Hi Jonathan Tooker,

You are correct that quite a bit of explanation is included in the above comments, but it takes a while to plow through them. The short version is that Stern-Gerlach is not measuring spin directly; it is measuring spin-dependent scattering from an inhomogeneous field. And the inhomogeneous field is not described by Pauli's simple eigenvalue equation, due to the non-zero and non-trivial gradient of the field that must be included in the Hamiltonian. Instead, depending on the specifics of the gradient, there is a continuum of eigenstates, not binary eigenstates.

When the physics of the particle interactions are taken into account, the amplitude predicted by the local model can be correlated (in pairwise fashion) and the result (as shown on page 7) is the quantum correlation -a.b. Bell claims this is impossible, and the consensus today as evidenced by numerous statements in the physics literature is that "no local model can produce the quantum correlation". Bell assumes that the particle only precesses, but this is true only in a constant field, which yields null results and thus a logical contradiction. Bell apparently believes that he is measuring spin directly, and assumes spin can only have two possible results +/-1, thus he throws away the actual measurement data and replaces it with an abstraction, the +/-1 dichotomy. This prevents his constrained model from ever obtaining the correct correlation. In other words he is applying the wrong map, Pauli's (provisional) precession eigenvalue equation in a situation where it does not apply and it is likely that he is doing this because he is confusing the Pauli equation with the Dirac equation as I explain in the essay.

Believing that there is a difference between what local models (as constrained by Bell) and quantum models can produce in terms of correlations, physicists have looked for an explanation for that difference. They have settled on entanglement as the explanation of the difference. If a local model can produce the correct correlation, as mine does, then there is no difference between the local and quantum correlations, and this would seem to have some significance for entanglement. And as quantum mechanics does not contain the initial spin, and cannot predict each local result, but only the correlation, then quantum mechanics is incomplete, in Einstein's sense. My model should be capable of being tested experimentally, and this issue decided.

Thank you for your comments. I hope this short summary answers your questions and of course will be happy to try to answer any other question.

Best regards,

Edwin Eugene Klingman

Dear George Rajna,

Thank you for your most gracious comment.

Edwin Eugene Klingman

Dear Edwin,

Thank you for your interesting approach of the Stern Gerlach problem described by J,Bell.

In short I would describe his problem with the fact that there was no so called "smearing" of particle impacts on the screen observable which indicated that before entering the SG magnet, the particle magnetic moments had to be up or down. Right?

I think I could give you a practical test description to prove that indeed most particles do enter up or down!! By a mechanism called "internal oven entanglement".

Therefore you have to imagine that all particles in the silver oven are entangled and that the first SG entering particle(s) are the messenger particles to influence the total polarization of the oven.

This could be checked by a new SG experiment with TWO opposing SG magnets, ( see image) and perhaps:

See: http://vixra.org/pdf/1103.0015v1.pdf

Figure 7,

To solve the Q.M. problem described by J.S.Bell about the standard Stern Gerlach experiment.

Experiment proposal to support the existence of a new kind of Entanglement, which should show up inside a double Stern Gerlach experiment with two S-G magnets with different orientation.

The proposal for this experiment, is based on the hypothesis that all heated and vaporized

silver atoms inside the silver oven are entangled as a whole and that magnetic measurement of

one atom travelling outside the oven influences the magnetic polarity of all the other atoms in

the oven.

If the oven sends the silver atoms (by shutters) alternately to the two magnets, then the

resulting impact pattern on both screens will show an additional BAR in the middle of the

original impact pattern. (see figure 7)

This could be the explanation for the fact that only up and down orientated atoms should enter

into the S-G magnet to explain the "non smearing" effect on the screen.

John S. Bell described his doubts about the Stern Gerlach experiment interpretation in his

book: "Speakable and unspeakable in Quantum Mechanics on chapter 16 page 140-141.

