On Wednesday, November 28, 2018 at 1:46:28 PM UTC, Bruno Marchal wrote: > > > On 26 Nov 2018, at 22:49, [email protected] <javascript:> wrote: > > > > On Monday, November 26, 2018 at 9:43:14 PM UTC, [email protected] wrote: >> >> >> >> On Monday, November 26, 2018 at 4:41:42 PM UTC, [email protected] >> wrote: >>> >>> >>> >>> On Monday, November 26, 2018 at 12:01:05 PM UTC, Bruno Marchal wrote: >>>> >>>> >>>> On 23 Nov 2018, at 13:30, [email protected] wrote: >>>> >>>> >>>> >>>> On Friday, November 23, 2018 at 11:29:14 AM UTC, Bruno Marchal wrote: >>>>> >>>>> >>>>> On 21 Nov 2018, at 18:03, [email protected] 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. * >>>> >>>> >>>> Did I say that? >>>> >>> >>> *IMO yes. You asserted the need for an observer. The interference >>> pattern exists if there are no observers. It's like saying the Moon exists >>> even if no one ever looks at it, which was the situation throughout most of >>> the Moon's lifetime. AG * >>> >>>> >>>> >>>> >>>> *All you need is a detector to record the results. Feynman made this >>>> point and I don't see anything problem with this logic.* >>>> >>>> I agree with Feynman and Everett on this. It is the advantage of NOT >>>> believing in the wave reduction: consciousness is entirely handle by the >>>> Mechanist theory of mind. But then we can associate consciousness to the >>>> apprehension of the distinction brought by the measuring apparatus, in all >>>> branches of the superposition, and you get the “many-worlds” or the >>>> “many-relative-histories”. >>>> >>> >>> *Where in Feynman's postulates does he assert or infer no wave packet >>> reduction? I have to check his postulates, but if he really developed a >>> particle-only theory, there are no wave packets. AG * >>> >>>> *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* >>>> >>>> >>>> It is just QM without reduction of the wave packet. If there is no wave >>>> packet reduction, you get the relative states, including consciousness >>>> differentiation, using just the mechanist theory of mind (the oldest >>>> theory >>>> of mind). >>>> >>> >>> *You're reading much too much into Sums Over Histories (or Relative >>> Dtates) to reach this conclusion. CMIIAW, but Feynman discovered another >>> way to calculate probabilities. He didn't, and couldn't explain why we get >>> one result and not another in, say, a slit experiment. At best he was >>> neutral as to what happens to the wf at measurement time, since, IIUC, he >>> has no wf's in his theory. AG* >>> >> >> *I checked the postulates in Feynman's Sums Over Histories (in link >> provided by Phil) and I see nothing related to waves, as expected, and thus >> nothing about collapse of anything. I would suppose the same applies to >> Heisenberg's Matrix Mechanics; no waves, no collapse. I suppose you could >> say they just produce correct probabilities, and imply nothing about >> relative states other than their probabilities (which wave mechanics does), >> but certainly nothing about consciousness. To summarize: you're right that >> they are "no collapse" theories, but IMO they say nothing about >> consciousness. AG* >> > > *One final point; In wave mechanics, I think you find the "disappearance" > of the Schrodinger equation at moment of collapse troubling. But if you > have varying probabilities, say for a horse race (Bruce's example), when > the winner crosses the finish line, the probabilities cease to vary. Isn't > this sort of what's expected of the Schrodinger equation at measurement > time? AG* > > > > If there is no collapse, the disappearance is explained > phenomenologically, but there is no ontological disappearance, and that it > is good, because we know that all terms of the waves are needed to get the > predictions exact. > > It is very simple: any collapse postulate is equivalent with saying that > the QM (schroedinger/heisnberg/feynman formalism) is wrong. >
*If you don't like collapse, then don't use Wave Mechanics, but Heisenberg's or Feynman's formulation of QM. I think you're creating a problem for yourself. AG* The collapse can only violate the linearity of the evolution and tensor > products. That’s why Boher insisted that QM does not apply to macroscopic > observers, but as Einstein shows, that makes not much sense, unless > accepting spooky action at a distance, a god who plays with dice and/or > that physics talk about mind, and never nature. > > Bruno > > > > > > >> >>> >>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> 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 * >>>> >>>> >>>> OK, then. >>>> >>>> Bruno >>>> >>>> >>>> >>>> >>>>> 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]. >>>>> 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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