On Tuesday, June 5, 2018 at 7:03:28 AM UTC, Bruce wrote: > > From: <[email protected] <javascript:>> > > > On Tuesday, June 5, 2018 at 1:18:29 AM UTC, Bruce wrote: >> >> From: <[email protected]> >> >> >> Remember that the analysis I have given above is schematic, representing >> the general progression of unitary evolution. It is not specific to any >> particular case, or any particular number of possible outcomes for the >> experiment. >> >> Bruce >> >> *OK. For economy we can write, ** (|+>|e+> + |->|e->), where e stands >> for the entire universe other than the particle whose spin is being >> measured. What is the status of the interference between the terms in this >> superposition? For a quantum superposition to make sense, there must be >> interference between the terms in the sum. At least that's my understanding >> of the quantum principle of superposition. But the universe excluding the >> particle being measured seems to have no definable wave length; hence, I >> don't see that this superposition makes any sense in how superposition is >> applied. Would appreciate your input on this issue. TIA, AG* >> >> >> A superposition is just a sum of vectors in Hilbert space. If these >> vectors are orthogonal there is no interference between them. >> > > *As a graduate student, in one of those standard problems, I seem to > recall solving for the wf of some system using the SWE, and then expanding > the solution using an orthonormal set of eigenfunctions as the basis (or > maybe it was claimed there exists such an expansion). Are you saying there > is no interference between the basis eigenvectors? TIA, AG* > > > Basis vectors need not be orthogonal. But if you choose and orthonormal > set then the individual basis vectors do not interfere, though the > superposition made up of such a set may be thought of as an interference > between them. But unless you take the product of this superposition with > something else, you do not have interference cross terms. This is similar > to the basis problem I referred to earlier. If we have a basis of |dead> > and |alive>, being mutually orthogonal, then the basis vectors > (|dead>+|alive>) and (|dead>-|alive>) are also orthonormal. But this basis > is not stable under decoherence, so the environmental states corresponding > to this basis do interfere to produce the stable |e_dead> and |e_alive> > states. > > Thus, if the orthogonal basis you choose is such that the interaction of > each basis vector with the environment leads to orthogonal environment > vectors, then there is no interference between these environmental states > -- this is how classical states emerge. > > Bruce >
*So in the case of the S Cat, the superposition, ( |alive> |undecayed> + |dead>|decayed> ) , does NOT imply the cat is simultaneously alive and dead because the states in this superposition are orthogonal? If that's your conclusion, and if I am not misreading the discussions of this problem incorrectly, most, if not all of the texts which discuss this problem are completely misleading. Is that the situation? 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.