John Bell argued that there is no logic to be found behind the fact, that there is a so called

"absence of smearing" of the particle impact pattern on the screen.Attachment #1: Stern_Gerlach_1.jpg

    Dear Leo Vuyk,

    I see that you have put some effort into studying Stern-Gerlach. I was somewhat surprised by your statement of 'no smearing' of particle impacts on the screen, as there appears to be visible 'smearing' on the iconic postcard that Stern-Gerlach sent to Bohr, and Messiah (a primary QM text at the time of Bell) describes "the appearance on the screen of a more or less spread out distribution of impacts..." indicating that the atoms are not all in the same initial condition and implying a statistical distribution.

    But I see you are referring to the lack of a continuous distribution with no separation. Please note that this is compatible with my model and can be explained with classical physics when energy-exchange between precession-mode energy and deflection-mode energy is taken into account.

    I do understand your suggestion, and I find it both interesting and well thought out, based on belief in entanglement as a fundamental phenomenon.

    My approach is not to deny entanglement as a starting proposition, but to explore Bell's conclusion that no local model can produce the QM correlation. I have presented a local model that does produce the QM correlations, unless Bell's constraints are imposed. This would seem to call Bell's constraints into question, and so I have analyzed the reason why he might have imposed such constraints. My essay offers an explanation, based on confusion of Dirac and Pauli eigenvalue equations, and assumptions of eigenvalue measurements. If this analysis is valid, then the rationale for entanglement is called into question.

    But if one assumes entanglement from the start, then I believe your analysis is reasonable. The good news is that we have proposed two experiments that should be able to settle the question. As the belief in non-locality is certainly one of the most major challenges to intuitive understanding of physics, it seems very important to perform these experimental tests. I am beginning efforts to have my experiment performed, and I hope you are doing the same.

    Thank you very much for reading, thinking, and commenting.

    Best,

    Edwin Eugene Klingman

    Dear Ed,

    1. I refer to this comment of yours; cited 2 posts above:

    "I have employed a robot as a vehicle to eliminate bias and "baggage", while providing pattern recognition, learning algorithms (neural nets, self organizing maps, etc.) and have shown how counting, derived from logical physical structures, is essentially (along with simple arithmetic logic circuitry, silicon or biological) all that is required to go from raw measurement data to feature vectors of the quantum persuasion. "

    Is this a reference to the model that you used to construct the two graphs on p.7 of your essay?

    2. Am I correct in thinking that the second graph is a modification of the first graph (via the application of Bell constraints) and not a graph published from a new run of your model under Bell constraints and with new random inputs?

    3. Perhaps I'm missing something here, re #2; but I ask because the density of the data-points varies over the range of θ; being low at the extremities. Could this indicate some θ-based noise or bias in your model?

    4. In these graphs I take it that you here are using θ as the angle (a,b). Does your model allow a and b to be vectors in 3-space?

    Thanks, and best regards; Gordon

    DearEdwin,

    Thank you for your extensive answer.

    You wrote:

    I am beginning efforts to have my experiment performed, and I hope you are doing the same.

    I have no connection to university PhD experiments , but perhaps both experiments are perhaps interesting for such a student.

    Edwin -

    Thanks for the challenging article! I wonder what Bell would think. I like the map-territory analogy for math and physics - it highlights the difference between abstract proof (math) and empirical claim (physics). Yet it may tend to the platonist (as do I) in the sense that the map is real too.

    Thanks as well for reading my essay. Best of luck - George Gantz (http://fqxi.org/community/forum/topic/2381)

    I read your essay since long ago and I did not see it worth commenting earlier because it is pure nonsense. You claim to provide a possibility of something that was famously, clearly and rigorously proven impossible. If there was a consensus on this impossibility, it is not because physicists are idiots having fanciful beliefs that something cannot be done just because they did not have the idea how to do it (how ridiculous is this suspicion : in fact they are not idiots and they are well willing to find a possible explanation of something, when it is possible, and especially when it is as elementary simple as the kind of things you wrote), but because a rigorous proof of this impossibility was given and verified. You claim to show what is clearly impossible. Like claiming to have proven that 2+2=5 that can be funny but does not deserve attention. But in the content of your text you do not prove anything because you only put a small pack of words and formulas with no sense (your so-called "energy exchange theorem" that does not even say if it is for a local system or a system of 2 separate particles at different places, which the EPR paradox is about) and then you just boringly spend most of your text repeating like a parrot the claim that this senseless pack of words and formulas succeeded to do that impossible thing. Just making a nice graphic is not a proof of anything.

