4 ms·

Ok, how does one derive the Born rule from that idea?

ben_w 6y ago
Could you ELI5 why the Born rule is incompatible with MWI? (It being a problem with MWI is new to me, I am absolutely a physics amateur).
- millstone 6y ago
  Say there's a quantum bowl with two identical red balls, and one blue ball. You take a ball with your eyes closed. Probably your ball is red, maybe it's blue. You open your eyes, see a color - what happened! Here's three choices, none of them good: 1. Local Hidden Variables: When you open your eyes, you see which color your ball had all along! This is so obvious, but it's wrong for tricky reasons (Bell's Theorem) which I can't fit into the analogy; basically the ball cannot have "had a color all along." 2. Copenhagen: When you open your eyes, the ball just decides what color it is. The other balls will mysteriously agree, so there's not two blue or three red or whatever. How did they do that? Is that a real physical change, or just learning something new? (This is wavefunction collapse and it's very uncomfortable for obvious reasons.) 3. MWI: When you open your eyes, one version of you sees a red ball, and one version of you sees blue. Ok, but if there's red you and blue you, how can the red ball be "more probable?" Are there two separate "red ball" yous? Or maybe the red ball you is "more real?" (This is the relationship between the measure of the wavefunction and experimental probability, aka Born's Rule; MWI struggles to explain it, Copenhagen just postulates it).
  - jiggawatts 6y ago
    > Are there two separate "red ball" yous? You answered your own question! Yes. There are multiple observers, they're cloned along with everything else. All the "mystery" disappears as soon as you accept that. It's like heliocentrism. Everything just "clicks" once you adjust you perspective.
    - millstone 6y ago
      It ought not to click, because it's a deep objection. In the ball example, the wavefunction is a sum of two components: there are two possible measurement outcomes. How do you get three worlds from two states? Say you have an electron which is either up or down, a 2/3 percent chance to be up. The wavefunction looks like `2/3 * up + 1/3 * down`. In the MWI picture, when you measure the electron, you split into two worlds: how do you get 2/3 probability of "up" from two worlds? You can say you split into three worlds, two of them identical. But that is not found in the Schrödinger equation (so now you have new postulates, which MWI hoped to avoid), and what if the probability were 1/pi, how many worlds would that be?
      - jsmith45 6y ago
        Your problem is in assuming that there is a finite number of universes created. Instead Think in terms of an infinite number of universes created, of which 2/3 of them are red, and 1/3 of them are blue. (E.g. Imagine all the universes created map to the range 0 to 1, and the first 2/3's come up red, and the last blue (or reverse that, or shuffle it up). The mapping onto 0 to 1 is merely for visualization purposes, and is thus arbitrary.)
        millstone 6y ago
        The hope and appeal of MWI is that the Schrödinger equation is sufficient. What you describe is way beyond what may be found in it. "Many worlds" may arise naturally from the Schrödinger equation in this way: if you measure a system, the components of its wavefunction decohere, so that they no longer interfere. These components may be intuitively understood as "worlds." We find ourselves in the world corresponding to the larger-measure component more often. But why? If your answer is "because more universes were created for larger measures," that is not found in the Schrödinger equation; it requires additional axioms, which is precisely what MWI hopes to avoid.
    - fallingfrog 6y ago
      I see people asking, “but how do you get 3 realities from 2 possibilities?” This is a misunderstanding. For simplicity’s sake, mwi people say that the universe “splits” into one child universe for each possibility- but that’s not what mwi actually says, just the pop science simplified layman version. In actuality just as the quantum wave function is a continuous, analog wave there is a continuous analog sea of possible universes, and some have greater measure than others. And some are more correlated than others. The discorrelated ones appear to be separate from each other. But they’re all part of the same multiverse. Think about it this way: we have no trouble conceiving of the universe having multiple possible futures, but only one past. That is not the case however. We also have multiple possible pasts, and in fact they’re not just possibilities but are real. Each future universe with this one as a past is real. Each past universe with this one as a future is equally real (that’s the mwi view of Schrödinger’s cat). Because of the arrow of entropy there will be more of the former than the latter. Hope that helps..
  - klyrs 6y ago
    > Ok, but if there's red you and blue you, how can the red ball be "more probable?" My understanding is that there are two "red yous" for every "blue you"

