The Born rule states that the probability of an outcome is given by the square of the amplitude associated with that outcome.
If amplitudes were arbitrary and did not influence observed frequencies, then the Born rule itself would be meaningless. Quentin Le mar. 18 févr. 2025, 02:22, Alan Grayson <[email protected]> a écrit : > > > On Monday, February 17, 2025 at 6:06:35 PM UTC-7 Quentin Anciaux wrote: > > AG, > > The problem with your claim is that you're assuming what needs to be > proven. The amplitudes don’t just "drop out" when considering observed > frequencies, because they determine how many copies of an observer exist in > each branch. This is exactly why naive branch counting is incorrect. > > Consider the thought experiment I described to Bruce: If an observer is > duplicated 10 times, and 9 copies see "1" while 1 sees "0," then after > multiple trials, we still get 2^N sequences, but they are not equiprobable. > The overwhelming majority of observers will experience frequencies biased > toward "1" simply because there are exponentially more of them. > > In MWI, the amplitudes govern the relative number of observers in each > branch, just like the duplication process in the analogy. Saying the > amplitudes "drop out" is only true if you assume each branch has an equal > number of observers, which is exactly what is in question. > > You claim that the math says amplitudes don’t matter—but then why do we > always observe Born-rule frequencies? If amplitudes were irrelevant, we > would expect uniform distributions across experiments, contradicting every > quantum measurement ever made. > > Quentin > > > *I think amplitudes don't matter for two reasons; they aren't solved for > using S's equation, and they can be arbitrarily assigned without changing > the results of Born's rule. AG* > > > Le mar. 18 févr. 2025, 01:47, Alan Grayson <[email protected]> a écrit : > > > > On Monday, February 17, 2025 at 5:09:58 PM UTC-7 Bruce Kellett wrote: > > On Tue, Feb 18, 2025 at 11:01 AM Quentin Anciaux <[email protected]> > wrote: > > > You didn’t prove that MWI is inconsistent with the Born rule, you assumed > it by asserting that all 2^N sequences contribute equally, which is not how > MWI works. The amplitude coefficients do matter, they determine the measure > of each sequence, which affects the relative frequency of observed outcomes. > > Your argument rests on the assumption that sequences exist independently > of their amplitudes, but you haven’t justified why the observer should > expect a uniform distribution rather than one weighted by the > wavefunction’s structure. This is precisely the question that needs to be > answered, not assumed away. > > > The basic premise of MWI is that every possible outcome of an experiment > actually occurs, albeit on a separate branch with a separate copy of the > experimenter. This means that N trials on the binary state, give 2^N binary > sequences, covering all possible binary sequences of length N. This same > set of binary sequences is obtained for any values of the original > amplitudes. > > If you disagree with this simple mathematics, then I challenge you to > point out where it is wrong. And that does not mean just assuming that it > has something to do with the emplitues. The mathematics of the Schrodinger > equation says that they play no role in the formation of these 2^N > sequences. > > Bruce > > > Strange isn't it how the strong advocates of the MWI generally rely on > mathematics, but ignore it when it clearly says something they refuse to > believe; namely, that the amplitudes drop out when calculating > probabilities of complex functions. It's no wonder that they can't prove > Born's rule for the MWI, when they ignore basic mathematics. Lesson > learned; the amplitudes do NOT matter in determining relative frequency of > observed outcome. They can be changed arbitrarily without changing the > outcomes. AG > > -- > 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/e017423d-235b-4804-ae9a-5f5621b8574fn%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/e017423d-235b-4804-ae9a-5f5621b8574fn%40googlegroups.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/CAMW2kArzUn_v3K3nkB%3DTGZYNTDXLmgH9qrJHuv%3D1OzPsoqsxWg%40mail.gmail.com.