    I suspect a possible source of error of your reasoning, in case you sincerely mean something that has some minimum of coherence in your head (which is impossible to check), is that you did not make it clear how you define the convention of unit of correlation between spins. I cannot know it because you did not make it clear what is the unit you use.

    The fact of quantum physics, that might be written by the sentence "quantum correlation -a.b" is that for example if a and b have the same direction then there is 100% certainty to get observed results with opposite signs. Of course if you did not interpret it like this but only provide a correlation that varies, for example, in the interval [25%, 75%] of probability of being found the same sign, depending on the angle according to the law of dot product then your system respects Bell's inequalities and does not reproduce the results of quantum physics.

      Another possible source of nonsense of your article, and of your ignorance of the problem (that seems to be more precisely your ignorance of what the predictions of quantum physics actually are and how they break Bell's inequalities, so that of course you have no problem to classically reproduce some incorrect description that does not break the Bell's inequalities and in which you misinterpret what needs to be explained), is, if you did not even get what the terms of the observation are about: the fact that spin measurement results are only one binary digit of information, and nothing else such as any continuum of possible positions on a screen. If done well, the Stern-Gerlach experiment only has 2 spots on the screen (independent of the initial spin direction of the electron that entered), with no bridge between them. Because, when we measure a spin along a direction, there are only 2 possible values of the spin we can find along this direction: either +1/2 or -1/2 but nothing else, leading to either spot on the screen. Of course it is always possible to blur this fact by referring to pictures made during the prehistory of spin measurement experiments where the separation between both spots was not clear.

      For more explanations about the predictions of quantum physics: a basic list of examples of consequences of quantum physics that cannot be classically explained are given in my page on interpretations ("Description of a quantum correlation experiment" and links to similar descriptions written by others); to understand the formalism of quantum physics and how it can give such predictions in logically coherent manners (but escaping classical explanations), see my introduction to quantum physics. I find it so amazing to see most participants of this contest so deeply ignorant about quantum physics and its incompatibility with classical realism that they failed to detect earlier the total falsity of this article and gave it such good rates in average.

      Ed, further to my earlier questions (above): but now re Silvain's comments above.

      As you know, I've long maintained the view (and worked toward): "a correct theory of particle-device interactions" will deliver the correct results for EPRB ++ and breach the relevant Bell-inequalities. So Silvain could be a good sounding-board as we work toward that common goal -- given that not many others (so far) engage with the details.

      But NB: I believe some of Silvain's seeming passion might arise from your desire to keep the low hanging fruit for yourself at the moment; especially as you say you keep finding more things in your model. For this puts you at risk of giving the impression of making it up as you go -- the basis for my suggestion that you should put some corrected/expanded views at viXra.org ASAP -- in that I believe your method needs to be more clearly expressed. For example, with me using X for your x for clarity below:

      1. Using θ in several senses is confusing: so use α for (a,λ) and β for (b,λ')?

      2. Reason: Your key formula, eqn (4), appears to need rewriting (possibly with "X is proportional to "...? Otherwise, how does X become constant for a given angular input if it's related to a velocity? Though I'm sure we differ here.)

      3. Now your (4) yields X as positive only, and you've explained to me that the sign of X is in the direction of the velocity of deflection. So is it correct to presume that your model (from figure on p.6) is using variants of (4) with velocity-sign thrown in?

      4. Suggestion: Derive a new signed Xa based on α -- not θ -- and call it (4A); and a new signed Xb based on β -- not θ -- and call it (4B).

      5. Then the graph on top of p.7 correctly retains θ as you derive E(AB) from a straight-forward comparison of your new (4A) and (4B)?

