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* > 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.
