On Monday, December 25, 2017 at 5:49:34 AM UTC, [email protected] wrote: > > > > On Monday, December 25, 2017 at 3:11:25 AM UTC, [email protected] wrote: >> >> >> On Sunday, December 24, 2017 at 9:33:56 AM UTC, Russell Standish wrote: >>> >>> On Sat, Dec 23, 2017 at 02:10:44PM -0800, [email protected] wrote: >>> > >>> > >>> > On Saturday, December 23, 2017 at 2:11:32 PM UTC-7, Russell Standish >>> wrote: >>> > > >>> > > On Sat, Dec 23, 2017 at 09:20:05AM -0800, [email protected] >>> > > <javascript:> wrote: >>> > > > >>> > > > My tentative solution to the wave collapse problem is to trash >>> wave >>> > > > mechanics (which is not Lorentz invariant) and use Heisenberg's >>> Matrix >>> > > > Mechanics. No waves, nothing to collapse. Is this a cop-out? AG >>> > > >>> > > In matrix mechanics, the wave function is replaced by a vector, and >>> > > collapse is replaced by a projection onto a basis vector. >>> > > >>> > > Projections are not unitary (except for the identity matrix), and >>> that >>> > > is the problem with any collapse type theory. >>> > > >>> > >>> > Thanks. That's clears enough. Collapse by another name. CMIIAW, but >>> even if >>> > it were a unitary process, it would in effect be a local hidden >>> variable, >>> > forbidden by results of Bell experiments. But let's talk about >>> "unitary" >>> > which I think is equivalent to "linear". Why is non unitary, that is >>> non >>> > linear bad? Because it means irreversible? I do believe that some >>> > measurement processes are in fact irreversible in principle, and not >>> simply >>> > in the statistical sense, that is, FAPP. IIRC, Bruce proved that for >>> spin >>> > measurements on Avoid2, but it was not well received. AG >>> > >>> I >>> Unitary does not mean linear. >> >> >> *OK. I was thinking of the time evolution operator, denoted by U, which I >> believe is linear in t. AG* >> > > *Not linear in t, but also named "unitary operator", not to be confused > with the operator by the same name that preserves inner products. AG* >
*Another correction: the time evolution operator is a unitary operator since it preserves inner products, but it is NOT NAMED a unitary operator. AG * > > > >> Projection operators are linear. >> >> >> >> >> >> *IIUC, projection operators model the "collapse" of the superposition of >> states to a single state within the superposition. Since the measurement >> process is believed to be non linear, how can the projection operator be >> linear? AGThis raises a question about decoherence. If the myriad of >> individual processes are linear, which I believe is what the model affirms, >> how can any measurement be non linear as it presumably is for spin >> measurements. AG* >> >>> Unitary >>> means that applying the operator to a group of vectors preserves their >>> lengths and the angles between them. Effectively just a coordinate >>> transformation. Another property conserved is overall probability. >>> >>> By constrast projections (or as my maths lecturer was fond of saying >>> "elephant foot map") squash things. Like the cockroach under my shoe, >>> lengths and angles between components are not preserved. >>> >>> Cheers >>> >>> -- >>> >>> ---------------------------------------------------------------------------- >>> >>> >>> Dr Russell Standish Phone 0425 253119 (mobile) >>> Principal, High Performance Coders >>> Visiting Senior Research Fellow [email protected] >>> Economics, Kingston University http://www.hpcoders.com.au >>> ---------------------------------------------------------------------------- >>> >>> >>> >> -- 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 post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
