> On 29 Oct 2018, at 13:55, agrayson2...@gmail.com 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 <javascript:> 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 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 It explains very well the difference between mixtures and pure states. 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 <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.