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* > > > >> >> >> >> >> >> >> >> >> 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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