My read of the post is not that many worlds is wrong, but rather it’s not uniquely correct, and that many worlds has some issues of it’s own, and that other theories are at least coherent.
I guess it’s hard to answer because it depends on three degrees of freedom:
Whether you agree with my assessment that it’s mostly arbitrary to demand the fundamental ontology to be deterministic rather than stochastic or quantum,
Whether you count “many worlds” as literally asserting that the wavefunction as a classical mathematical object is real or as simply distancing oneself from collapse/hidden variables,
Whether you even aim to describe what is ontologically fundamental in the first place.
I’m personally inclined to say the many-worlds interpretation is technically wrong, hence the title. But I have basically suggested people could give different answers to these sorts of degrees of freedom, and so I could see other people having different takeaways.
Why do you speak of deterministic, stochastic, and quantum as three options for a fundamental ontology? In the absence of a measurement/collapse postulate, quantum mechanics is a deterministic theory, and with a collapse postulate, it’s a stochastic theory in the sense that the state of the system evolves deterministically except for instantaneous stochastic jumps when “measurements” occur.
Also, what do you mean by “the wavefunction as a classical mathematical object”?
In the absence of a measurement/collapse postulate, quantum mechanics is a deterministic theory
You can make a deterministic theory of stochasticity using many-worlds too.
In the absence of a postulate that the wavefunction is Literally The Underlying State, rather than just a way we describe the system deterministically, quantum dynamics doesn’t fit under a deterministic ontology.
Also, what do you mean by “the wavefunction as a classical mathematical object”?
If you have some basis E={e1,e2,…}, you can represent quantum systems using functions E→C (or perhaps more naturally, as FC[E] where F denotes the free vector space, but then we get into category theory, and that’s a giant nerdsnipe).
Okay, so by “wavefunction as a classical mathematical object” you mean a vector in Hilbert space? In that case, what do you mean by the adjective “classical”?
Okay, so by “wavefunction as a classical mathematical object” you mean a vector in Hilbert space?
Yes.
In that case, what do you mean by the adjective “classical”?
There’s a lot of variants of math; e.g. homotopy type theory, abstract stone duality, nonstandard analysis, etc.. Maybe one could make up a variant of math that could embed wavefunctions more natively.
Hmmm, I think there’s still some linguistic confusion remaining. While we certainly need to invent new mathematics to describe quantum field theory, are you making the stronger claim that there’s something “non-native” about the way that wavefunctions in non-relativistic quantum mechanics are described using functional analysis? Especially since a lot of modern functional analysis theory was motivated by quantum mechanics, I don’t see how a new branch of math could describe wavefunctions more natively.
Measure theory and probability theory was developed to describe stochasticity and uncertainty, but they formalize it in many-worlds terms, closely analogous to how the wavefunction is formalized in quantum mechanics. If one takes the wavefunction formalism literally to the point of believing that quantum mechanics must have many worlds, it seems natural to take the probability distribution formalism equally literally to the point of believing that probability must have many worlds too. Or well, you can have a hidden variables theory of probability too, but the point is it seems like you would have to abandon True Stochasticity.
True Stochasticity vs probability distributions provides a non-quantum example of the non-native embedding, so if you accept the existence of True Stochasticity as distinct from many worlds of simultaneous possibility or ignorance of hidden variables, then that provides a way to understand my objection. Otherwise, I don’t yet know a way to explain it, and am not sure one exists.
As for the case of how a new branch of math could describe wavefunctions more natively, there’s a tradeoff where you can put in a ton of work and philosophy to make a field of math that describes an object completely natively, but it doesn’t actually help the day-to-day work of a mathematician, and it often restricts the tools you can work with (e.g. no excluded middle and no axiom of choice), so people usually don’t. Instead they develop their branch of math within classical math with some informal shortcuts.
My read of the post is not that many worlds is wrong, but rather it’s not uniquely correct, and that many worlds has some issues of it’s own, and that other theories are at least coherent.
Is this a correct reading of this post?
I guess it’s hard to answer because it depends on three degrees of freedom:
Whether you agree with my assessment that it’s mostly arbitrary to demand the fundamental ontology to be deterministic rather than stochastic or quantum,
Whether you count “many worlds” as literally asserting that the wavefunction as a classical mathematical object is real or as simply distancing oneself from collapse/hidden variables,
Whether you even aim to describe what is ontologically fundamental in the first place.
I’m personally inclined to say the many-worlds interpretation is technically wrong, hence the title. But I have basically suggested people could give different answers to these sorts of degrees of freedom, and so I could see other people having different takeaways.
Why do you speak of deterministic, stochastic, and quantum as three options for a fundamental ontology? In the absence of a measurement/collapse postulate, quantum mechanics is a deterministic theory, and with a collapse postulate, it’s a stochastic theory in the sense that the state of the system evolves deterministically except for instantaneous stochastic jumps when “measurements” occur.
Also, what do you mean by “the wavefunction as a classical mathematical object”?
You can make a deterministic theory of stochasticity using many-worlds too.
In the absence of a postulate that the wavefunction is Literally The Underlying State, rather than just a way we describe the system deterministically, quantum dynamics doesn’t fit under a deterministic ontology.
If you have some basis E={e1,e2,…}, you can represent quantum systems using functions E→C (or perhaps more naturally, as FC[E] where F denotes the free vector space, but then we get into category theory, and that’s a giant nerdsnipe).
Okay, so by “wavefunction as a classical mathematical object” you mean a vector in Hilbert space? In that case, what do you mean by the adjective “classical”?
Yes.
There’s a lot of variants of math; e.g. homotopy type theory, abstract stone duality, nonstandard analysis, etc.. Maybe one could make up a variant of math that could embed wavefunctions more natively.
Hmmm, I think there’s still some linguistic confusion remaining. While we certainly need to invent new mathematics to describe quantum field theory, are you making the stronger claim that there’s something “non-native” about the way that wavefunctions in non-relativistic quantum mechanics are described using functional analysis? Especially since a lot of modern functional analysis theory was motivated by quantum mechanics, I don’t see how a new branch of math could describe wavefunctions more natively.
Measure theory and probability theory was developed to describe stochasticity and uncertainty, but they formalize it in many-worlds terms, closely analogous to how the wavefunction is formalized in quantum mechanics. If one takes the wavefunction formalism literally to the point of believing that quantum mechanics must have many worlds, it seems natural to take the probability distribution formalism equally literally to the point of believing that probability must have many worlds too. Or well, you can have a hidden variables theory of probability too, but the point is it seems like you would have to abandon True Stochasticity.
True Stochasticity vs probability distributions provides a non-quantum example of the non-native embedding, so if you accept the existence of True Stochasticity as distinct from many worlds of simultaneous possibility or ignorance of hidden variables, then that provides a way to understand my objection. Otherwise, I don’t yet know a way to explain it, and am not sure one exists.
As for the case of how a new branch of math could describe wavefunctions more natively, there’s a tradeoff where you can put in a ton of work and philosophy to make a field of math that describes an object completely natively, but it doesn’t actually help the day-to-day work of a mathematician, and it often restricts the tools you can work with (e.g. no excluded middle and no axiom of choice), so people usually don’t. Instead they develop their branch of math within classical math with some informal shortcuts.