I feel like branches being in fact an uncountable continuum is essentially a given, at least unless we were to fundamentally rewrite quantum mechanics to use something other than complex numbers with a cardinality of 2ℵ0. Talking about branches in terms of countable outcomes only makes sense if we group them by measurement outputs for specific discrete observables; but each of the uncountable infinity of worlds will continuously spawn uncountable infinite worlds and that’s just something you gotta deal with. If you want to do ethics over this very confusing multiverse your best bet is probably to normalize everything—“adjust for inflation”, so to speak.
I also don’t think that even if the worlds were countable (and I have seen arguments to the effect of “actually only integer numbers exist and thus if we looked close enough we’d find that all equations and fields etc are discrete-valued”) this would make a lot of difference. You making or not making the experiment does not create more branches, it just determines the outcome of branches that would already exist anyway. Assuming that we can purposefully create branches would require defining “measurement” as an actual discrete specific process, which is a much stronger claim (and I don’t think any non-objective interpretation of QM really suggests how to do that, though some gesture towards such a thing existing in theory; and objective QM theories do not admit many worlds). “By looking at specific phenomena, sentient beings create new world-lines” would certainly be A Take; if true, it would beget an ethical nightmare, the Quantum Repugnant Conclusion that we all ought to spend all our time collapsing the wavefunctions that result in the most new worlds being created.
(as a side note, have you read Quarantine, by Greg Egan? I won’t explain how precisely to avoid spoiling it, but it deals precisely with these sort of questions)
You’re right, I didn’t discuss the possibility of infinite numbers of branches, though as you suggest this leads to essentially the same conclusion as I reach in the case of finite branches, which is that it causes problems for consequentialist ethics (Joe Carlsmith’s Infinite Ethics is good on this). If what you mean by ‘normalize everything’ is to only consider the quantum weights (which are finite as mathematical measures) and not the number of worlds, then that seems more a case of ignoring those problems rather than addressing them.
I hope it was clear that I was suggesting a third approach (the number of worlds is neither finite, nor infinite, but indefinite) which does I think address the ethical problems better, since if there is no definite number of worlds then we have a reason to ignore the number of worlds and focus on the weights.
This third approach is based on the idea that ‘worlds’ are macroscopic, emergent phenomena created through decoherence (Wallace’s book contains a full mathematical treatment of this). This supports both the claim that the number of worlds is indefinite (since it depends on ultimately arbitrary mappings of macroscopic to microscopic states) and the claim that worlds are created through quantum processes (since they are macroscopically indistinguishable before decoherence occurs). My point in the post was that these two claims in combination can avoid the repugnant conclusion via the approach of focusing on the weights.
(And when it comes to the virtue-theoretic implications, I’ve again tried to follow a weight-based approach, and not make assumptions about whether worlds are created or revealed.)
Thanks for the Egan suggestion, yea I love his work though need to read Quarantine more fully. It seems like the most philosophically relevant bit might be the ending which of course is the source of Egan’s Law (it all adds up to normality). I also need to read his short story ‘Singleton’, which I gather is very relevant too.
If what you mean by ‘normalize everything’ is to only consider the quantum weights (which are finite as mathematical measures) and not the number of worlds, then that seems more a case of ignoring those problems rather than addressing them.
I mean that the amount of universes that is created will be created anyway, just as a consequence of time passing. So it doesn’t matter anyway. If your actions e.g. cause misery in 20% of those worlds, then the fraction is all that matters; the worlds will exist anyway, and the total amount is not something you’re affecting or controlling.
This third approach is based on the idea that ‘worlds’ are macroscopic, emergent phenomena created through decoherence (Wallace’s book contains a full mathematical treatment of this). This supports both the claim that the number of worlds is indefinite (since it depends on ultimately arbitrary mappings of macroscopic to microscopic states) and the claim that worlds are created through quantum processes (since they are macroscopically indistinguishable before decoherence occurs). My point in the post was that these two claims in combination can avoid the repugnant conclusion via the approach of focusing on the weights.
