> On 29 Oct 2018, at 13:55, [email protected] wrote: > > > > On Monday, October 29, 2018 at 10:22:02 AM UTC, Bruno Marchal wrote: > >> On 28 Oct 2018, at 13:21, [email protected] <javascript:> wrote: >> >> >> >> On Sunday, October 28, 2018 at 9:27:56 AM UTC, Bruno Marchal wrote: >> >>> On 25 Oct 2018, at 17:12, [email protected] <> wrote: >>> >>> >>> >>> On Tuesday, October 23, 2018 at 10:39:11 PM UTC, [email protected] >>> <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 [email protected] <>. >>> To post to this group, send email to [email protected] <>. >>> 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 [email protected] <javascript:>. >> To post to this group, send email to [email protected] >> <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 [email protected] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > 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 [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.