      NB: If you use just the sign-X (in your terms, the sign of the velocity deflection) then that reproduces Bell's (1964: 196) failed "Illustration" -- given that the sign of your velocity change appears to depend only on the hemisphere of the lambda wrt the principal axis of their respective polarisers -- right? So I'd like to see a clearer focus on why your variable X does not need a Y if you are modelling the second figure on p.3 -- thereby avoiding the conversion of each X to sign-X?

      With apologies if some of my own confusions re your model are showing here; Gordon

      Hi Gordon,

      I hope this means that you got your essay in on time. The local model used to generate the data on page 7 in my essay has not changed. The data shown are good and reproducible. Finding different ways to analyze the data does not invalidate or "make it up as I go". Instead of "finding more things", it's probably better to say "understanding more things", and that is as it should be. There are no "corrected" views to be posted, but, of course, views can always be expanded.

      1. All uses of θ in the essay refer to the local angle between the local spin and the local magnetic field. The one (unfortunate) exception is the appearance in the depicted correlation data, where θ is the angle between Alice and Bob's orientations (a, b). As this appears in the graphical data it was not easy to edit, and it is easy to explain. I don't believe anything is gained by specifying a specific θ for Alice versus a specific θ for Bob. The angles are completely determined by the local settings and the local spin.

      2. I'm not sure exactly what you're asking here, but there's more detail on pages 32 and 33 in my reference [2].

      3. I think you're missing the key term relevant to equation (4), which is "contribution". X is not the measured deflection. It is the θ-dependent contribution to the deflection. The sign works out automatically when all terms are combined.

      4. Again, not sure what you're after here. As you know, you and I don't always agree on symbolism.

      5. As the QM correlation is always -a.b, and that is what the graph at the top of page 7 depicts, you should scratch out θ and write (a,b) to label the horizontal axis. Then all θs in the essay will refer to the local angle between the local field orientation and the local spin.

      You say my term is "velocity deflection". Where does this appear? A search does not return this term.

      Most treatments of Stern-Gerlach assume that the 'Y' direction is symmetric, and is due to the fact that the simplest 1-dimensional gradient does not satisfy Maxwell's equation. Adding the 'Y'-gradient term significantly complicates the math, but adds nothing significant to the physics. It is the 'X' direction that is in contention here. And, per 3, above, there is no explicit 'sign-X' required.

      I hope this serves as a first cut at clarifying things for you.

      Best regards,

      Edwin Eugene Klingman

        Nature's grammar, mathematics, settles the physics in Bell-v-Einstein.

        So Yes Ed, my essay is in and waiting approval:-

        Among other things, I'm hoping to make the point that Nature speaks in many ways - from whispering snow-flakes to falling apples and roaring avalanches; etc. - what I call her many languages. She doesn't speak via mathematics (well, not very often to me). RATHER: mathematics is the grammar that governs all her languages and we must parse those languages to get at the maths -- ie, the LAWS that govern the cosmos.

        Re your listed matters:

        1. OK, as long as it's all consistent, no problem of course.

        2-3. My point was concerning (4) where each θ-dependent x-direction contribution is non-negative?

        Now you say: "It is the θ-dependent contribution to the deflection. The sign works out automatically when all terms are combined."

        So which term is it that combines with the output of (4) to give the X-plus and X-minus terms, please?

        And which term comes from the hemispheric models on pp.73-76 of your QSLR essay?

        4. My view was just that θ = (a,b) is the norm in much of the Bell-lit. But see #1 above.

        5. NB: The conventional θ = (a,b) is also in your Peres' quote on p.6.

        6. "Velocity OF deflection" -- correcting my typo -- see non-typo statement in my #3; the expression was in the reply you sent me when I asked about non-negative (4).

