On Friday, April 20, 2018 at 11:40:13 AM UTC, Bruce wrote: > > From: <[email protected] <javascript:> > > > On Friday, April 20, 2018 at 1:18:32 AM UTC, Bruce wrote: >> >> From: Bruno Marchal <[email protected]> >> >> On 18 Apr 2018, at 15:45, Bruce Kellett <[email protected]> wrote: >> >> From: Bruno Marchal <[email protected]> >> >> On 17 Apr 2018, at 13:52, Bruce Kellett <[email protected]> wrote >> >> >> But note particularly that the spin measurement is made in the basis >> chosen by the experimenter (by orienting his/her magnet). >> >> >> OK. >> >> The outcome of the measurement is + or -, >> >> >> For Alice and Bob, OK. >> >> not one of the possible infinite set of possible basis vector >> orientations. The orientation is not measured, it is chose by the >> experimenter. So that is one potential source of an infinite set of worlds >> eliminated right away. The singlet is a superposition of two states, + and >> -: it is not a superposition of possible basis vectors. >> >> >> ? (That is far too ambiguous). >> >> >> ????? It is not in the least ambiguous. The singlet state is not a >> superposition of basis vectors. >> >> > Actually, to clarify, I meant a superposition of vectors from different > bases. > > >> ? >> >> The singlet state is the superposition of Iup>IMinus> and (Minus>Iup>. >> >> >> Those are not generalized basis vectors: they are eigenfunctions of the >> spin projection operator in a particular basis. The singlet state is not a >> superposition of vectors from different bases. >> > > *Bruce; I found your above comment confusing and it led to subsequent > questions that LC found inappropriately technical or detailed for this > forum (which it isn't IMO). Why do you bring in superpositions from > different bases? I never saw that used in QM texts.* > > > No, you wouldn't see it in QM texts because it is not something that one > would usually do, because, as Brent and I discussed, it is rather > pointless. Any vector in the Hilbert space can be expressed as a linear > superposition of basis vectors, and the basis vectors in any basis are just > further vectors in the space, after all. So expanding in multiple bases can > always be reduced to an expansion in a single base. Which base is > immaterial. > > *Additionally, isn't Bruno correct that the above expression for the > singlet state which your earlier wrote down, IS a superposition in the > UP/DN basis? AG* > > > No, what Bruno wrote was "a superposition of "Iup>IMinus> and > (Minus>Iup>", which I took to mean an attempt to expand the singlet state > in two bases simultaneuosly -- the (|Plus>, |Minus>) base and the > (|up>,|down>) base. It is difficult to see exactly what this would achieve; > it seems to be merely a more complicated base. > > Bruce >
I think by |minus> he just meant |dn>. AG -- 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.