I honestly don’t think decoherence means the worlds are indefinite. I think it means they are an infinite continuum with the cardinality of the reals. Decoherence is just something you observe when you divide system from environment, in reality the Universe should have only a single, always coherent, giant wavefunction.
I feel like branches being in fact an uncountable continuum is essentially a given, at least unless we were to fundamentally rewrite quantum mechanics to use something other than complex numbers with a cardinality of 2ℵ0. Talking about branches in terms of countable outcomes only makes sense if we group them by measurement outputs for specific discrete observables; but each of the uncountable infinity of worlds will continuously spawn uncountable infinite worlds and that’s just something you gotta deal with. If you want to do ethics over this very confusing multiverse your best bet is probably to normalize everything—“adjust for inflation”, so to speak.
I also don’t think that even if the worlds were countable (and I have seen arguments to the effect of “actually only integer numbers exist and thus if we looked close enough we’d find that all equations and fields etc are discrete-valued”) this would make a lot of difference. You making or not making the experiment does not create more branches, it just determines the outcome of branches that would already exist anyway. Assuming that we can purposefully create branches would require defining “measurement” as an actual discrete specific process, which is a much stronger claim (and I don’t think any non-objective interpretation of QM really suggests how to do that, though some gesture towards such a thing existing in theory; and objective QM theories do not admit many worlds). “By looking at specific phenomena, sentient beings create new world-lines” would certainly be A Take; if true, it would beget an ethical nightmare, the Quantum Repugnant Conclusion that we all ought to spend all our time collapsing the wavefunctions that result in the most new worlds being created.
(as a side note, have you read Quarantine, by Greg Egan? I won’t explain how precisely to avoid spoiling it, but it deals precisely with these sort of questions)
Thanks for the interesting comments.
You’re right, I didn’t discuss the possibility of infinite numbers of branches, though as you suggest this leads to essentially the same conclusion as I reach in the case of finite branches, which is that it causes problems for consequentialist ethics (Joe Carlsmith’s Infinite Ethics is good on this). If what you mean by ‘normalize everything’ is to only consider the quantum weights (which are finite as mathematical measures) and not the number of worlds, then that seems more a case of ignoring those problems rather than addressing them.
I hope it was clear that I was suggesting a third approach (the number of worlds is neither finite, nor infinite, but indefinite) which does I think address the ethical problems better, since if there is no definite number of worlds then we have a reason to ignore the number of worlds and focus on the weights.
This third approach is based on the idea that ‘worlds’ are macroscopic, emergent phenomena created through decoherence (Wallace’s book contains a full mathematical treatment of this). This supports both the claim that the number of worlds is indefinite (since it depends on ultimately arbitrary mappings of macroscopic to microscopic states) and the claim that worlds are created through quantum processes (since they are macroscopically indistinguishable before decoherence occurs). My point in the post was that these two claims in combination can avoid the repugnant conclusion via the approach of focusing on the weights.
(And when it comes to the virtue-theoretic implications, I’ve again tried to follow a weight-based approach, and not make assumptions about whether worlds are created or revealed.)
Thanks for the Egan suggestion, yea I love his work though need to read Quarantine more fully. It seems like the most philosophically relevant bit might be the ending which of course is the source of Egan’s Law (it all adds up to normality). I also need to read his short story ‘Singleton’, which I gather is very relevant too.
I mean that the amount of universes that is created will be created anyway, just as a consequence of time passing. So it doesn’t matter anyway. If your actions e.g. cause misery in 20% of those worlds, then the fraction is all that matters; the worlds will exist anyway, and the total amount is not something you’re affecting or controlling.
I honestly don’t think decoherence means the worlds are indefinite. I think it means they are an infinite continuum with the cardinality of the reals. Decoherence is just something you observe when you divide system from environment, in reality the Universe should have only a single, always coherent, giant wavefunction.