It's not the same thing, because classical mechanics explicitly models the time - it can predict that at time T the system is in one state, and indeed when I look at a the system at time T, I see it in a single state.

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.

Isn't the problem that you're only looking at the system in a single world W, when viewing all solutions requires viewing it in multiple worlds?

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.

> 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.

This explanation only works if either the detector is not itself made of particles, or if there is a detector wave that you could become entangled with by observing.

But the first one can essentially be discarded, and the second one is not experimentally confirmed. The equations happen the way I described whether you observe the detector or not. The detector could be hundreds of light years away from you, but you would still be able to predict what happened after the particle hit it with classical mechanics. So one particle's interaction with a detector instantly branches at least its entire future light-cone, but two particles interacting doesn't have the same effect. So at what scale does this happen? Or in what conditions?