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] > <javascript:> 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* > 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] > <javascript:> > 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.
