4 ms·

Why doesn't that apply to photons and electrons, then? At what scale do things stop interacting with the other worlds and stay in their own world only? This is

Why doesn't that apply to photons and electrons, then? At what scale do things stop interacting with the other worlds and stay in their own world only? This is exactly the measurement problem, essentially identical between Copenhagen and MWI.

DavidSJ 6y ago
It does apply to photons and electrons. As I understand it, it becomes ever more difficult to maintain a coherent quantum state among larger and larger collections of particles (this is why making large quantum computers is difficult), so for most practical purposes large aggregates of particles behave like a single "world". But there is no sharp dividing line, and the same math applies at all scales. Unfortunately, this is where the imperfect mapping to which I referred above — between the math and our intuition — becomes misleading, and why I don't like the term "world" to begin with.
- simiones 6y ago
  MWI actually postulates that coherence of the system is always preserved, even up to the level of the entire universe. It's only locally that decoherence seeps in, at some scales. But still, the problem I was questioning was different: you are saying "there is one of us in each world". In fact, that is not what QM predicts: in QM, there is only one of us in the entire system described by the wave function, with different amplitudes in different states. A system with 1 electron with some amplitude < 1 in state A and some amplitude < 1 in state B is not the same as a system with 2 electrons, one with amplitude 1 in state A and another with amplitude 1 in state B. So, if we took a detector that could measure state A or state B, we should expect that it detects state A with some amplitude and, simultaneously, state B with some other amplitude. Instead, MWI postulates that there are 2 detectors, one which measures state A with amplitude 1, and the other state B with amplitude 1 (in fact, it postulates an infinity of detectors, out of which some number measure state A and some measure state B, such that the Born rule predictions by "counting" detectors). This is the part that remains unexplained.
  - DavidSJ 6y ago
    "One of us in each world" is shorthand for "one of us in the entire system described by the wave function, with different amplitudes in different states". There is only 1 detector, and it, along with the detected particle, is in a superposition of states. Again, this is where the language of "worlds" becomes misleading, and why I don't like it.
im3w1l 6y ago
Different worlds interact by interference. To interfere they must be in some sense "adjacent" so that they can both evolve into the exact same world - but with opposite phase. If you have a huge object like a human it's very hard to get every single atom to line up with those of the other world.
GoblinSlayer 6y ago
It applies to photons and electrons: when superposition consists of valid solutions of the schrodinger equation, these components evolve independently as if the other components didn't exist. It's possible to measure them in a rotated basis because a single elementary particle doesn't have inner structure. If you want to analyze the structure, you will have difficulty measuring in a rotated basis, this starts with two particles.

DavidSJ 6y ago

It does apply to photons and electrons. As I understand it, it becomes ever more difficult to maintain a coherent quantum state among larger and larger collections of particles (this is why making large quantum computers is difficult), so for most practical purposes large aggregates of particles behave like a single "world". But there is no sharp dividing line, and the same math applies at all scales. Unfortunately, this is where the imperfect mapping to which I referred above — between the math and our intuition — becomes misleading, and why I don't like the term "world" to begin with.

simiones 6y ago
MWI actually postulates that coherence of the system is always preserved, even up to the level of the entire universe. It's only locally that decoherence seeps in, at some scales. But still, the problem I was questioning was different: you are saying "there is one of us in each world". In fact, that is not what QM predicts: in QM, there is only one of us in the entire system described by the wave function, with different amplitudes in different states. A system with 1 electron with some amplitude < 1 in state A and some amplitude < 1 in state B is not the same as a system with 2 electrons, one with amplitude 1 in state A and another with amplitude 1 in state B. So, if we took a detector that could measure state A or state B, we should expect that it detects state A with some amplitude and, simultaneously, state B with some other amplitude. Instead, MWI postulates that there are 2 detectors, one which measures state A with amplitude 1, and the other state B with amplitude 1 (in fact, it postulates an infinity of detectors, out of which some number measure state A and some measure state B, such that the Born rule predictions by "counting" detectors). This is the part that remains unexplained.
- DavidSJ 6y ago
  "One of us in each world" is shorthand for "one of us in the entire system described by the wave function, with different amplitudes in different states". There is only 1 detector, and it, along with the detected particle, is in a superposition of states. Again, this is where the language of "worlds" becomes misleading, and why I don't like it.

im3w1l 6y ago

Different worlds interact by interference. To interfere they must be in some sense "adjacent" so that they can both evolve into the exact same world - but with opposite phase. If you have a huge object like a human it's very hard to get every single atom to line up with those of the other world.

GoblinSlayer 6y ago

It applies to photons and electrons: when superposition consists of valid solutions of the schrodinger equation, these components evolve independently as if the other components didn't exist. It's possible to measure them in a rotated basis because a single elementary particle doesn't have inner structure. If you want to analyze the structure, you will have difficulty measuring in a rotated basis, this starts with two particles.