On Monday, December 25, 2017 at 8:28:30 PM UTC, Russell Standish wrote: > > On Sun, Dec 24, 2017 at 07:11:25PM -0800, [email protected] > <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 [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.