Could you ELI5 why the Born rule is incompatible with MWI? (It being a problem with MWI is new to me, I am absolutely a physics amateur).

millstone 6y ago
Say there's a quantum bowl with two identical red balls, and one blue ball. You take a ball with your eyes closed. Probably your ball is red, maybe it's blue. You open your eyes, see a color - what happened! Here's three choices, none of them good: 1. Local Hidden Variables: When you open your eyes, you see which color your ball had all along! This is so obvious, but it's wrong for tricky reasons (Bell's Theorem) which I can't fit into the analogy; basically the ball cannot have "had a color all along." 2. Copenhagen: When you open your eyes, the ball just decides what color it is. The other balls will mysteriously agree, so there's not two blue or three red or whatever. How did they do that? Is that a real physical change, or just learning something new? (This is wavefunction collapse and it's very uncomfortable for obvious reasons.) 3. MWI: When you open your eyes, one version of you sees a red ball, and one version of you sees blue. Ok, but if there's red you and blue you, how can the red ball be "more probable?" Are there two separate "red ball" yous? Or maybe the red ball you is "more real?" (This is the relationship between the measure of the wavefunction and experimental probability, aka Born's Rule; MWI struggles to explain it, Copenhagen just postulates it).
- jiggawatts 6y ago
  > Are there two separate "red ball" yous? You answered your own question! Yes. There are multiple observers, they're cloned along with everything else. All the "mystery" disappears as soon as you accept that. It's like heliocentrism. Everything just "clicks" once you adjust you perspective.
  - millstone 6y ago
    It ought not to click, because it's a deep objection. In the ball example, the wavefunction is a sum of two components: there are two possible measurement outcomes. How do you get three worlds from two states? Say you have an electron which is either up or down, a 2/3 percent chance to be up. The wavefunction looks like `2/3 * up + 1/3 * down`. In the MWI picture, when you measure the electron, you split into two worlds: how do you get 2/3 probability of "up" from two worlds? You can say you split into three worlds, two of them identical. But that is not found in the Schrödinger equation (so now you have new postulates, which MWI hoped to avoid), and what if the probability were 1/pi, how many worlds would that be?
    - jsmith45 6y ago
      Your problem is in assuming that there is a finite number of universes created. Instead Think in terms of an infinite number of universes created, of which 2/3 of them are red, and 1/3 of them are blue. (E.g. Imagine all the universes created map to the range 0 to 1, and the first 2/3's come up red, and the last blue (or reverse that, or shuffle it up). The mapping onto 0 to 1 is merely for visualization purposes, and is thus arbitrary.)
      - millstone 6y ago
        The hope and appeal of MWI is that the Schrödinger equation is sufficient. What you describe is way beyond what may be found in it. "Many worlds" may arise naturally from the Schrödinger equation in this way: if you measure a system, the components of its wavefunction decohere, so that they no longer interfere. These components may be intuitively understood as "worlds." We find ourselves in the world corresponding to the larger-measure component more often. But why? If your answer is "because more universes were created for larger measures," that is not found in the Schrödinger equation; it requires additional axioms, which is precisely what MWI hopes to avoid.
  - fallingfrog 6y ago
    I see people asking, “but how do you get 3 realities from 2 possibilities?” This is a misunderstanding. For simplicity’s sake, mwi people say that the universe “splits” into one child universe for each possibility- but that’s not what mwi actually says, just the pop science simplified layman version. In actuality just as the quantum wave function is a continuous, analog wave there is a continuous analog sea of possible universes, and some have greater measure than others. And some are more correlated than others. The discorrelated ones appear to be separate from each other. But they’re all part of the same multiverse. Think about it this way: we have no trouble conceiving of the universe having multiple possible futures, but only one past. That is not the case however. We also have multiple possible pasts, and in fact they’re not just possibilities but are real. Each future universe with this one as a past is real. Each past universe with this one as a future is equally real (that’s the mwi view of Schrödinger’s cat). Because of the arrow of entropy there will be more of the former than the latter. Hope that helps..
- klyrs 6y ago
  > Ok, but if there's red you and blue you, how can the red ball be "more probable?" My understanding is that there are two "red yous" for every "blue you"