On Tuesday, November 6, 2018 at 9:27:31 AM UTC, Bruno Marchal wrote: > > > On 4 Nov 2018, at 22:02, [email protected] <javascript:> 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 * > > 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] <javascript:>. > To post to this group, send email to [email protected] > <javascript:>. > 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.
