3 ms·

To summarize the argument that the blog post makes: The multiverse interpretation accounts for cases where the probabilities of each distinct observable outcom

To summarize the argument that the blog post makes: The multiverse interpretation accounts for cases where the probabilities of each distinct observable outcome are equal according to the Born rule. But it cannot account for cases where the Born rule says there are non-equal probabilities for the possible outcomes. This is a fairly common problem which critics of the multiverse interpretation raise. See [1] for another example where a critic raises that problem in more detail (with examples). Deutsch and others have responded. In short, the reply is that the mathematics of the Schrodinger equation describes a density of universes in the continuum which is the multiverse, not a finite set of distinct, interacting single universes. This undercuts the critics' argument. See [2] for an example of this kind of response. [1] https://arxiv.org/pdf/0810.2657.pdf https://arxiv.org/pdf/0810.2657.pdf [2] https://www.pnas.org/doi/pdf/10.1073/pnas.1324238111 https://www.pnas.org/doi/pdf/10.1073/pnas.1324238111

spekcular 4y ago
Your reference [2] is somewhat suspect. As far as I know, it is not generally accepted in the physics community that the Born rule can be derived directly from the Schrodinger equation. In fact, it seems generally accepted that such a derivation does not currently exist, and MWI has to stick it in as an additional postulate in some form (or otherwise give an auxiliary argument for it, none of which seem generally accepted either). Further, the author of that paper, Frank Tipler, is a notorious nutjob: https://en.wikipedia.org/wiki/Frank_J._Tipler https://en.wikipedia.org/wiki/Frank_J._Tipler. I don't have time at the moment to review the paper in detail to locate any potential flaws, but I wanted to flag this for others. I think there is substantial reason to be skeptical.
- boole1854 4y ago
  I agree that Tipler is far off the deep end on on some topics. But you should check out that one paper I linked nevertheless. PNAS is not a junk journal. I also agree there is no consensus that the problem of getting Born's rule from the Schrodinger equation has been solved to everyone's satisfaction.
  - spekcular 4y ago
    PNAS publishes a lot of junk. If you're connected to the Academy you can get papers through with very light review. In fact, one can even seen this happened in the Tipler paper: "This Direct Submission article had a prearranged editor." [0] Andrew Gelman calls it a "tabloid": https://statmodeling.stat.columbia.edu/2014/06/17/hurricaneshimmicanes-extra-problematic-nature-scientific-publication-process/ https://statmodeling.stat.columbia.edu/2014/06/17/hurricanes.... I will check the paper out though. [0] https://www.science.org/content/blog-post/no-more-prearranged-editors-pnas https://www.science.org/content/blog-post/no-more-prearrange... Edit: I read the paper. It is borderline crank work. There are decent arguments for the Born rule in MWI but this is not one of them. (I like David Wallace's book, for example.)
    - boole1854 4y ago
      Care to elucidate some critiques of the paper?
      - spekcular 4y ago
        Care to outline a precise argument for me to respond to? I'm honestly not sure one can even be extracted from pages 3 through 5, and I don't want to attack a strawman. One basic problem is that using symmetry arguments to justify the assignment of subjective probabilities (cf. page 4, right column) is going to fail when there isn't a symmetry available, for example for irrational probabilities. A deeper issue is the implicit assumption that one can coarse-grain into discrete "effectively distinguishable universes" for the purpose of doing these counting arguments. There are significant conceptual difficulties doing this, and this claim is much stronger than the bare MWI. Wallace discusses this at length; see for instance the citations in the blog post you responded to.
        ahazred8ta 4y ago
        Perhaps it occupies the gray area between "wrong" and "not even...". O:-)
lisper 4y ago
FYI, I am the author of the blog post. > This undercuts the critics' argument. No, it doesn't, for all of the reasons given in the blog post and the subsequent discussion. The Born rule is an observable fact of nature, and you cannot derive it from the Schroedinger equation, Duetsch and Wallace's claims to the contrary notwithstanding.
- boole1854 4y ago
  Maybe you can help me understand your argument better. If the Schrodinger equation describes a density of universes, doesn't that undercut the argument in the blog post? Edited to add my understanding: if the cardinality of the multiverse is uncountable, one has to talk about densities of branches. In that scheme, the problems which branch counting introduce do not arise.
  - lisper 4y ago
    > If the Schrodinger equation describes a density of universes, It doesn't (see below) but even if it did... > doesn't that undercut the argument in the blog post? No. It's really very simple: the SE is linear. The BR is not. You can't derive a non-linear result from a linear equation. The only thing that is even a tiny bit complicated about this is figuring out where the Deutsch-Wallace argument fails, because Deutsch and Wallace are not idiots and they hid their questionable assumption very well. So... why does the SE not describe a "density of universes"? It's because the SE does not describe universes at all! Deutsch and Wallace specifically acknowledge this, which makes their argument all that much more untenable. The SE describes the behavior of a function called "the wave function". The wave function is not a description of anything physical. The domain of the wave function is not physical space, it is configuration space. This is the reason entanglement seems weird to us, because we live in physical space and the wave function does not. In order to get anything physical out of the wave function -- particles, universes, anything resembling our classical reality -- you have to add some additional assumption, and any additional assumption that you add will be in some sense isomorphic to the Born rule. There is no way around this. Trying to derive the BR from the SE is like trying to prove Euclid's fifth postulate.

