On Saturday, November 17, 2018 at 4:39:08 PM UTC, [email protected] wrote: > > > > On Saturday, November 17, 2018 at 4:22:35 PM UTC, [email protected] > wrote: >> >> >> >> On Friday, November 16, 2018 at 4:39:42 PM UTC, scerir wrote: >>> >>> >>> Il 16 novembre 2018 alle 15.38 [email protected] ha scritto: >>> >>> >>> >>> On Friday, November 16, 2018 at 10:14:32 AM UTC, scerir wrote: >>> >>> >>> Il 16 novembre 2018 alle 10.19 [email protected] ha scritto: >>> >>> >>> >>> On Thursday, November 15, 2018 at 2:14:48 PM UTC, scerir wrote: >>> >>> >>> Il 15 novembre 2018 alle 14.29 [email protected] 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 [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. >>> >>> >>> -- >>> 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.