        With thanks, and best regards; Gordon Watson

        Ed, still striving to understand your essay:

        1. In conventional terms the expectation E(AB|Z) with Z = EPRB (Bell 1964) is:

        E(AB|Z) = P(A+B+|Z) - P(A+B-|Z) - P(A-B+|Z) + P(A-B-|Z) = -a.b. (A)

        2. But at p.7 you say: A+ = +1, etc., are "constraining measurement values" due to Bell that you reject.

        3. So what is your probabilistic formulation for E(AB|Z), please?

        4. What I mean is this: It is one thing to derive E(AB|Z) = [?] = -a.b; but for that output to be a true expectation, the intermediate [?] must be the probabilistic average over all measurement outcomes.

        5. So, given your key equation (4) yields X and X' as a function of the relevant θ and θ': your probabilistic weightings must apply to a near continuum of X- and X'-outcomes built from the θ-based X and X'-direction contributions and their final modification by your theory.

        6. So is this what is represented in top chart, p.7? And what then are the components in [?].

        Thanks; Gordon Watson

        Dear Edwin, I adhere to the "map" metaphor for the mathematical image of physical reality, with the evident strong simplification of the latter within a too low-dimensional map of actual mathematical tools and approaches. In order to avoid the arising contradictions, one should obviously increase the "map" dimensionality, as your analysis seems to imply too. In my own presentation here (Extended Mathematics) I describe a universal way to increase the map (dynamic) dimensionality to that of the unreduced reality, which is equivalent to resolution of all "mysteries" and "difficult" problems, as in this case one can clearly "see" the full, non-simplified image of "dynamically multivalued" reality. In particular, "quantum mysteries" are transformed into non-contradictory but complex (multivalued) dynamics of elementary particles and interactions, after which reduced visions like Bell's theorem become even senseless. This conclusion correlates with your results here, I just add a working version of "full-dimensional map".

          Dear Andrei,

          Thank you for reading my essay and commenting. As I noted on your thread, yours is a more general approach to the "unreduced reality" where "reduced" reality typically means models reduced to a lower dimensionality, such as 1-D or oversimplified models. But in some cases even a 1-D treatment represents progress over a 0-D current treatment. For example John Bell analyzes the scattering of a particle in an inhomogeneous field by assuming that the field is constant (thus zeroing out the gradient) and assumes that the resultant scattering continuum distribution is reduced to a binary result. A less reduced (i.e., simplified) local model of the interaction of the particle with the unreduced field produces exactly the quantum mechanical correlations that are impossible with Bell's oversimplified model.

          As you say in your comment, when the complex dynamics of elementary particles and interactions is considered, Bell's theorem becomes senseless.

          My best wishes for your success in your program.

          Edwin Eugene Klingman

          Gordon,

          First to your point 5 in your 9:42 comment. Yes, I did miss one. The Peres reference on page 6 does refer to θ = (a,b) and not the local θ defined above. Thanks for catching that exception. I'll now address the rest of your 9:42 comment.

          A good number of these essays make the point that it is a mistake to attempt to understand most physics from math. Physicists attempt to understand the physics and use math as a tool. Thus look at the physics of what's happening:

          Given the dynamics of a 3-D spin vector with a 3-D velocity in a 3-D field and a 3-D gradient, one can generate some rather complex math. But physically, one sees that, in Stern-Gerlach, the deflection is caused by the force of the gradient on the magnetic moment. If the magnetic moment is aligned with the field, the force is maximum and hence the deflection is maximum. Call this deflection X and calculate that it is given by the first term in parentheses in equation (4).

          If the spin is (initially) not aligned, then the force is less than maximum, and I use energy-exchange physics to calculate how much less and show it as x in equation (4). Thus to get the actual deflection you must calculate X-x. I think you'll find that this takes care of the sign you've been so worried about.

          Alice's deflection then ranges from full max to full min, based on the local angle θ between her spin and her field, (a,λ).

          Next, one might remark that this is the classic continuum and there is no binary splitting. If the length of the device is not sufficient to bring the magnetic moment into full alignment, then this is what is to be expected, and I believe that accounts for the neutron data I presented to Tim above.