spekcular 4y ago

Your reference [2] is somewhat suspect. As far as I know, it is not generally accepted in the physics community that the Born rule can be derived directly from the Schrodinger equation. In fact, it seems generally accepted that such a derivation does not currently exist, and MWI has to stick it in as an additional postulate in some form (or otherwise give an auxiliary argument for it, none of which seem generally accepted either). Further, the author of that paper, Frank Tipler, is a notorious nutjob: https://en.wikipedia.org/wiki/Frank_J._Tipler https://en.wikipedia.org/wiki/Frank_J._Tipler. I don't have time at the moment to review the paper in detail to locate any potential flaws, but I wanted to flag this for others. I think there is substantial reason to be skeptical.

boole1854 4y ago
I agree that Tipler is far off the deep end on on some topics. But you should check out that one paper I linked nevertheless. PNAS is not a junk journal. I also agree there is no consensus that the problem of getting Born's rule from the Schrodinger equation has been solved to everyone's satisfaction.
- spekcular 4y ago
  PNAS publishes a lot of junk. If you're connected to the Academy you can get papers through with very light review. In fact, one can even seen this happened in the Tipler paper: "This Direct Submission article had a prearranged editor." [0] Andrew Gelman calls it a "tabloid": https://statmodeling.stat.columbia.edu/2014/06/17/hurricaneshimmicanes-extra-problematic-nature-scientific-publication-process/ https://statmodeling.stat.columbia.edu/2014/06/17/hurricanes.... I will check the paper out though. [0] https://www.science.org/content/blog-post/no-more-prearranged-editors-pnas https://www.science.org/content/blog-post/no-more-prearrange... Edit: I read the paper. It is borderline crank work. There are decent arguments for the Born rule in MWI but this is not one of them. (I like David Wallace's book, for example.)
  - boole1854 4y ago
    Care to elucidate some critiques of the paper?
    - spekcular 4y ago
      Care to outline a precise argument for me to respond to? I'm honestly not sure one can even be extracted from pages 3 through 5, and I don't want to attack a strawman. One basic problem is that using symmetry arguments to justify the assignment of subjective probabilities (cf. page 4, right column) is going to fail when there isn't a symmetry available, for example for irrational probabilities. A deeper issue is the implicit assumption that one can coarse-grain into discrete "effectively distinguishable universes" for the purpose of doing these counting arguments. There are significant conceptual difficulties doing this, and this claim is much stronger than the bare MWI. Wallace discusses this at length; see for instance the citations in the blog post you responded to.
      - ahazred8ta 4y ago
        Perhaps it occupies the gray area between "wrong" and "not even...". O:-)

lisper 4y ago

FYI, I am the author of the blog post. > This undercuts the critics' argument. No, it doesn't, for all of the reasons given in the blog post and the subsequent discussion. The Born rule is an observable fact of nature, and you cannot derive it from the Schroedinger equation, Duetsch and Wallace's claims to the contrary notwithstanding.

boole1854 4y ago
Maybe you can help me understand your argument better. If the Schrodinger equation describes a density of universes, doesn't that undercut the argument in the blog post? Edited to add my understanding: if the cardinality of the multiverse is uncountable, one has to talk about densities of branches. In that scheme, the problems which branch counting introduce do not arise.
- lisper 4y ago
  > If the Schrodinger equation describes a density of universes, It doesn't (see below) but even if it did... > doesn't that undercut the argument in the blog post? No. It's really very simple: the SE is linear. The BR is not. You can't derive a non-linear result from a linear equation. The only thing that is even a tiny bit complicated about this is figuring out where the Deutsch-Wallace argument fails, because Deutsch and Wallace are not idiots and they hid their questionable assumption very well. So... why does the SE not describe a "density of universes"? It's because the SE does not describe universes at all! Deutsch and Wallace specifically acknowledge this, which makes their argument all that much more untenable. The SE describes the behavior of a function called "the wave function". The wave function is not a description of anything physical. The domain of the wave function is not physical space, it is configuration space. This is the reason entanglement seems weird to us, because we live in physical space and the wave function does not. In order to get anything physical out of the wave function -- particles, universes, anything resembling our classical reality -- you have to add some additional assumption, and any additional assumption that you add will be in some sense isomorphic to the Born rule. There is no way around this. Trying to derive the BR from the SE is like trying to prove Euclid's fifth postulate.