From: <agrayson2...@gmail.com <mailto:agrayson2...@gmail.com>
On Friday, April 20, 2018 at 1:18:32 AM UTC, Bruce wrote: From: *Bruno Marchal* <mar...@ulb.ac.be>On 18 Apr 2018, at 15:45, Bruce Kellett <bhke...@optusnet.com.au> wrote: From: *Bruno Marchal* <mar...@ulb.ac.be>On 17 Apr 2018, at 13:52, Bruce Kellett <bhke...@optusnet.com.au> wroteBut 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.
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