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] > <javascript:>> wrote: > >> >> On 30 Oct 2018, at 14:21, [email protected] <javascript:> 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, since they're not eigenstates of the spin operator, or any operator. 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.
