Many Worlds and Occam’s Razor

One of the common objections to the Many Worlds Interpretation (MWI) of quantum physics is to invoke Occam’s Razor (“Entities should not be multipled without necessity.”) and to say that MWI certainly violates this principle with its infinity of actual universes. Many physicists (including both MWI proponents and others) consider this to not be a strong objection. I’d boil their responses down to the following:

  1. In some important sense, MWI is actually simpler than the alternatives.
  2. We shouldn’t expect the universe to conform to our expectations and intuitions. It could be much more extravagant than we can imagine.

Point 1 is basically a claim that MWI is “close to the math,” i.e. it is essentially just Schrodinger’s equation. There is no collapse that needs to be explained. If you just take Schrodinger’s equation literally, MWI is what you get. In that light, you could use Occam’s Razor to argue for MWI. I would like to push back on this in a couple of ways. First, it’s not clear that “close to the math” is really what we should care about. Second, and relatedly, it seems there is a mistaken reification of the Schrodinger equation happening — in MWI, it is not just an incredibly successful equation for prediction, but a literal description of reality. This move does not seem justified. Finally, even if you care about how “close to the math” a theory is, you could opt for pilot-wave theory, which also does not require collapse. MWI is still mathematically simpler, since pilot-wave theory requires additional rules, but pilot-wave theory does not require an infinity of universes. I agree with Lee Smolin that, at the very least, pilot-wave theory is underappreciated and deserves more consideration as a viable interpretation of quantum physics.

Regarding Point 2, I agree that the universe could be much stranger than we imagine, and we shouldn’t expect it to line up with our intuitions. But there is a stronger reading of this claim that seems to reject Occam’s Razor altogether, and since we can have an infinity of theories purporting to describe a given phenomenon, we need Occam’s Razor to help sift through them.

Even if you think Occam’s Razor cannot be wielded against MWI, there are other major challenges facing MWI, such as how to make sense of probability when everything that can happen does happen. Again, Lee Smolin’s book has a very good discussion of this challenge, and Philip Ball has an article that discusses this as well. Ball also talks about the challenge of making sense of the self in the context of MWI. Near the end of Smolin’s book, he also talks about the moral implications of MWI: in a multiverse where everything that can happen does happen, how do we make sense of moral decision-making?

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  1. Allan Olley

    There is a problem that there is an ambiguity between simplicity and the more universally admitted requirement that you need evidence of things in order to justify claims that they exist/happen. So as far as I can tell there is no real evidence of a collapse process or the like, so its not so much a question of simplicity and more of where’s the evidence or is it?

    I mean advocates of collapse theories will point to stuff as evidence of collapse but I don’t find the phenomena they bring up good evidence for their theory, but part of that is I think it would only be evidence given assumptions I find overly complicated, makes too many assumptions and so (so they would say look you only remember one history so clearly that is the only one that happened but under MWI I would only remember one history, so I don’t think the evidence is clear cut). So what is evidence and what is good evidence and does it depend in any way on simplicity strikes me as a very difficult question.

    If you are allowed to make endless assumptions anything can be evidence for anything, the requirement of evidence is a requirement that we justify assumptions at some point and part of something being good evidence is how directly (simply) it relates to the theory in question without a bunch of speculative assumptions.

    For example Ball mentions phlogiston, one of Lavoisier’s attacks on it was that things that burned (so released phlogiston) were heavier than their unburnt counterparts meaning that Phlogiston had negative weight, you could either say well that’s just impossible or could make some assumptions to justify Phlogiston’s negative weight. Some peopel tried to made those sorts of assumptions in various ways, but it seems like at best those are worse explanations then that burning is process of combination and at some point if you are allowed to just keep making assumptions then evidence just becomes meaningless…

    Note on the issue of whehter the Schrodinger Equation is a literal description versus just what it predicts. Part of the problem is it is tricky to say what it predicts versus what is just background and further depends on what you allow as evidence. So when EPR originally put forward their experiment everyone thought it was meaningless because the non-local correlations they talked about, would never be detectable as non-local, you could never prove the perfectly anticorrelated measurements were anticorrelated due to simple local conservation or something versus some kind of non-local effect. Bell showed that those correlations were not just some inscrutable unreal background of the theory but that indeed you could show a non-local effect (the correlation of space like separated phenomenon that could not be explained by local interactions). So where the predictions of the Schrodinger Equation are tricky, what you might see as some inert bit of background abstraction of the theory may turn out to be a prediction, if you are clever enough to design the right experiment and you believe all the assumptions going in to the experiment.

    Just one more thing Ball suggests the interpretation of QM is the only real case of debates about theories with the same evidence. I would point to one more. Einstein’s view of length contraction and time dilation in relative motion versus Lorentz’s view. According to Einstein things do not actually physically contract etc. rather the very basis of measurement varies in a non-Galilean sort of way and motion relative to the ether (the seat of em phenomenon) is meaningless, whereas Lorentz assumed the contractions and dilations were real physical effects (induced presumably by motion relative to the ether) and one could be said to move relative to the ether.

    As Lorentz summed up the difference between the two: “the chief difference being that Einstein simply postulates what we have deduced, with some difficulty and not altogether satisfactorily, from the fundamental equations of the electromagnetic field. By doing so, he may certainly take credit for making us see in the negative result of experiments like those of Michelson, Rayleigh and Brace, not a fortuitous compensation of opposing effects, but the manifestation of a general and fundamental principle.” (Lorentz, Theory of Electrons, 1909, 1916, page 230 in 1916 edition, section 194, it was in the 1909 edition)

    Lorentz goes on to defend his interpretation of motion relative to the ether arguing we should see the ether, the seat of em phenomenon, as something substantial “In this line of thought, it seems natural not to assume at starting that it can never make any difference whether a body moves through the ether or not, and to measure distances and lengths of time by means of rods and clocks having a fixed position relatively to the ether.” (previously cited)

    But this would be as much to assume that the Lorentz equations/transformations breakdown somewhere and some how motion relative to the ether becomes detectable, still arguably this is just a question of subjective simplicity (at least until General Relativity comes along, also someone told me once people did try to measure effects that would exist if length contraction were physical and so on, but that does not seem to have been decisive). It is my favourite example of the thing and I think it nicely illustrates how simplicity can be about something like fit of evidence, if yuo have to invoke a conspiracy (or fortuitous compensation of opposing effects) to make the evidence fit this is not a good fit.

    Anyway the concept of simplicity in science is a bit more complex then I think your engaging with…

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