I mean that it correctly predicts the results of experiments and our observations—which, yes, would be different if we were sampled from a different measure. That’s the point. I’m taking for granted that we have some pre-theoretical observations to explain here, and saying that the Hilbert measure is needed to explain them.
I’m saying that the classical notions of prediction, knowledge, observations and the need to explain them in classical sense should not be fundamental part of the theory with MWI. It is a plain consequence of QM equations that amplitudes of the branches, where frequency of repeated experiments contradicts Born rule, tends to zero. Theory just doesn’t tell us why Born probabilities are right for specific observables in absolute sense, because there are no probabilities or sampling on physical level and wavefunction containing all worlds continues to evolve as it did before. We can label “amplitudes of the branches, where x is wrong, tend to zero” situation as “we observe x”, but it would be arbitrary ethical decision. The Hilbert measure is correct only if you want to sum over branches, but there is nothing in the physics that forces you to want anything.
I think some notion of prediction/observation has to be included for a theory to qualify as physics. By your definition, studying the results of e.g. particle accelerator experiments wouldn’t be part of quantum mechanics, since you need the Born rule to make predictions about them.
It has some notion—that notion is just not classical and not fundamental. What happens when you study the results of any experiments or make predictions is described by the theory. It just doesn’t describe it in classical or probabilistic terms because they are not real. And doesn’t tell you how to maximize knowledge, because it’s ambiguous without specifying how to aggregate knowledge in different branches.
I think you’re misusing the word ‘real’ here. We only think QM is ‘real’ in the first place because it predicts our experimental results, so it seems backwards to say that those (classical, probabilistic) results are actually not real, while QM is real. What happens if we experimentally discover a deeper layer of physics beneath QM, will you then say “I thought QM was real, but it was actually fake the whole time”? But then, why would you change your notion of what ‘real’ is in response to something you don’t consider real?
The main reason is the double-slit experiment: if you start with a notion of reality that expects photon to travel through either one or the other slit, and then the nature is like ~_~, it is already a sufficient reason to rethink reality. Different parts of probability distribution don’t influence each other.
What happens if we experimentally discover a deeper layer of physics beneath QM
I mean, there is no need for hypotheticals—it’s not like we started with probabilistic reality—we started with gods. And then everyone already changed their notion of reality to the probabilistic one in response to QM. Point is, changing one’s ontology may not be easy, but if you prohibit continuous change then the Spirit of the Forest welcomes you. So yes, if we discover new better physics and it doesn’t include interference between worlds, then sure, we dodged this bullet. But until then I see no reason to not assume MWI without special status for any measure. We don’t even lose any observations that way—we just now know what it meant to observer something.
I mean that it correctly predicts the results of experiments and our observations—which, yes, would be different if we were sampled from a different measure. That’s the point. I’m taking for granted that we have some pre-theoretical observations to explain here, and saying that the Hilbert measure is needed to explain them.
I’m saying that the classical notions of prediction, knowledge, observations and the need to explain them in classical sense should not be fundamental part of the theory with MWI. It is a plain consequence of QM equations that amplitudes of the branches, where frequency of repeated experiments contradicts Born rule, tends to zero. Theory just doesn’t tell us why Born probabilities are right for specific observables in absolute sense, because there are no probabilities or sampling on physical level and wavefunction containing all worlds continues to evolve as it did before. We can label “amplitudes of the branches, where x is wrong, tend to zero” situation as “we observe x”, but it would be arbitrary ethical decision. The Hilbert measure is correct only if you want to sum over branches, but there is nothing in the physics that forces you to want anything.
I think some notion of prediction/observation has to be included for a theory to qualify as physics. By your definition, studying the results of e.g. particle accelerator experiments wouldn’t be part of quantum mechanics, since you need the Born rule to make predictions about them.
It has some notion—that notion is just not classical and not fundamental. What happens when you study the results of any experiments or make predictions is described by the theory. It just doesn’t describe it in classical or probabilistic terms because they are not real. And doesn’t tell you how to maximize knowledge, because it’s ambiguous without specifying how to aggregate knowledge in different branches.
I think you’re misusing the word ‘real’ here. We only think QM is ‘real’ in the first place because it predicts our experimental results, so it seems backwards to say that those (classical, probabilistic) results are actually not real, while QM is real. What happens if we experimentally discover a deeper layer of physics beneath QM, will you then say “I thought QM was real, but it was actually fake the whole time”? But then, why would you change your notion of what ‘real’ is in response to something you don’t consider real?
The main reason is the double-slit experiment: if you start with a notion of reality that expects photon to travel through either one or the other slit, and then the nature is like ~_~, it is already a sufficient reason to rethink reality. Different parts of probability distribution don’t influence each other.
I mean, there is no need for hypotheticals—it’s not like we started with probabilistic reality—we started with gods. And then everyone already changed their notion of reality to the probabilistic one in response to QM. Point is, changing one’s ontology may not be easy, but if you prohibit continuous change then the Spirit of the Forest welcomes you. So yes, if we discover new better physics and it doesn’t include interference between worlds, then sure, we dodged this bullet. But until then I see no reason to not assume MWI without special status for any measure. We don’t even lose any observations that way—we just now know what it meant to observer something.