5 ms·

>If the electron is both spin up and spin down every time we run this experiment, how come we observe the spin up version more often than the spin down version?

>If the electron is both spin up and spin down every time we run this experiment, how come we observe the spin up version more often than the spin down version? Because after a series of measurements your state asymptotically approaches |we observe the spin up version more often than the spin down version>, which is in fact a mere tautology: if it didn't, you wouldn't conclude it. You don't even need any interpretation for this, you can just calculate it, and asymptotic certainty is trivial to interpret. In this sense MWI is a shut up and calculate interpretation, the only difficulty is to formulate your question in a computable form. If your question has no computable form, it probably doesn't match reality.

tsimionescu 2y ago
No, why would it? If we never collapse the wave function, we'll still have states where we only saw spin up, states where we only saw spin down, states where we saw more spin up, and states where we saw more spin down. And all of these are understood to be real in the MWI, so some observers will be guaranteed to exist that calculate that some state has a high amplitude, but they will never experience it, no matter how many billions of times they run the same experiment.
- GoblinSlayer 2y ago
  Marginal outcomes are possible in any interpretation. It's not absolute certainty, only exponential asymptotic certainty.
  - tsimionescu 2y ago
    These outcomes are marginal in many interpretations, but they are certain to happen in MWI (since all possible results of the wave function actually happen). And the point I was trying to make is that, if you don't postulate the Born rule in addition to the Schrodinger equation, then you don't even have a way to say that this "happens for fewer observers". But then, if you do have to postulate the Born rule, then the MWI has no more explanatory power than any other interpretation, it's not just "following the math", and it still needs a definition for what consitutes a measurement for purposes of applying the Born rule.
    - GoblinSlayer 2y ago
      Postulate what? The Born rule doesn't hold with absolute certainty in any interpretation, it holds only with asymptotic certainty, and the latter is a quantitative observable computable property, and it computes the same way in any interpretation, otherwise interpretations would be quantitatively different.
      - tsimionescu 2y ago
        Some people claim that the MWI doesn't need the Born rule as a postulate, that it can be deduced from the Schrodinger equation if we just assume that entire universe is described by a universal wavefunction. This is generally why some claim that the MWI is actually the "most serious" interpretation, since it supposedly only has one postulate (that the wavefunction describes the universe), while other interpretations require at least two postulates (the one above, plus the Born rule). I believe that this is the claim that evanb was making at the beginning of this thread: that you don't need the Born rule, that decoherence (which is to some extent a consequence of the Schrodinger equation, not an extra postulate) is enough to explain how the classical physics we observe in day to day life emerge from the wavefunction description of the universe in QM.
        GoblinSlayer 2y ago
        He answered a question about collapse, not Born rule, it's two different phenomena. Decoherence replaces collapse and explains why you observe one result, Born rule is replaced by the law of big numbers. Born rule is an abductive explanation for empirically observed statistics, and as abduction allows alternative explanations, it's empirical observation that needs to be explained, not postulates. Ironically, the law of big numbers is calculated MWI style: it considers all outcomes equally as if they all happen somehow even though they are mutually exclusive, but they all add up to the final statistics of statistics. The Schrodinger equation gives your state, you project it to the Born rule basis and see the projection asymptotically approaches 1. What's left after that is how to interpret asymptotic certainty, but that looks easy.
- GoblinSlayer 2y ago
  Oh, wait, did you understand what it means for your state to asymptotically approach |we observe the spin up version more often than the spin down version>? This reasoning doesn't involve collapse or something like that.

tsimionescu 2y ago

No, why would it? If we never collapse the wave function, we'll still have states where we only saw spin up, states where we only saw spin down, states where we saw more spin up, and states where we saw more spin down. And all of these are understood to be real in the MWI, so some observers will be guaranteed to exist that calculate that some state has a high amplitude, but they will never experience it, no matter how many billions of times they run the same experiment.

GoblinSlayer 2y ago
Marginal outcomes are possible in any interpretation. It's not absolute certainty, only exponential asymptotic certainty.
- tsimionescu 2y ago
  These outcomes are marginal in many interpretations, but they are certain to happen in MWI (since all possible results of the wave function actually happen). And the point I was trying to make is that, if you don't postulate the Born rule in addition to the Schrodinger equation, then you don't even have a way to say that this "happens for fewer observers". But then, if you do have to postulate the Born rule, then the MWI has no more explanatory power than any other interpretation, it's not just "following the math", and it still needs a definition for what consitutes a measurement for purposes of applying the Born rule.
  - GoblinSlayer 2y ago
    Postulate what? The Born rule doesn't hold with absolute certainty in any interpretation, it holds only with asymptotic certainty, and the latter is a quantitative observable computable property, and it computes the same way in any interpretation, otherwise interpretations would be quantitatively different.
    - tsimionescu 2y ago
      Some people claim that the MWI doesn't need the Born rule as a postulate, that it can be deduced from the Schrodinger equation if we just assume that entire universe is described by a universal wavefunction. This is generally why some claim that the MWI is actually the "most serious" interpretation, since it supposedly only has one postulate (that the wavefunction describes the universe), while other interpretations require at least two postulates (the one above, plus the Born rule). I believe that this is the claim that evanb was making at the beginning of this thread: that you don't need the Born rule, that decoherence (which is to some extent a consequence of the Schrodinger equation, not an extra postulate) is enough to explain how the classical physics we observe in day to day life emerge from the wavefunction description of the universe in QM.
      - GoblinSlayer 2y ago
        He answered a question about collapse, not Born rule, it's two different phenomena. Decoherence replaces collapse and explains why you observe one result, Born rule is replaced by the law of big numbers. Born rule is an abductive explanation for empirically observed statistics, and as abduction allows alternative explanations, it's empirical observation that needs to be explained, not postulates. Ironically, the law of big numbers is calculated MWI style: it considers all outcomes equally as if they all happen somehow even though they are mutually exclusive, but they all add up to the final statistics of statistics. The Schrodinger equation gives your state, you project it to the Born rule basis and see the projection asymptotically approaches 1. What's left after that is how to interpret asymptotic certainty, but that looks easy.
GoblinSlayer 2y ago
Oh, wait, did you understand what it means for your state to asymptotically approach |we observe the spin up version more often than the spin down version>? This reasoning doesn't involve collapse or something like that.