          But if the SG-device is of such strength of gradient that the moment becomes fully aligned (or anti-aligned) then the contribution from θ ceases, and the maximum force is applied to the dipole until it leaves the device, which means that the magnetic moment continues to be deflected away from the centerline, and a split develops, with separation dependent on the distance from the device to the screen; pure geometry.

          Edwin Eugene Klingman

          Gordon, re. your 11:34 comment

          As I have explained above, Alice and Bob are treating the scattering problem of a particle in an inhomogeneous field. This is not the simplistic direct measurement of spin as typically believed. According to my physical analysis, Bob and Alice calculate the deflection that is measured by the position of the particle on the screen. This calculation is labeled A(a,λ) for Alice and B(b,λ') for Bob. It is not +/-1. It is the X-x described above. Bell, for reasons described in my essay and my references, demands that we erase this actual measurement data in favor of his oversimplified abstraction, +/-1, by constraining Alice and Bob's results to +/-1. In this case the formula you show [as (A)] is the expectation value. When I constrain Alice and Bob's outputs to +/-1 by truncating the actual measurement, then I obtain the second, straight line, figure on page 7, labeled "Energy Exchange with Bell Constraints".

          The "correlation" of Alice and Bob's results is simply the expectation value of the product of A and B, i.e. AB, weighted by the probability distribution,

          E(AB) = sum [ p(AB) * (AB) ]

          As each of the 10,000 spins is (randomly) generated, Alice computes her A and Bob computes his B. These values are 100% locally generated, based on Alice's setting a and Bob's setting b. The values are sent to the decision module, as shown on page 6, and stored as a pair until sufficient data has been received to apply statistics.

          For the data shown, all resultant AB values [for a given θ = (a,b) ] are known and it is a simple matter to compute their distributions. This probability distribution, p(AB), times the value of AB, is then summed to produce the top curve [for 300 different values of θ = (a,b) ] labeled as "Energy Exchange with No Constraints". It is the -a.b curve, predicted by quantum mechanics, but forbidden by Bell.

          Those who have a knee-jerk reaction to any suggestion that The Gospel According to Bell is physical nonsense, insist that this local model, which produces the correct correlation, is meaningless, because it does not throw away the information obtained by solving the scattering problem. They currently have the weight of numbers on their side, but the logic is on our side.

          Edwin Eugene Klingman

          Ed, a quick clarification please (while I continue to absorb your recent very helpful remarks).

          At 20: 18 you say:

          1. "The "correlation" of Alice and Bob's results is simply the expectation value of the product of A and B, i.e. AB, weighted by the probability distribution,

          E(AB) = sum [ p(AB) * (AB) ]." (1)

          But given your use and definition of local realism, should there be a crucial consequential separation in the form

          E(AB) = sum [ p(A1) * (A1) ]* [ p(B1) * (B1) ]? (2)

          2. Further, as I so far understand you work, given your important (4):

          A1 is not equal to A2, B1 is not equal to B2; and so on?

          PS: As my kids say, "Are we there yet?"

          Thanks; Gordon Watson

          Gordon,

          I believe that the definition of correlation as expectation value is given as I present it, i.e. your (1). I do not believe that your (2) makes any sense. In fact if you study your expectation value E(AB|Z) in your 11:34 comment above I think you will see that it is represented according to my definition.

          And yes, A1 is not equal to A2, B1 is not equal to B2, etc. as each of these outputs from Bob and Alice's devices are determined by the individual spin input to the device for that measurement, which spin is assumed randomly distributed.

          And yes, I think you might be able to see the finish line from here.

          Edwin Eugene Klingman

          Ed, OK, thanks; getting there.

          1. Could you answer some more possible "oops" in my: "Gordon Watson replied on Mar. 5, 2015 @ 20:35 GMT." - please?

          2. Re the neutron example (giving scattered results) at: "Author Edwin Eugene Klingman wrote on Feb. 9, 2015 @ 23:03 GMT."

          What was the source of the data for that please?

          Thanks again; Gordon