Bruce, You argue that quantum mechanics follows the Born rule, but MWI does not. However, this assumes that MWI should reproduce the Born rule directly from the Schrödinger equation without additional structure. The issue is not whether the Born rule holds in quantum mechanics—it clearly does—but whether MWI can account for it without collapse.
You say that deriving the Born rule in MWI requires additional assumptions, but that’s not a valid objection—it’s an open question that multiple approaches are trying to address. Decision theory, envariance, and self-locating uncertainty all attempt to show why observers should expect probabilities to follow . Dismissing them outright ignores that they provide serious motivation for why the Born rule emerges from unitary evolution Your argument rests on the claim that all sequences exist independently of their amplitudes, meaning that counting sequences alone should determine probabilities. But this contradicts experimental results. If naive sequence counting were correct, we would observe a uniform distribution of outcomes across experiments, which we do not. The fact that quantum mechanics consistently follows suggests that something in the structure of MWI must explain why high-measure branches dominate experience. You dismiss measure as a "made-up surrogate" for probability, but this ignores that measure is a mathematical property of the wavefunction, not an arbitrary postulate. Amplitudes determine the structure of the quantum state, and decoherence ensures that branches remain effectively independent. The question is whether measure also determines the relative frequency with which observers find themselves in different branches. If it did not, we would expect deviations from the Born rule, yet we see none. The fact that multiple approaches attempt to derive the Born rule within MWI—decision theory, envariance, self-locating uncertainty—shows that this is an open question, not a settled failure. Simply asserting that MWI "does not follow the Born rule" ignores the very problem that these derivations attempt to solve. The Born rule is an observed fact, and MWI needs to explain it—but dismissing all attempts to do so does not make the problem go away. You frame your argument as avoiding "spurious additional assumptions." But you are making an assumption yourself: that all branches contribute equally to experience. This is a choice, not a consequence of unitary evolution. Quentin Le mar. 11 févr. 2025, 23:29, Bruce Kellett <bhkellet...@gmail.com> a écrit : > On Tue, Feb 11, 2025 at 11:27 PM Quentin Anciaux <allco...@gmail.com> > wrote: > >> Bruce, >> >> I'll still give it a try to get a discussion (dumb me). >> >> If your response boils down to "this is nonsense" and "you’re not clever >> enough," then you’re not engaging with the actual argument. The question is >> not whether the Schrödinger equation explicitly encodes the Born rule—it >> does not, just as it does not encode classical probability either. The >> question is whether MWI can recover the Born rule without adding collapse, >> and there are multiple serious approaches to doing so. >> >> Your claim that "MWI does not match experiments because it cannot get the >> Born rule" is just an assertion. The Schrödinger equation does evolve >> amplitudes, and those amplitudes do determine the structure of the >> wavefunction. You dismiss measure as meaningless, yet every quantum >> experiment confirms that the statistics follow . If naive branch counting >> were correct, experiments would contradict the Born rule—but they do not. >> That means something in MWI must account for it. >> >> Saying "all branches exist equally" ignores what "equally" even means in >> a probabilistic context. Probability is not about "some things happen while >> others don’t"—that’s a description, not an explanation. Classical >> probability arises because there are more ways for some outcomes to occur >> than others. In MWI, the weight of a branch is not a degree of >> existence—it’s a statement about how many copies of an observer find >> themselves in that outcome. >> >> If you have a counterargument, provide one—just dismissing the approach >> as "fantasy" without addressing the core point doesn’t make your position >> stronger. If you want to argue that MWI cannot recover the Born rule, then >> you need to explain why all proposed derivations (Deutsch-Wallace, Zurek’s >> envariance, self-locating uncertainty, etc.) are fundamentally flawed, not >> just assert that they don’t count. >> > > Many others have pointed out the deficiencies of the arguments by > Deutsch-Wallace, Zurek, and many others. The problems usually boil down to > the fact that these attempts implicitly assume the Born rule from the > outset. For example, as soon as you involve separate non-interacting > worlds, and rely on decoherence to give (approximate) orthogonality, then > you have assumed that small amplitudes correspond to low probability -- > which is just the Born rule. Similar considerations apply to other > arguments. The paper by Kent that I referenced earlier looks at many of the > arguments and points out the many problems. > > As far as your basic argument goes, there is no evidence that the > Schrodinger equation itself "evolves the amplitude", or that it gives > different numbers of observers on branches according to the amplitudes. The > idea of "branch weight" is just a made-up surrogate for assuming a > probabilistic interpretation; namely, the Born rule. > > The position I am taking tries to avoid all these spurious additional > assumptions/interpretations. We take the Schrodinger equation with the > Everettian proposal that all outcomes occur on every trial, and see where > that takes us. In the binary case, with repeated trials on similarly > prepared systems, we get the 2^N binary strings. We get the same 2^N > strings whatever amplitudes the initial wave function started with. There > is only one copy of the initial observer on every such binary sequence. > That observer can count the number of zeros in his/her string to estimate > the probability. Since the string is independent of the amplitudes, the > same proportion of ones will be found for the same string in every case. > Since the Born probability varies according to the original amplitude, we > find that this simplest version of many worlds is in conflict with the Born > rule. Other conflicts with the Born rule are evident in other ways -- I > have mentioned some of them previously. To go beyond this you have to > introduce complications that are not inherent in the original Schrodinger > equation and are largely incompatible with simple unitary state evolution. > > Bruce > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com. > To view this discussion visit > https://groups.google.com/d/msgid/everything-list/CAFxXSLR50MgHVjm91s%3Dnz5urL98RSLGAC6FANmj23OMQbjOBXg%40mail.gmail.com > <https://groups.google.com/d/msgid/everything-list/CAFxXSLR50MgHVjm91s%3Dnz5urL98RSLGAC6FANmj23OMQbjOBXg%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. 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