> On 30 Nov 2019, at 02:35, 'Brent Meeker' via Everything List > <everything-list@googlegroups.com> wrote: > > > > On 11/28/2019 4:17 PM, Bruce Kellett wrote: >> On Fri, Nov 29, 2019 at 5:12 AM 'Brent Meeker' via Everything List >> <everything-list@googlegroups.com <mailto:everything-list@googlegroups.com>> >> wrote: >> On 11/27/2019 11:51 PM, Philip Thrift wrote: >>> >>> This was the issue about mass raised weeks ago when Sean Carroll's book >>> came out. >>> >>> There has never been an answer. >> >> If you think in terms of the wf of the multiverse, it's just a ray in >> Hilbert space and moves around. It doesn't split. What "splits" is the >> subspace we're on. So when we measure a spin as UP or DOWN, our subspace >> splits into two orthogonal subspaces on which the ray projects. But they >> are only orthogonal on that one dimension (the spin of that particle), so >> any other variable encoded in the ray gets projected with the same value as >> before, e.g. the energy or the particle. >> >> Right. The subsystem we are considering (an electron fired at a screen or >> through an S-G magnet) is just a subspace of the full Hilbert space. We can >> take the tensor product of this subspace with the rest of the universe to >> recover the full Hilbert space: >> >> |universe> = |system>{\otimes}|environment> >> >> We can then analyse the system in some basis: >> >> |system> = Sum_i c_i |basis_i>, >> >> where c_i are complex coefficients, and |basis_i> are the basis vectors for >> (i = 1, ..,, N), N being the dimension of the subspace. >> >> It is assumed that the normal distributive law of vector algebra acts over >> the tensor product, so each basis vector then gets convoluted with the same >> 'environment' in each case, we have >> >> |universe> = Sum_i c_i (|basis_i>|environment>). >> >> Each basis vector is a solution of the original Schrodinger equation, so it >> carries the full energy, moment, change etc, of the original state. > > ?? The basis just defines a coordinate system for the Hilbert space. It > doesn't mean that the wf ray has any component along a basis vector. The c_i > can be zero; in which case that basis vector doesn't carry anything. No > every Schrodinger equation solution is realized because initial conditions > may make it zero. > >> The environment is just the rest of the universe minus the quantum >> quantities associated with the system of interest. So each term in this sum >> has the full energy, charge, and so on of the original state. >> >> If we take each component of the above sum to represent a self-contained >> separate world, then all quantum numbers are conserved in each world. >> Whether there is global conservation depends on how we treat the >> coefficients c_i. But, on the face of it, there are N copies of the >> basis+environment in the above sum, so everything is copied in each >> individual world. Exactly how you treat the weights in this situation is not >> clear to me -- if they are treated as probabilities, it seems that you just >> have a stochastic single-world model. > > Yes, I think that's right. Which is the attraction of the epistemic > interpretation: you treat them as probabilities so you renormalize after the > measurement. And one problem with the ontic interpretation is saying what > probability means. But it seems that the epistemic interpretation leaves the > wf to be a personal belief.
It is a first person plural belief, sharable by vast collection of interacting universal entities whose existence can be proved in weak theory of arithmetic. It is a view from inside any model of arithmetic, but unprovable in any theory of arithmetic. Bruno > > Brent > > -- > 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 > <mailto:everything-list+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/22ed1ee3-fc94-89bd-475d-95a9f603bdc7%40verizon.net > > <https://groups.google.com/d/msgid/everything-list/22ed1ee3-fc94-89bd-475d-95a9f603bdc7%40verizon.net?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. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/93899B02-B27E-480B-8EF0-4CE04F3AB6AF%40ulb.ac.be.
