> On 30 Nov 2018, at 12:29, [email protected] wrote: > > > > On Friday, November 30, 2018 at 9:03:51 AM UTC, Bruno Marchal wrote: > >> On 28 Nov 2018, at 15:02, [email protected] <javascript:> wrote: >> >> >> >> On Wednesday, November 28, 2018 at 1:41:03 PM UTC, Bruno Marchal wrote: >> >>> On 26 Nov 2018, at 22:43, [email protected] <> wrote: >>> >>> >>> >>> On Monday, November 26, 2018 at 4:41:42 PM UTC, [email protected] >>> <http://gmail.com/> 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. >> >> >> You can derive Schroedinger's equation (even Dirac’s equation) from >> Feynman’s formulation. This should be intuitively obvious if you read >> Feynman popular book on the Nature of Light. >> >> Not at all obvious. Do you have a link which proves that? AG >> > > > It is common knowledge in quantum field theory. PBS promised to make a video > on this. I studied this in the book by Feyman and Hibbs (QM and Path > Integral). > > > >> The waves are there. >> >> Was that before or after Feynman disavowed his belief that QM can be derived >> totally using particles? AG > > I don’t know. > > > >> >> But yes: the collapse does not make sense in Feynman’s formulation (or it >> looks even more ad hoc and non covariant). That is a reason to disbelieve in >> the collapse, but then you get some version of the many-world view (which >> you dislike apparently). >> >> MW is too extravagant to be true, > > Why? Why would be that extravagant? > > MW is the most extravagant theory possible and you just can't see it? Take > your head out of the ground and report back. AG
Again, why is it extravagant. I predicted this well before I even knew the term “quantum”, when I discovered that arithmetic emulates all computations (and my only doubt at that time was about “Church’s thesis”, without which “computable” seems to remain an epistemic relative notion). > > > Nature loves to do many things, like the water molecules in the Ocean. In > this list, most people agree than many things is conceptually simpler than > one particular thing. > > Except for one little thing; you can't explain the processes by which these > worlds are created! You might think studying the theory before criticising it. I have no clues at all why you are saying this, except by referring to the usual current metaphysical prejudices. > It's really very silly IMO. AG You need to argue. > > >> and moreover, even its advocates like you cannot say what another world >> includes. > > > ? > > You said it earlier in slightly different words. You have no idea how another > world is created or what's in it. I think we've departed from any reality > thinking when it comes to MW. AG Mechanism and elementary arithmetic is enough. >> Go back to Bruce's horse race example to see what happens to Schrodinger's >> equation when the measurement occurs. AG > > ? You might develop a little bit. With the MW, a measurement is only an > interaction. > > Reliance on rhetoric won't help. AG ? Bruno > > > > >> >> >> >> >>> I would suppose the same applies to Heisenberg's Matrix Mechanics; no >>> waves, no collapse. >> >> Those are equivalent theories. Deustch defended the MW, even its locality, >> in the context of the Heisenberg Matrix formulation. The theories here are >> all equivalent (unless they populate some 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. >> >> OK. (In my approach I derive the MW and its quantum formalism from the >> natural numbers and the laws of addition and multiplication, and nothing >> else, except at the meta-level I use the mechanist hypothesis to make sense >> of this, but it is a very weak assumptions which can be weaken even more). >> >> Sorry, but I don't believe that is possible. AG > > Then you will be astonished, because with Mechanism, there is no other > solution available, unless adding some “magic” to computaionalism, which > makes no sense. > > Bruno > > > > > >>> To summarize: you're right that they are "no collapse" theories, but IMO >>> they say nothing about consciousness. AG >> >> Well, with mechanism (that you can see as a theory of consciousness) there >> is no collapse indeed. But the quantum aspect of nature is explained from >> that theory of consciousness, not the inverse. Usually it is those who >> believe in the collapse who mix quantum and consciousness, like Wigner, von >> Neuman, Walker, etc. With mechanism, a measurement is only an interaction, >> locally irreversible (due to big numbers, not to any physical indeterminacy). >> >> 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 >>>>>>>>> <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] <>. >>>>>>> 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] <>. >>>>> 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] <>. >>> 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] <javascript:>. >> To post to this group, send email to [email protected] >> <javascript:>. >> 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 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