On Sunday, November 3, 2019 at 4:17:28 PM UTC-6, Brent wrote: > > > > On 11/3/2019 10:43 AM, Philip Thrift wrote: > > In order for this statement to be useful, we need to solve the preferred > basis problem. For example, consider the mathematical identity > > |u a w> + |e d c> = |n+ s+ f+> + |n+ s- f-> + |n- s+ f-> + |n- s- f+> (2) > > where > > |n+> = |u> + |e>, |n-> = |u> - |e> > |s+> = |a> + |d>, |s-> = |a> - |d>, > |f+> = |w> + |c>, |f-> = |w> - |c>. > > Unless we introduce a further piece of interpretive apparatus, we are in > danger of supposing that the system described by |phi> is also described by > |n+ s+ f+> or each of the other components in (2), which would mean we have > not solved the original problem. However, this is easily solved, as follows: > Postulate 1. A quantum system and environment described by the state |phi> > is also described by one of the states of the basis in which the reduced > density matrix of |phi> is diagonal after the environment has been traced > over. > The `collapse' from |phi> to one of |u a w> and |e d c> is now no > different from the abrupt change in a classical probability distribution > when more information becomes available. > > > At this point one is then tempted to ask why not just say the wf > collapsed? Tracing over the environment is already something the > experimenter does on paper. It's not part of the Schroedinger equation > unitary evolution. Sure it makes the off-diagonal terms small...but it > doesn't make them zero. It's still just FAPP. > > > Brent >
In effect at this point it is much the same as with decoherence where a density matrix is reduced to diagaonals and it is a classical probability "collapse." LC -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/4b05b819-2c7e-4890-aa3a-117b683d46d1%40googlegroups.com.
