> On 4 Nov 2018, at 21:32, Jesse Mazer <[email protected]> wrote: > > > > On Wed, Oct 31, 2018 at 7:30 AM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > >> On 30 Oct 2018, at 14:21, [email protected] >> <mailto:[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] >>>>> <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. > > 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?
I limit myself to spin or polarisation. In some case there are selection or superselection rule, like with charge or other possible physical attribute, but not here. I use only the core formalism of quantum mechanics, where a change of base is a change of the experimental device, like a rotation of some Stern-Gerlach apparatus. 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] > <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.
