Bruce, Your argument assumes that all branches are equally weighted in terms of observer experience, which contradicts what we actually see in quantum experiments. The claim that the Schrödinger equation is "insensitive" to amplitudes is incorrect. The amplitudes evolve deterministically under the Schrödinger equation and define the measure associated with each outcome. The Born rule does not need to be "inserted" into MWI—it emerges naturally if one considers measure as determining how many observer instances experience each outcome.
Your claim that there are exactly 2^N observers after N trials and that each one "counts equally" ignores what measure represents. The fundamental point is that not all branches contribute equally to what an observer experiences. Yes, an observer exists on every branch, but that does not mean they exist in equal numbers. In standard probability theory, an event occurring in more instances is simply more likely to be observed. Similarly, in MWI: A branch with a higher amplitude means there are exponentially more copies of the observer experiencing that outcome. This is not "assigning degrees of existence"—it is stating that measure determines how many versions of an observer find themselves in a given sequence. You can call this "silly," but it's the only way MWI remains consistent with experiments. If each observer counted equally across all branches, we would expect uniform probabilities, contradicting the Born rule. The Schrödinger equation is not "insensitive" to amplitudes; it governs their evolution. The amplitudes define how much of the total wavefunction exists in each outcome. Saying that amplitudes are "inert" is like saying that in classical probability, event frequencies are "inert" because the probability distribution does not dynamically change per trial. The fact that amplitudes don’t directly affect local observations does not mean they are irrelevant. You do not need to "see" probability distributions to experience their effects. In classical cases, you observe probabilities through frequency distributions—not because you see an abstract probability function floating in space. Similarly, in MWI, you experience the effects of amplitude-based measure because the majority of your copies exist in branches that follow the Born rule. Your argument frames measure as a metaphysical claim about "degrees of existence," but that’s a strawman. Measure is not about some observers being "more real" than others—it’s about how many instances of a given observer exist in different branches. Imagine a lottery where some numbers are printed millions of times and others are printed once. Saying "each ticket exists, so all are equal" ignores the fact that you are overwhelmingly more likely to pick a ticket that was printed millions of times. This is exactly what happens in MWI: Yes, every sequence of outcomes exists. But observers overwhelmingly find themselves in high-measure sequences because there are simply more instances of them there. If your claim were correct, quantum mechanics would fail to match experiment, because the observed frequencies would not match the Born rule. Since that never happens, the conclusion is clear: measure, not naive branch counting, determines what observers experience. Yes, there is currently no clear cut theories to recover the born rule from Schrödinger equation alone, doesn’t mean there aren't. Also I'm not an advocate of MWI per se, I prefer information theory approach from which we should be able to recover MW like theories and a measure (maybe mixing some UD and speed prior) Quentin Le mar. 11 févr. 2025, 00:36, Bruce Kellett <[email protected]> a écrit : > On Tue, Feb 11, 2025 at 9:32 AM Quentin Anciaux <[email protected]> > wrote: > >> >> Your argument is based on treating the measurement process as merely >> counting sequences of zeros and ones, while dismissing the amplitudes as >> “just numbers.” But this ignores that the wavefunction governs the >> evolution of the system, and the amplitudes are not arbitrary labels—they >> encode the structure of reality. The Schrodinger equation evolves the >> system deterministically, and when measurement occurs, the measure of each >> branch determines how many observer instances find themselves in it. >> > > The Schrodinger equation is completely insensitive to the amplitudes. They > are just carried along as inert parameters. It is the interpretation > according to the Born rule that makes sense of this structure. But the Born > rule, and probability interpretations per se, are not in the Schrodinger > equation. > > You claim that the amplitude of a sequence does not affect what is >> measured, yet this is exactly what determines how many observers experience >> a given sequence. >> > > Where on earth did you get that incredible idea -- that the number of > observers depends on the amplitudes? > > According to MWI there is a branch for every possible value, and the > observer splits along with the branching, so there is an observer on every > branch. After N trials of the binary case, there are 2^N branches, with an > observer (copy of the original experimenter) on every branch. These all > exist equally, so your idea of weighting the branches according to the > amplitudes makes no sense: there can be no "degrees of existence". All the > observers exist equally, so all are equally entitled to count zeros to get > an estimate of the underlying probability. > > The claim that “you do not ever see the amplitude” misses the point: you >> do not directly observe measure, but you observe its consequences. The >> reason we see Born-rule statistics is that the measure dictates the >> relative number of observers experiencing different sequences. >> > > That is assuming that there can be "degrees of existence" such that > observers on Born-anomalous branches do not exist as strongly as those who > see the correct statistics. This is not an idea that is in the Schrodinger > equation, it is not in the mathematics, it is just plain silly. The > amplitudes do not give 'degrees of existence" nor do they give different > relative numbers of observers for each sequence. The mathematics of the > Schrodinger equation are clear, and they do not support any such ideas. > > 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/CAFxXSLSnE0YvUR3SqKZZwPsGyzxOvaXRk3CHoSk52M3qSMq_GQ%40mail.gmail.com > <https://groups.google.com/d/msgid/everything-list/CAFxXSLSnE0YvUR3SqKZZwPsGyzxOvaXRk3CHoSk52M3qSMq_GQ%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/CAMW2kAp665GXSOaxJEoFjR5nEed7XNMpynK7YtuiSJ6bpJzPTg%40mail.gmail.com.
