> On 30 Oct 2018, at 14:21, agrayson2...@gmail.com wrote: > > > > On Tuesday, October 30, 2018 at 8:58:30 AM UTC, Bruno Marchal wrote: > >> On 29 Oct 2018, at 13:55, agrays...@gmail.com <javascript:> wrote: >> >> >> >> On Monday, October 29, 2018 at 10:22:02 AM UTC, Bruno Marchal wrote: >> >>> On 28 Oct 2018, at 13:21, agrays...@gmail.com <> wrote: >>> >>> >>> >>> On Sunday, October 28, 2018 at 9:27:56 AM UTC, Bruno Marchal wrote: >>> >>>> On 25 Oct 2018, at 17:12, agrays...@gmail.com <> wrote: >>>> >>>> >>>> >>>> On Tuesday, October 23, 2018 at 10:39:11 PM UTC, agrays...@gmail.com >>>> <http://gmail.com/> wrote: >>>> If a system is in a superposition of states, whatever value measured, will >>>> be repeated if the same system is repeatedly measured. But what happens >>>> if the system is in a mixed state? TIA, AG >>>> >>>> If you think about it, whatever value you get on a single trial for a >>>> mixed state, repeated on the same system, will result in the same value >>>> measured repeatedly. If this is true, how does measurement distinguish >>>> superposition of states, with mixed states? AG >>> >>> That is not correct. You can distinguish a mixture of particles in the up >>> or down states with a set of 1/sqrt(2)(up+down) by measuring them with the >>> {1/sqrt(2)(up+down), 1/sqrt(2)(up-down}) discriminating apparatus. With the >>> mixture, half the particles will be defected in one direction, with the >>> pure state, they will all pass in the same direction. Superposition would >>> not have been discovered if that was not the case. >>> >>> And someone will supply the apparatus measuring (up + down), and (up - >>> down)? No such apparatuses are possible since those states are inherently >>> contradictory. We can only measure up / down. AG >> >> You can do the experience by yourself using a simple crystal of calcium >> (CaCO3, Island Spath), or with polarising glass. Or with Stern-Gerlach >> devices and electron spin. Just rotating (90° or 180°) an app/down >> apparatus, gives you an (up + down)/(up - down) apparatus. >> >> I don't understand. With SG one can change the up/down axis by rotation, but >> that doesn't result in an (up + down), or (up - down) measurement. If that >> were the case, what is the operator for which those states are eigenstates? >> Which book by Albert? AG > > David Z Albert, Quantum Mechanics and Experience, Harvard University Press, > 1992. > https://www.amazon.com/Quantum-Mechanics-Experience-David-Albert/dp/0674741137 > > <https://www.amazon.com/Quantum-Mechanics-Experience-David-Albert/dp/0674741137> > > Another very good books is > > D’Espagnat B. Conceptual foundations of Quantum mechanics, I see there is a > new edition here: > https://www.amazon.com/Conceptual-Foundations-Quantum-Mechanics-Advanced/dp/0738201049/ref=sr_1_1?s=books&ie=UTF8&qid=1540889778&sr=1-1&keywords=d%27espagnat+conceptual+foundation+of+quantum+mechanics&dpID=41NcluHD6fL&preST=_SY291_BO1,204,203,200_QL40_&dpSrc=srch > > <https://www.amazon.com/Conceptual-Foundations-Quantum-Mechanics-Advanced/dp/0738201049/ref=sr_1_1?s=books&ie=UTF8&qid=1540889778&sr=1-1&keywords=d%27espagnat+conceptual+foundation+of+quantum+mechanics&dpID=41NcluHD6fL&preST=_SY291_BO1,204,203,200_QL40_&dpSrc=srch> > > It explains very well the difference between mixtures and pure states. > > Bruno > > Thanks for the references. I think I have a reasonable decent understanding > of mixed states. Say a system is in a mixed state of phi1 and phi2 with some > probability for each. IIUC, a measurement will always result in an eigenstate > of either phi1 or phi2 (with relative probabilities applying).

If the measurement is done with a phi1/phi2 discriminating apparatus. Keep in mind that any state can be seen as a superposition of other oblique or orthogonal states. > So if we're measuring spin, the result will always be an eigenstate of the > spin vector for phi1 or phi2. But (up + down) and (up - down) are NOT > eigenstates of either. How then can you justify your claim of measuring (up + > down) or (up - down)? AG By rotating the polariser filter: (abstracting from some normalising factor which is supposed to be 1/sqrt(2)) up’ = up + down down’ = up - down up = up’ + down’ down = up’ - down’ If you measure a set of photons all in the state up’= up+down in the base {up’, down’}, they all get the same result up'. If you measure a set of photons from a mixture of up and down, in the same base {up’, down’}, half of them will be up’, and half of them will be down’. Bruno > >> Buy the book by David Albert. It will help you a lot, I think. >> >> Bruno >> >> >> >> >> >>> >>> Bruno >>> >>> >>> >>> >>> >>>> >>>> -- >>>> 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-li...@googlegroups.com <>. >>>> To post to this group, send email to everyth...@googlegroups.com <>. >>>> Visit this group at https://groups.google.com/group/everything-list >>>> <https://groups.google.com/group/everything-list>. >>>> For more options, visit https://groups.google.com/d/optout >>>> <https://groups.google.com/d/optout>. >>> >>> >>> -- >>> 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-li...@googlegroups.com <>. >>> To post to this group, send email to everyth...@googlegroups.com <>. >>> Visit this group at https://groups.google.com/group/everything-list >>> <https://groups.google.com/group/everything-list>. >>> For more options, visit https://groups.google.com/d/optout >>> <https://groups.google.com/d/optout>. >> >> >> -- >> 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-li...@googlegroups.com <javascript:>. >> To post to this group, send email to everyth...@googlegroups.com >> <javascript:>. >> Visit this group at https://groups.google.com/group/everything-list >> <https://groups.google.com/group/everything-list>. >> For more options, visit https://groups.google.com/d/optout >> <https://groups.google.com/d/optout>. > > > -- > 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 > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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.