same time? And if there isn't, it makes no sense to restrict attention to "the boundary conditions defined on the lab" but also talk about the possibility of @DrChinese being president, because those two things are mutually exclusive: if we are in a world in which a lab at the same place at the same time exists, then @DrChinese is not US president in that world, because none of the worlds in which @DrChinese is president have a lab at that time and place.
And in fact, even that doesn't fully unpack the issue, because to even have a world in which @DrChinese is the US president, it has to be that there is a US with a president, and a person who is properly identified as @DrChinese, and that person has to have gone through all the process of getting to the point where he is elected US president. And you can't tell whether such a world is even possible by just looking at the boundary conditions of your lab. And we can go further: there has to be a planet Earth that had humans evolve on it, with a history the same as our Earth; which means there has to be a solar system the same as ours, of the same age, in the same galaxy, etc., etc.
The point I'm making is that all this blithe talk about "multiple worlds" fails to pay attention to specifically how such multiple worlds get created, if the MWI is true. They don't get created by magic. They don't get created just because we humans can imagine them. They get created by having genuine quantum mechanical uncertainty, "Schrodinger's Cat" type uncertainty where single quantum branch points have macroscopic consequences, involved in particular key events in particular timelines. And the only point in the entire universe's development where we are pretty sure that actually happened was at the end of inflation, when the quantum fluctuations in the inflaton field got transferred to the Standard Model fields and the particular pattern of small-scale inhomgeneities was formed that were to eventually evolve into our present galaxies and stars and planets. Everything after that is classical evolution and need only have led to a single macroscopic world. And if other universes exist in MWI "worlds" that correspond to other possible patterns of small-scale inhomogeneities created at the end of inflation, they won't even have a solar system like ours, or a planet Earth like ours, or humans like us, or a US with a president--let alone have all that stuff be the same but still have just enough difference to have @DrChinese as the US president in 2019.