On Tuesday, November 6, 2018 at 11:22:21 AM UTC, [email protected] wrote: > > > > On Tuesday, November 6, 2018 at 9:27:31 AM UTC, Bruno Marchal wrote: >> >> >> On 4 Nov 2018, at 22:02, [email protected] wrote: >> >> >> >> On Sunday, November 4, 2018 at 8:33:10 PM UTC, jessem wrote: >>> >>> >>> >>> On Wed, Oct 31, 2018 at 7:30 AM Bruno Marchal <[email protected]> wrote: >>> >>>> >>>> On 30 Oct 2018, at 14:21, [email protected] wrote: >>>> >>>> >>>> >>>> On Tuesday, October 30, 2018 at 8:58:30 AM UTC, Bruno Marchal wrote: >>>>> >>>>> >>>>> 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] 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] >>>>>>> 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 >>>>> >>>> >>>> *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. >>>> >>> >>> I don't know if you're restricting the definition of phi1 and phi2 to >>> some particular type of eigenstate or not, but in general aren't there pure >>> states that are not eigenstates of any physically possible measurement >>> apparatus, so there is no way to directly measure that a system is in such >>> a state? >>> >> >> *Yes, such states exist IIUC. That's why I don't understand Bruno's claim >> that Up + Dn and Up - Dn can be measured with any apparatus, * >> >> >> Not *any*¨apparatus, but a precise one, which in this case is the same >> apparatus than for up and down, except that it has been rotated. >> >> >> >> >> *since they're not eigenstates of the spin operator, or any operator. * >> >> >> This is were you are wrong. That are eigenstates of the spin operator >> when measured in some direction. >> > > *If what you claim is true, then write down the operator for which up + dn > (or up - dn) is an eigenstate? AG * >
*If you measure up/dn in one orientation, and then rotate the apparatus to measure up/dn in another orientation, how does that result in an up + dn or up - dn measurement which is now an eigenstate of some spin operator? AG* > > >> Julian Swinger (and Townsend) showed that the formalism of (discrete, >> spin, qubit) quantum mechanics is derivable from 4 Stern-Gerlach >> experiments, using only real numbers, but for a last fifth one, you need >> the complex amplitudes, and you get the whole core of the formalism. >> >> Bruno >> >> >> >> >> *Do you understand Bruno's argument in a previous post on this topic? 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. >> >> >> -- 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.
