On Monday, December 25, 2017 at 8:28:30 PM UTC, Russell Standish wrote: > > On Sun, Dec 24, 2017 at 07:11:25PM -0800, agrays...@gmail.com > <javascript:> wrote: > > > > *OK. I was thinking of the time evolution operator, denoted by U, which > I > > believe is linear in t. AG* > > Yes, it is linear and unitary. Unitary operators are linear, but > linear operators are not necessarily unitary. That is what I meant > when I said "unitary is not linear". They are not synonyms. > > > > > > > > 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? > > I've never heard of a nonlinear measurement process. Who believes > that? The only person who's done any work researching nonlinear QM was > Weinberg IIRC. >
*Spin measurements are irreversible in principle, not simply FAPP. Bruce showed that on Avoid2 IIRC. I think this means the measurement process,at least in this case, must be non-linear. If that's true, then how can a linearprocess such as decoherence, model measurements? AG* > > von Neumann's proposal was to use projection operators, which are > linear, but non-unitary. Being non-unitary is a problem, given unitary > evolution is one of the foundational axioms of QM. > *Unitary evolution does not extend to the measurement process; onlyevolution of the wf prior to measurement. AG * > > > This 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* > > > > Indeed that would be a problem. A sum of unitary operators need not be > unitary, though. > > > > -- > > ---------------------------------------------------------------------------- > > Dr Russell Standish Phone 0425 253119 (mobile) > Principal, High Performance Coders > Visiting Senior Research Fellow hpc...@hpcoders.com.au > <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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
