On Friday, November 23, 2018 at 11:29:14 AM UTC, Bruno Marchal wrote: > > > On 21 Nov 2018, at 18:03, [email protected] <javascript:> wrote: > > > > On Monday, November 19, 2018 at 3:52:37 PM UTC, Bruno Marchal wrote: >> >> >> On 18 Nov 2018, at 14:00, [email protected] wrote: >> >> >> >> On Sunday, November 18, 2018 at 12:19:20 PM UTC, Bruno Marchal wrote: >>> >>> >>> On 16 Nov 2018, at 15:38, [email protected] wrote: >>> >>> >>> >>> 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 >>> >>> >>> Which one? >>> >> >> *Good question. AG* >> >> There are spin operator for each direction in space. The superposition of >>> up and down is a precise pure state, with precise eigenvalues, when >>> measuring state in the complementary directions. >>> >> >> *As I wrote earlier, based on scerir's superpositions on different axes, >> and simulation, I now think that Up + Dn and Up - Dn can be measured along >> the x axis but not along the z axis (which I was focused on). * >> >> >> All you need to do is a change of base. The operator will be defined >> clearly by the Eigen value on the diagonal in the corresponding base. You >> can prepare any state, and measure them “in any base”. >> > > > *I'll get back to this issue in my next post. AG * > >> *You were probably correct about x axis measurements, but perhaps were >> not clear enough. You were not explicit that measurements along the x axis >> is a different SG experiment from along z axis.* >> >> >> OK. Sorry. >> >> * I thought you meant do them in succession, not as separate experiments.* >> >> >> Ah? OK. >> >> >> * Also introducing an infinity of universes seems extraneous and >> confusing for a solution to this problem. AG * >> >> I are probably different on this. I don’t take the word “universe” too >> much seriously, as with mechanism we know at the start that there is >> “physical universe” at all, just the natural numbers with the laws of >> addition and multiplication. Both the computational and the quantum state >> are relative, and high level, pertaining to what is “observable” for some >> the point of view of some locally finite subject, run by some computation. >> >> The empirical point, though, is that to predict correctly an event in >> quantum mechanics, we have to take into account may simultaneous >> “incompatible path”, like going through each hole in a plane. Quantum >> computations, for example, exploits that seemingly parallelism. >> > > *I don't like this approach -- in fact I abhor it -- since it implies > simultaneous interference among a multitude of paths to the same point on > the detection screen. This adds an unnecessary mystery to QM. In the > Hilbert Space representation, the wf is what it is, but can be represented > in a multitude of different bases. It is therefore misleading to claim the > system being analyzed is in a multitude of states; rather it is in one > state, which due to linear algebra, has many representations. AG * > > > > I can be OK with this, if you agree that the consciousness of the observer > is relatively associated to those representations, in the base “chosen” by > nature in the evolution of the brain. That gives rise to the “relative > state” view of QM. >
*I don't agree. I am not even sure what you mean. You don't need a conscious observer to detect the results of a slit experiment. All you need is a detector to record the results. Feynman made this point and I don't see anything problem with this logic. The problem IMO with sums over histories is that it adds a superfluous mystery (in spades) to the results, say, of a slit experiment. We still have the mystery as to why interference for every point along the screen in a single trial, yields a single impact. But with sums over histories IIUC, for each impact point or result, we also have an infinite set of histories which the particle is in simultaneously. I don't see that anything has been gained, other than having an additional baffling mystery used to sell books which confuse the lay public as well as professional physicists. AG * > 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 >>> >>> >>> You add the probabilities, but you need to add the amplitudes of >>> probabilities instead, and then take their square. You simply dismiss the >>> quantum formalism, it seems to me. >>> >> >> *I did not; an incorrect inference on your part.* >> >> All right. (I was just trying to figure out what you did, to be sure). >> >> *I** never mentioned Born's rule (it wasn't necessary), * >> >> >> You did use the probability 1/2 at some place, with the particle in a >> state 1/sqrt(2)(up + down). We use all the time the Born rule when we talk >> about measurement. >> > > > *I just assumed a probability of .5 for Up and Dn states after application > of Born's rule. AG * > > > That was my point. > *Your point, IIUC, was that I was denying the postulates of QM by ignoring Born's Rule, but I was not doing that. I just chose not to mention it. Nothing more. AG * > > Bruno > > PS I got a mail back as undelivered. I will try to resend it later. > > > > > >> *from which one cannot infer I am criticizing QM itself. AG * >> >> >> I am just trying to understand what you don’t understand, which is not >> easy in a context where the more we understand the formalism, the less we >> understand what it could mean, even more so if we give sense to a dualist >> wave packet reduction. >> >> I am a logician: it is clear that Copenhagen and Everett are not two >> different interpretations, but two different theories. One is Schroedinger >> equation + wave packet reduction + a dualist theory of mind/observation), >> the other is just Schroedinger equation only + the “usual” mechanist theory >> of mind. There are many possible debate on all his of course. >> >> I urge you to study the treatment of the interferometer in David Albert >> books. It is weird. Bohr is right on this: to understand it means to get >> the point that is hard to figure out how nature could to that, but from the >> mechanist post Gödel view, it is rather natural, as we observe is given by >> a statistics on infinitely many computations/histories. >> >> Bruno >> >> >> >> >> >> The states constituted a vector space: the sum (superposition) of >>> orthogonal states are pure state, after a change of base, and I did give >>> you the corresponding operator. You are not criticising an interpretation >>> of QM, but QM itself. >>> >> >> >>> Bruno >>> >>> >>> >>> >>> >>>> >>>> >>>> >>>> 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. >> >> >> > -- > 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] <javascript:>. > To post to this group, send email to [email protected] > <javascript:>. > 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. 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