If you believe in MWI, then this whole argument is… not “wrong”, but very incomplete...
Where is the consideration of branches? What does it mean for one entity to be vastly superior to another, if there are many branches?
If one believes in MWI, then the linked proof does not even start to look like a proof. It obviously considers only a single branch.
And a “subjective navigation” in the branches is not assumed to be computable, even if the “objective multiverse” is computable; that is the whole point of MWI, the “collapse” becomes “subjective navigation”, but this does not make it computable. If a consideration is only of a single branch, that branch is not computable, even if it is embedded in a large computable multiverse.
Not every subset of a computable set (say, of a set of natural numbers) is computable.
An interpretation of QM can’t be “wrong”. It is a completely open research and philosophical question, there is no “right” interpretation, and the Sequences is (thankfully) not a Bible (if even a very respected thinker says something, this does not yet mean that one should accept that without questions).
I don’t think so. If it were classical, we would not be able to observe effects of double-slit experiments and so on.
And, also, there is no notion of “our branch” until one has traveled along it. At any given point in time, there are many branches ahead. Only looking back one can speak about one’s branch. But looking forward one can’t predict the branch one will end up in. One does not know the results of future “observations”/”measurements”. This is not what a classical universe looks like.
(Speaking of MWI, I recall David Deutsch’s “Fabric of Reality” very eloquently explaining effects from “neighboring branches”. The reason I am referencing this book is that this was the work particularly strongly associated with MWI back then. So I think we should be able to rely on his understanding of MWI.)
Something like, “for all branches, [...]”? That might be not that easy to prove or even to formulate. In any case, the linked proof has not even started to deal with this.
Something like, “there exist a branch such that [...]”? That might be quite tractable, but probably not enough for practical purposes.
“The probability that one ends up in a branch with such and such properties is no less than/no more than” [...]? Probably something like that, realistically speaking, but this still needs a lot of work, conceptual and mathematical...
bringing QM into this is not helping. All these types of questions are completely generic QM questions and ultimately they come down to measure ||Psi>|²
It’s just… having a proof is supposed to boost our confidence that the conclusion is correct...
if the proof relies on assumptions which are already quite far from the majority opinion about our actual reality (and are probably going to deviate further, as AIs will be better physicists and engineers than us and will leverage the strangeness of our physics much further than we do), then what’s the point of that “proof”?
how does having this kind of “proof” increase our confidence in what seems informally correct for a single branch reality (and rather uncertain in a presumed multiverse, but we don’t even know if we are in a multiverse, so bringing a multiverse in might, indeed, be one of the possible objections to the statement, but I don’t know if one wants to pursue this line of discourse, because it is much more complicated than what we are doing here so far)?
(as an intellectual exercise, a proof like that is still of interest, even under the unrealistic assumption that we live in a computable reality, I would not argue with that; it’s still interesting)
No. I can only repeat my reference to Fabric of Reality as a good presentation of MWI and to remind that we do not live in a classical world, which is easy to confirm empirically.
And there are plenty of known macroscopic quantum effects already, and that list will only grow. Lasers are quantum, superfluidity and superconductivity are quantum, and so on.
Coherent light produced by lasers is not microscopic, we see its traces in the air. And we see the consequences (old fashioned holography and the ability to cut things with focused light, even at large distances). Room temperature is fine for that.
Superconductors used in the industry are not microscopic (and the temperatures are high enough to enable industrial use of them in rather common devices such as MRI scanners).
If you believe in MWI, then this whole argument is… not “wrong”, but very incomplete...
Where is the consideration of branches? What does it mean for one entity to be vastly superior to another, if there are many branches?
If one believes in MWI, then the linked proof does not even start to look like a proof. It obviously considers only a single branch.
And a “subjective navigation” in the branches is not assumed to be computable, even if the “objective multiverse” is computable; that is the whole point of MWI, the “collapse” becomes “subjective navigation”, but this does not make it computable. If a consideration is only of a single branch, that branch is not computable, even if it is embedded in a large computable multiverse.
Not every subset of a computable set (say, of a set of natural numbers) is computable.
An interpretation of QM can’t be “wrong”. It is a completely open research and philosophical question, there is no “right” interpretation, and the Sequences is (thankfully) not a Bible (if even a very respected thinker says something, this does not yet mean that one should accept that without questions).
Thanks to decoherece, you can just ignore any type of interference and treat each branch as a single classical universe.
I don’t think so. If it were classical, we would not be able to observe effects of double-slit experiments and so on.
And, also, there is no notion of “our branch” until one has traveled along it. At any given point in time, there are many branches ahead. Only looking back one can speak about one’s branch. But looking forward one can’t predict the branch one will end up in. One does not know the results of future “observations”/”measurements”. This is not what a classical universe looks like.
(Speaking of MWI, I recall David Deutsch’s “Fabric of Reality” very eloquently explaining effects from “neighboring branches”. The reason I am referencing this book is that this was the work particularly strongly associated with MWI back then. So I think we should be able to rely on his understanding of MWI.)
yes one can—all of them!
Yes, but then what do you want to prove?
Something like, “for all branches, [...]”? That might be not that easy to prove or even to formulate. In any case, the linked proof has not even started to deal with this.
Something like, “there exist a branch such that [...]”? That might be quite tractable, but probably not enough for practical purposes.
“The probability that one ends up in a branch with such and such properties is no less than/no more than” [...]? Probably something like that, realistically speaking, but this still needs a lot of work, conceptual and mathematical...
bringing QM into this is not helping. All these types of questions are completely generic QM questions and ultimately they come down to measure ||Psi>|²
It’s just… having a proof is supposed to boost our confidence that the conclusion is correct...
if the proof relies on assumptions which are already quite far from the majority opinion about our actual reality (and are probably going to deviate further, as AIs will be better physicists and engineers than us and will leverage the strangeness of our physics much further than we do), then what’s the point of that “proof”?
how does having this kind of “proof” increase our confidence in what seems informally correct for a single branch reality (and rather uncertain in a presumed multiverse, but we don’t even know if we are in a multiverse, so bringing a multiverse in might, indeed, be one of the possible objections to the statement, but I don’t know if one wants to pursue this line of discourse, because it is much more complicated than what we are doing here so far)?
(as an intellectual exercise, a proof like that is still of interest, even under the unrealistic assumption that we live in a computable reality, I would not argue with that; it’s still interesting)
yes, but thanks to decoherence this generally doesn’t affect macroscopic variables. Branches are causally independent once they have split.
No. I can only repeat my reference to Fabric of Reality as a good presentation of MWI and to remind that we do not live in a classical world, which is easy to confirm empirically.
And there are plenty of known macroscopic quantum effects already, and that list will only grow. Lasers are quantum, superfluidity and superconductivity are quantum, and so on.
Decoherence means that different branches don’t interfere with each other on macroscopic scales. That’s just the way it works.
Superfluids/superconductors/lasers are still microscopic effects that only matter at the scale of atoms or at ultra-low temperature or both.
No, not microscopic.
Coherent light produced by lasers is not microscopic, we see its traces in the air. And we see the consequences (old fashioned holography and the ability to cut things with focused light, even at large distances). Room temperature is fine for that.
Superconductors used in the industry are not microscopic (and the temperatures are high enough to enable industrial use of them in rather common devices such as MRI scanners).