On Saturday, November 17, 2018 at 4:39:08 PM UTC, agrays...@gmail.com wrote: > > > > On Saturday, November 17, 2018 at 4:22:35 PM UTC, agrays...@gmail.com > wrote: >> >> >> >> On Friday, November 16, 2018 at 4:39:42 PM UTC, scerir wrote: >>> >>> >>> Il 16 novembre 2018 alle 15.38 agrays...@gmail.com ha scritto: >>> >>> >>> >>> On Friday, November 16, 2018 at 10:14:32 AM UTC, scerir wrote: >>> >>> >>> Il 16 novembre 2018 alle 10.19 agrays...@gmail.com ha scritto: >>> >>> >>> >>> On Thursday, November 15, 2018 at 2:14:48 PM UTC, scerir wrote: >>> >>> >>> Il 15 novembre 2018 alle 14.29 agrays...@gmail.com ha scritto: >>> >>> >>> >>> On Thursday, November 15, 2018 at 8:04:53 AM UTC, scerir wrote: >>> >>> Imagine a spin-1/2 particle described by the state psi = sqrt(1/2) >>> [(s+)_z + (s-)_z] . >>> >>> If the x-component of spin is measured by passing the spin-1/2 particle >>> through a Stern-Gerlach with its field oriented along the x-axis, the >>> particle will ALWAYS emerge 'up'. >>> >>> >>> *Why? Won't the measured value be along the x axis in both directions, >>> in effect Up or Dn? AG* >>> >>> "Hence we must conclude that the system described by the |+>x state is >>> not the >>> same as a mixture of atoms in the |+> and !-> states. This means that >>> each atom in the >>> beam is in a state that itself is a combination of the |+> and |-> >>> states. A superposition >>> state is often called a coherent superposition since the relative phase >>> of the two terms is >>> important." >>> >>> .see pages 18-19 here *https://tinyurl.com/ybm56whu >>> <https://tinyurl.com/ybm56whu>* >>> >>> >>> *Try answering in your own words. When the SG device is oriented along >>> the x axis, now effectively the z-axix IIUC, and we're dealing with >>> superpositions, the outcomes will be 50-50 plus and minus. Therefore, >>> unless I am making some error, what you stated above is incorrect. AG * >>> >>> sqrt(1/2) [(s+)_z +(s-)_z] is a superposition, but since sqrt(1/2) >>> [(s+)_z +(s-)_z] = (s+)_x the particle will always emerge 'up' >>> >>> >>> I'll probably get back to on the foregoing. In the meantime, consider >>> this; I claim one can never MEASURE Up + Dn or Up - Dn with a SG apparatus >>> regardless of how many other instruments one uses to create a composite >>> measuring apparatus (Bruno's claim IIUC). The reason is simple. We know >>> that the spin operator has exactly two eigenstates, each with probability >>> of .5. We can write them down. We also know that every quantum measurement >>> gives up an eigenvalue of some eigenstate. Therefore, if there existed an >>> Up + Dn or Up - Dn eigenstate, it would have to have probability ZERO since >>> the Up and Dn eigenstates have probabilities which sum to unity. Do you >>> agree or not, and if not, why? TIA, AG >>> >>> I think the question should rather be how to prepare a superposition >>> state like sqrt(1/2) [(s+)_z +(s-)_z] . But when you have this specific >>> state, and when you orient the SG along "x", you always get "up". >>> >> >> *If the SG field is oriented perpendicular to z axis, the usual situation >> for a measurement along z, you get Up or Dn along z axis. If field is along >> x axis, which is perpendicular to z axis, the device blocks the stream of >> electrons, so no measurement is possible.* >> > > > *Correction; the SG device doesn't block stream of elections when its > field is oriented along x axis. But what has this to do with whether one > can measure Up + Dn, or Up - Dn along z axis, or any axis? Does it show Up > + Dn can be measured along x axis? AG* >

*I still have to check your math. I think you've shown that Up + Dn can be measured along x axis, and presumably Up - Dn can also also be measured when a negative sign is used between elements of the above superposition. I suppose this is what Bruno was trying to say, whereas I was focused on measurements along z axis with the SG device in the standard orientation. Nonetheless, I don't see that this result has anything to do with Bruno's introduction of an infinity of universes, a concept I find totally extraneous (and for my aesthetics, abhorrent) to this issue. AG * > > > >> >> *Also, note that your simulation uses only Up or Dn, as I did above, to >> show it's impossible to measure Up + Dn, or Up - Dn. Can you respond to my >> comments above? AG * >> >>> >>> >>> >>> >>> In fact (s+)_z = sqrt(1/2) [(s+)_x + (s-)_x] >>> >>> and (s-)_z = sqrt(1/2) [(s+)_x - (s-)_x] >>> >>> (where _z, _x, are the z-component and the x-component of spin) >>> >>> so that psi = sqrt(1/2)[(s+)_z +(s-)_z] = (s+)_x. (pure state, not >>> mixture state).. >>> >>> AGrayson2000 asked "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?" >>> >>> Does Everett's "relative state interpretation" show how to interpret a >>> real superposition (like the above, in which the particle will always >>> emerge 'up') and how to interpret a mixture (in which the particle will >>> emerge 50% 'up' or 50% 'down')? >>> >>> >>> -- >>> 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 everything-li...@googlegroups.com. >>> To post to this group, send email to everyth...@googlegroups.com. >>> 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 everything-li...@googlegroups.com. >>> To post to this group, send email to everyth...@googlegroups.com. >>> 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 everything-li...@googlegroups.com. >>> To post to this group, send email to everyth...@googlegroups.com. >>> 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.