On Wed, Feb 26, 2025 at 7:08 PM Quentin Anciaux <[email protected]> wrote:
> Le mer. 26 févr. 2025, 01:53, Brent Meeker <[email protected]> a > écrit : > >> On 2/25/2025 5:09 PM, Russell Standish wrote: >> >> On Wed, Feb 26, 2025 at 11:01:11AM +1100, Bruce Kellett wrote: >> >> On 2/24/2025 6:09 PM, Quentin Anciaux wrote: >> >> Your claim that "one observer per branch" follows directly from >> unitary >> evolution is an assumption, not a derivation. >> >> >> No, it is a straightforward derivation from the formalism. If you don't >> understand that, it is just further confirmation of the fact that you >> understand very little about quantum mechanics. >> >> Not at all - it is an assumption you're making, and the nub of the entire >> argument between you and Quentin. >> >> Do you understand Quentin's theory? ISTM it's just "Observer counting" >> where the counts instantiate the Born rule ex hypothesi. It's branch >> counting by another name. >> >> Brent >> > > Brent, > > You’re still misrepresenting the argument. It’s not branch counting under > another name, it’s about how measure determines observer frequencies. The > issue is whether the number of observer instances scales with amplitude > squared, not whether we simply count branches. If all branches were > weighted equally, MWI would have been dead on arrival, because it wouldn’t > match experiments. > > The claim that “one observer per branch” is a direct consequence of > unitary evolution is just an assumption, it’s not something derived from > the Schrödinger equation. > It is derived from that, or the Schrodinger equation enhanced with unitary evolution and the linearity of Hilbert space. Since you clearly don't get it. Let me spell it out in baby steps. We start from the wave function for some system, say |psi>. This is the expanded in some basis like |psi> = a|0> + b|1>, where I have taken a two dimensional space for clarity and convenience, although the argument is easily expanded to an arbitrary number of independent basis states. We then measure this state (or subject it to some interaction). |psi>|O>|E> where |O> is an observer, and |E> is the environment which can include anything else that is relevant. Linear unitary evolution then entangles both the observer and the environment with the object state: |psi>|O>|E> = (a|0> + b|1>)|O>|E> --> a|O sees zero>|E records zero>|0> + b|O sees one>|E records one>|1>, One can readily see that there is one, and only one, copy of the observer for each branch. Decoherence renders these branches approximately orthogonal, and leads to the notion of independent worlds. The argument can, of course, be readily generalized to a state with any number of basis vectors. In no case, do we get more than one copy of the observer on any branch, and there are no branches without a copy of the observer. All of this is just elementary linear unitary evolution, taught in general quantum mechanics courses. If you want to deny this, you have to go to some other theory which is incompatible with quantum mechanics. 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/CAFxXSLR8x8s7N6-gQmgSmAj_TD8MCi%3DB7nKTpbxkGWB1PUXEOA%40mail.gmail.com.
