On Sun, Dec 24, 2017 at 07:11:25PM -0800, agrayson2...@gmail.com 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. 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. > 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* > 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 hpco...@hpcoders.com.au 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.
