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For each event you experience as a "collapse", you "branch" the wave function. You put a particle into a superposition between two eigenstates representing two

by mort96 4y ago

For each event you experience as a "collapse", you "branch" the wave function. You put a particle into a superposition between two eigenstates representing two positions, then you observe the particle, and as a result, you as the observer enter a superposition; you now have two eigenstates, one where you observed the particle being in the one location, and one where you observed the particle being in the other location. And since you and your measurement equipment and everything else macroscopic is highly entangled with the rest of the world, the whole world also enters the same superposition, one where the particle was in one place, and one where it was in the other. Repeat until one "branch" in the "tree" has observed the particle moving a meter.

Jensson 4y ago
But the particle moving a meter in this scenario isn't described by the Schrödinger equation or any other part of quantum mechanics. If you just measured the chance of it being there originally it would be 0% chance, it isn't there. The only thing moving the particle is the wave function collapse. I don't see how the theory can be both correct and ignore that the wavefunction collapse can move particles into states they weren't originally in. You would need new rules for the wave function in order for MWI to work, one that handles the collapses. But if you do that I wouldn't call the theory "just standard quantum mechanics without collapses".
- mort96 4y ago
  But you're influencing the particle between each step, right? Is my understanding correct that you put the particle in a superposition, observe it a little bit further along, then put it in another superposition, observe it further along again, etc until it has moved a meter? I don't see why you would expect there to be some probability to see the particle as having moved a whole meter after the first observation. Obviously you putting it in a superposition in between steps is an important factor. And each time you've first put it in a superposition and then observed it, you've created two branches of what we would classically call the universe. The only thing which really changes between an interpretation with collapse and an interpretation without collapse, is that in one without collapse (i.e MWI), the universal wave function splits into two "branches" which can't interact after the split. Sadly, I don't know much about the math though, so it's completely possible that I've missed some detail in your question and given a reply which doesn't address what you're getting at. If that's the case, I've probably reached my limit and you'd have to ask someone who has studied this way, way more than me.
  - Jensson 4y ago
    > the universal wave function splits into two "branches" which can't interact after the split. And how is that different from "wave function collapse"? How is that purer? To me that just looks like a wave function collapse with another name, and a whole slew of universes as extra garbage.
    - mort96 4y ago
      The difference is that it's something which already necessarily happens in quantum systems. Say you have two isolated particles A and B, and A is in a superposition between eigenstates 0 and 1. If those two particles interact, we say that they have formed a quantum system in a superposition between "A is in state 0 and B interacted with A in state 0" and "A is in state 1 and B interacted with state 1", right? MWI "simply" lets the same happen with observers. You have a particle in a superposition between states 0 and 1. You observe (i.e interact with) the particle, which puts the "you + particle" system in a superposition between "the particle was in state 0 and you observed the particle in state 0" and "the particle was in state 1 and you observed the particle in state 1". There is no wave function collapse mechanism, what we describe as "wave function collapse" is nothing more than the particles in the macro world becoming entangled with the particle we're testing.

by mort96 4y ago

Jensson 4y ago

But the particle moving a meter in this scenario isn't described by the Schrödinger equation or any other part of quantum mechanics. If you just measured the chance of it being there originally it would be 0% chance, it isn't there. The only thing moving the particle is the wave function collapse. I don't see how the theory can be both correct and ignore that the wavefunction collapse can move particles into states they weren't originally in. You would need new rules for the wave function in order for MWI to work, one that handles the collapses. But if you do that I wouldn't call the theory "just standard quantum mechanics without collapses".

mort96 4y ago
But you're influencing the particle between each step, right? Is my understanding correct that you put the particle in a superposition, observe it a little bit further along, then put it in another superposition, observe it further along again, etc until it has moved a meter? I don't see why you would expect there to be some probability to see the particle as having moved a whole meter after the first observation. Obviously you putting it in a superposition in between steps is an important factor. And each time you've first put it in a superposition and then observed it, you've created two branches of what we would classically call the universe. The only thing which really changes between an interpretation with collapse and an interpretation without collapse, is that in one without collapse (i.e MWI), the universal wave function splits into two "branches" which can't interact after the split. Sadly, I don't know much about the math though, so it's completely possible that I've missed some detail in your question and given a reply which doesn't address what you're getting at. If that's the case, I've probably reached my limit and you'd have to ask someone who has studied this way, way more than me.
- Jensson 4y ago
  > the universal wave function splits into two "branches" which can't interact after the split. And how is that different from "wave function collapse"? How is that purer? To me that just looks like a wave function collapse with another name, and a whole slew of universes as extra garbage.
  - mort96 4y ago
    The difference is that it's something which already necessarily happens in quantum systems. Say you have two isolated particles A and B, and A is in a superposition between eigenstates 0 and 1. If those two particles interact, we say that they have formed a quantum system in a superposition between "A is in state 0 and B interacted with A in state 0" and "A is in state 1 and B interacted with state 1", right? MWI "simply" lets the same happen with observers. You have a particle in a superposition between states 0 and 1. You observe (i.e interact with) the particle, which puts the "you + particle" system in a superposition between "the particle was in state 0 and you observed the particle in state 0" and "the particle was in state 1 and you observed the particle in state 1". There is no wave function collapse mechanism, what we describe as "wave function collapse" is nothing more than the particles in the macro world becoming entangled with the particle we're testing.