It is true that one cannot add correlations from a single classical probability space. I agree with the three standard assumptions that go into Bell’s inequality
Where I differ is that Bell’s theorem contains a fourth assumption that is never stated explicitly (I think):
All correlations arise from a single classical convex set of probability measures. Bell inequalities bound the extremal points of one convex set. My model has two independent convex sets: one for the vector/polarization sector and one for the bivector/coherence sector. These produce two binary streams, not one.
Bell’s inequality is valid within each convex set individually. But the physics supplies data from two complementary indistinguishable state spaces (we only get clicks), so the correlations are produced independently, The single-space CHSH bound does not apply to that combined structure. Therefore, it is not "odd" to sum.
The fundamental basis for the sum is the geometric product--gives two complementary spaces:
sigma_i sigms_j = delta_{ij} + epsilon_{ijk} i sigma_k
so if you think I should average those two terms, then you must show the geo product should be averaged and not summed. You cannot do that.
So I do not disagree with Bell’s mathematics. I disagree with the usual interpretation of the theorem, the claim that any LHV model must satisfy the single-convex-set CHSH ≤ 2 bound. A model with dual complementary sectors remains local while giving the quantum correlation from vectors and from bivectors, which is what I have shown.
Thus I am consistent with Bell’s algebra but not with the standard physical explanation that ties locality to a single classical probability space. So you guys can say, "he should average not sum", because that is what Bell did, and you might argue I cannot change his statistics. But I am changing the statistics from one to two binary streams, and I think it is correct. If you require Bell's single binary stream of coincidences, then I am wrong, but if I have two independent streams, I am correct. So you can choose.
It is not odd that I violate BI with two, but it is odd if I violate BI with only one binary stream.
I will reply to the second question soon.
Bryan
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Still this nonsense.
Bryan, you are wrong. This has been proven to you, in writing over and over.
No, you cannot add correlations. You need to take convex combination.
My patience has run out.
/Jan-Åke
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Dear Austin,
Your second question you raised has to do with my discussion in the FSC paper of bivector spin. I suggest it is a bit premature of you to prefer the SM over the BiSM because you have not had the time to appreciate it. It is a perfectly good linearization of the KG equation that Dirac missed, and it gives the classical origin of spin. To reject it so quickly, seems to me to be more biased than logic.
I think the bivector spin is compelling, so rather than jumping to a like or dislike, please give it a chance.
You say you see a connection between your preon model but I cannot. I cannot begin to visualize preons and how they work and build, and successfully compare them to bivectors. They are apples and oranges. Preons are hypothetical constituents of quarks and leptons; they have never been observed, have no spectroscopic or scattering consequences, and are not visualizable within any consistent dynamical framework. That is basically also my critique of all of QFT. Preons are also not currently treated seriously I gather. There are NO hypothetical particles in the BiSM, like there are no neutrinos.
To understand the bivector spin, you must forget QFT and think of Geometric Algebra. You must also forget about fermions as fundamental. Only spin-1 bosons exist and fermions emerge as the blades (m = \pm 1), of the boson. It is a totally different ontology.
My spin is a spinning bivector in our 3D space. The SM cannot explain the FSC and I can, and also I can explain the ZBW: paper in prep now. In fact, all the issues with the SM are removed with the BiSM. Ask me.
Again, this is a result of solving the Dirac equation with Cl(2,2). Dirac used Cl(1,3), and that change is significant.
Bryan
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On 24 Nov 2025, at 22:32, 'Mark Hadley' via Bell inequalities and quantum foundations <Bell_quantum...@googlegroups.com> wrote:
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Here’s some reading on the topic:
Mair, A., Vaziri, A., Weihs, G. et al. Entanglement of the orbital angular momentum states of photons. Nature 412, 313–316 (2001).
Krenn, M., Malik, M., Erhard, M., & Zeilinger, A. Orbital angular momentum of photons and the entanglement of Laguerre–Gaussian modes. Phil. Trans. R. Soc. A 375 (2017).
This is a bit off the usual Bell/CHSH path, but it’s still relevant. One thing that bugs me in the usual physics literature is the “Hilbert space solves everything” attitude. When the Nature paper talks about OAM modes defining an infinitely dimensional Hilbert space, it feels like a way of avoiding giving a real physical picture.
Nevertheless, your bi-vector model doesn’t give a physical explanation for OAM or its entanglement, and you tend to brush off criticism instead of addressing it. Also, paying to publish doesn’t really strengthen the argument.
Just wanted to put this out there.
Dear Austin and Anton,
I had missed this thread earlier, but thank you both for taking the time to look at the FSC work. Although I do have a bivector model of the photon, here I am thinking specifically of electrons.
The first hurdle is that the usual QFT picture must be set aside, not easy after about a century. QFT treats spin as a chiral vector on a two-state Hilbert space. In the BiSM, spin is neither postulated nor abstracted; it is a real bivector object in 3D geometric space, with a classical origin. Classical properties become quantum not through Hilbert-space axioms, but through the geometry. As an example, in our classical domain neutrinos do not exist, so they cannot exist in the quantum domain either. No neutrino has ever been detected in a way that does not have alternative explanations (e.g. cosmic rays). Likewise, parity, charge, and time are all independently conserved. In the BiSM, parity is not violated. The list is long.
Crucially, there is no usual superposition of spin states. There is no wavefunction collapse. There is also no non-local entanglement. What is usually called entanglement (i.e locally) can be removed with properly constructed non-Hermitian states, (I worked that out more than a decade ago
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so entanglement in QM is an approximation (that is why I get CHSH of 3 and qm gives 2.282--QM missed correlation).
Regarding criticism: I certainly do not intend to brush it off. I want it, and I’ve had to respond to critics for many years, often hostile one. I take every objection seriously.
On publishing: none of my papers were paid for — they were all free. I got waivers. I chose MDPI simply because mainstream journals have been unwilling to engage with papers that reject non-locality. MDPI at least sends the work to referees who read the manuscripts.
As for physical intuition: QFT, for all its calculational success, is largely devoid of geometric understanding. The BiSM, in contrast, is geometric, visualizable, and internally consistent.
The model is laid out here:
This is the first application:
I am now completing the Zitterbewegung analysis, which drops out naturally from the bivector geometry. After that, my plan is to work through the successes of the Standard Model and show how they emerge from the BiSM. My goal is to replace the SM.
This should address Anton’s point that the bivector model “doesn’t give a physical explanation for OAM.” In fact I am sure it does: everything stems from the internal bivector structure, and extending the framework to OAM is, I think, straightforward. In my view, QFT is overly mathematical and lacks physical clarity, for example no gauge bosons have ever been directly detected, and few truly understand the Higgs mechanism. The SM is overly complicated and cumbersome. It allows for anything within some rules. The BiSM is geometrically constrained.
The only fundamental change I made to the Dirac equation is to replace the Clifford algebra Cl(1,3) with Cl(2,2). That is all, yet the resulting geometry is entirely different, and physically sensible.
Understanding the model requires working in geometric algebra, not QFT. It is not easy to put all those ideas aside, even though GA is much simpler.
I appreciate both of you engaging with this, and I’m always happy to answer questions. Fundamentally, you must decide if Dirac's linearization of the KG equation is correct, or whether my linearization is corrrect. Only one can be.
Best regards,
Bryan
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On 28 Nov 2025, at 18:21, Fred Diether <fredi...@gmail.com> wrote:
CHSH assumes broken physics. It's junk.
On Wednesday, November 26, 2025 at 1:51:24 AM UTC-8 Richard Gill wrote:Exactly. Bell-CHSH assumes local classical hidden variables,
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