Why can you see the solution of the equation for the entire surface of the pond at once, but only for a single instant of time at any given moment?
Conversely, the Schrodinger equation gives an amplitude to the same particle/wave at many locations at time T. However, when you look for it at time T at all of those locations at once, you only find it in one of them. If you perform the experiment many times, you will find it at all of those locations some amount of the time. But then, if you try to use the Schrodinger equation to model movement before AND after interaction with the detector, you will not be able to find the particle at any position that doesn't match what the detector initially saw.
That is, say the Schrodinger equation predicts the particle has the same amplitude at locations X and Y. Then, after interacting with something at locations X and Y at time T1, it will have some amplitude at locations X1, X2, Y1, Y2 at time T2.
Now, if we try an experiment where the interaction at time T1 happens with a particle, and you have detectors at positions X1, X2, Y1, Y2, you will find it with equal probabilities at any of the 4 locations. However, if at X and Y there is a detector, and you detect the particle at X, it will never be found at positions Y1 or Y2. You have to update the Schrodinger equation after you find out that the particle is found at X, which is never how classical mechanics work.
I mean, I get that time is a little different in that you will eventually experience and remember all possible solutions as you stand there watching the system, because classical time is a linear chain of events. In the multi-world case, it's a branching chain, and your experience and memories of the different solutions are stuck in their own branches.
That does make worlds weird and different from the other dimensions, but we accepted time as being weird and different from space for a very long time.
> Now, if we try an experiment where the interaction at time T1 happens with a particle, and you have detectors at positions X1, X2, Y1, Y2, you will find it with equal probabilities at any of the 4 locations. However, if at X and Y there is a detector, and you detect the particle at X, it will never be found at positions Y1 or Y2. You have to update the Schrodinger equation after you find out that the particle is found at X, which is never how classical mechanics work.
This makes total sense if it's actually a wave and the particle is merely a solution for a particular world W. The detector didn't change anything about the wave. It just coupled you to the wave system earlier, so now your branch of the many-world tree can only see the subset of solutions that correspond with whatever you detected. The only thing that has changed, though, is your ability to see the other solutions. You branched earlier, so now each branch you exist in only sees a subset of the full solution.
That said, I am not a physicist. The many worlds explanation was just the first thing that actually made sense to me about quantum mechanics. It's so conceptually simple.
Now, the question is: what causes this discontinuity in the equations of motion? Why is interaction with a detector different than interaction with another particle? Many Worlds simply reframes this problem, but doesn't get rid of it. In MWI, you would say 'the particle moves in all universes according to the wave function, until it interacts with a detector, possibly interfering with versions of itself in other universes. Then, when it encounters the detector, the world line of the detector splits - in some universes it passes the detector, in others it doesn't. However, it no longer interacts with other versions of itself,so we must update the wave function inside the universe where it passed the detector'.
> Many Worlds simply reframes this problem, but doesn't get rid of it.
Maybe I'm misunderstanding. It's like asking "why is there a difference between me jumping in a swimming pool and someone else jumping in it? I don't get wet when someone else is swimming." The difference is... one of you is in the pool. It's not going to spontaneously make the other person wet.
In MWI the difference is that if it interacts with a particle, you're not entangled, the particle is. If it interacts with a detector then you're entangled. So, there is no difference except for what gets entangled.
What that means is the wave function can only appear to collapse when you entangle. If some particle entangles, it will collapse for that particle and branch into a new world, but you're not in that world; for you it's still a waveform.
Edited for clarity.
If the alternative universes are in different dimensional planes, it's pretty obvious why we couldn't observe them.
