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* > > >> >> >>> >>> >>> >>> >>> >>> >>> >>> >>> 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. 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