Bruce, You insist that no matter what is added to MWI, it cannot recover the Born rule. But that’s not an argument, it’s a claim. The fact that multiple approaches attempt to derive it suggests the issue is far from settled. Dismissing them without engaging with their reasoning does not refute them. (I still have to read the links from Brent)
You also say you don’t know what it would mean to "count sequences" yet your argument relies on using observed frequency in a single binary sequence to estimate probability. But this only works if all sequences contribute equally to experience, which is precisely the assumption you claim not to make. If every observer in MWI experiences a sequence independent of its amplitude, then we should observe a uniform distribution of outcomes rather than Born-rule statistics. That does not happen, which suggests that something in the structure of MWI suppresses low-measure branches from dominating experience. (See lottery example with multiple printing of same number) You ask why the same 2^N sequences appear regardless of the initial amplitudes. That’s expected, unitary evolution does not prevent sequences from existing, all do exists exhypothesi. But the real question is whether all sequences contribute equally to observer experience. If you believe MWI fundamentally cannot account for the Born rule, you need more than dismissals. Naive sequence (aka branch) counting is not correct to infer probability without measure of such sequence in the set. Your argument that measure has no effect remains unsupported imo. Quentin Le mer. 12 févr. 2025, 23:00, Bruce Kellett <[email protected]> a écrit : > On Wed, Feb 12, 2025 at 9:51 AM Quentin Anciaux <[email protected]> > wrote: > >> 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 >> > > But the point is that no matter what you add to MWI, the basic structure > of the theory makes any attempt to draft in the Born rule impossible. > > > Your argument rests on the claim that all sequences exist independently of >> their amplitudes, meaning that counting sequences alone should determine >> probabilities. >> > > Where on earth did you get this idea? I don't even know what it might mean > to count sequences. The idea is that in any observed sequence of zeros and > ones, the proportion of zeros gives an estimate of the probability of > finding a zero. This is basic statistics 101. > > > 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. >> > > This is just incoherent rubbish. > > 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. >> > > Explain to me why it is that in the binary case under discussion, with N > trials, you get the same 2^N binary sequences of length N for any > combination of initial amplitudes. > > > 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. >> > > I do not know what such an assumption could mean, and I challenge you to > point out exactly where I make such an assumption. If you mean no more than > that the same conclusion is reached regardless of which binary sequence one > looks at, then I agree. But that is not an assumption, it is a conclusion > of the argument. > > 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 [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/everything-list/CAFxXSLQfoiMf-L%3DUT7af2PL_h9easFWDDAzHaVfOx8-Ns-p35A%40mail.gmail.com > <https://groups.google.com/d/msgid/everything-list/CAFxXSLQfoiMf-L%3DUT7af2PL_h9easFWDDAzHaVfOx8-Ns-p35A%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 [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/CAMW2kAq%2BqhWgDQf-3rzjzh7HsK5L8aGKhTTFWFPfBz5wGxiBOA%40mail.gmail.com.
