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* > > *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.
