> 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 > > > > > > > > > > > > > > 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". > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > 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 > > > > > 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 > > > 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] > 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. > 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.
