8 ms·
It should be noted though that few interpretations have an explanation for the born rule.
by doubleunplussed 7y ago
It should be noted though that few interpretations have an explanation for the born rule.
- lisper 7y agoRight, most of them just take it as an axiom. But the MWI explicitly rejects the Born rule as an axiom, insisting that the Schrödinger equation is all the actual physics there is.
- lmm 7y agoMWI is not incompatible with postulating the Born rule if you want to. It just doesn't elevate it to an axiom of the theory. It's like doing constructive mathematics: you're not denying the law of excluded middle, you can postulate it and it will have the usual consequences, but the core theory doesn't rely on it, and it's possible to hope for a more elegant alternative.
- lisper 7y agoYes, you can just add the Born rule as an additional axiom, but that undermines the whole point of adopting the MWI in the first place, which is to remain mathematically "clean" with no ad-hoc assumptions.
- lmm 7y agoYes and no. I'd argue that the Born rule as a rule for subjective probabilities in a MWI context is much cleaner than a full Copenhagen-style collapse operation.
- lisper 7y agoYou are, of course, free to argue that. But most advocates of the MWI will disagree with you. That's why they put so much effort into trying to derive the Born rule.
- lmm 7y agoThere's a significant gap between "cleaner than a Copenhagen-style collapse" and "clean enough to be a good part of our fundamental theory of nature" :).
- akvadrako 7y agoNot that it really matters but I disagree that MWI advocates like it because of the born rule derivations. Actually most born rule derivations apply equally to all interpretations. I’m with Vaidman on this, who is one of the best known supporters of MW, which is that the clearest solution is just to postulate the connection between psi magnitude and subjective experience. It’s an empirical discovery that works.
- platz 7y agoHe didn't say to re-add it as an axiom. He's pointing out that the "born rule" (or something that gives you probabilities in the way that you need to agree with experiment) can potentially "emerge" i.e. be recovered (if they can find the right proof for it), without having had to assume that up front. It's like when GR can "recover" F=MA, despite not having assumed F=MA that as an axiom.
- tim333 7y agoThough Everett in his disertation doesn't call it an axiom he kind of assumes it: >It is convenient at this point to introduce some notational conventions... >For a complete orthonormal set we define... [the Born rule] >In the probabilistic interpretation this distribution represents the probability distribution over the results of a measurement... https://www-tc.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf https://www-tc.pbs.org/wgbh/nova/manyworlds/pdf/dissertation... page 34
- akvadrako 7y agoActually most interpretations have the same explanations for the Born rule, it's just that people who study many worlds are more inclined to consider them. People who believe in Copenhagen don't care about this stuff. For a recent high-quality example: https://www.nature.com/articles/s41467-019-09348-x https://www.nature.com/articles/s41467-019-09348-x