On the physical grounding of bivectors and scope of further arguments
anton vrba
Dear Bryan,
Let me try once more to be very clear about the point of difficulty.
My original question was narrowly focused: where, explicitly, do your bivectors enter Maxwell’s theory as physical objects? In particular, how they arise from, couple to, or are constrained by the standard electromagnetic field structure. Your Classical Origin of Spin paper does not, in my reading, make this connection.
Because of this gap, I asked ChatGPT to examine the work purely at the level of mathematical structure and physical interpretation. The attached PDF summarizes the result: there are numerous unproven assumptions, heuristic identifications, and category shifts (mathematical ↔ physical) that are never justified. Whatever one thinks of the conclusions, these issues occur at the foundational level.
My concern is methodological rather than adversarial: when foundational questions remain unresolved, it is not productive to argue over finer points of derivative constructions. From the outside, this gives the impression of defending consequences while the premises themselves remain unclear.
I also want to say this directly: when you respond to foundational criticism with strong assertions rather than explicit derivations or physical mappings, it tends to escalate exchanges unnecessarily. That escalation then draws responses you understandably find personal or unfair.
None of this is meant as a personal attack. It is an invitation to step back and address the most basic question first: what, precisely, makes these bivectors physical within established classical field theory? Until that is made explicit, further discussion will continue to talk past itself.
Regards,
Anton
------ Original Message ------From "Bryan Sanctuary" <bryancs...@gmail.com>Subject Re: [Bell_quantum_foundations] Re: The correct derivationAntonPlease see this paperThe answers to all your questions are there. Please read the first 3 sections, which are mostly Classical Mechanics.Let me know if you have other questions.Bryan
Bryan Sanctuary
spin quantization, entanglement correlations, or SU(2) representations.":
anton vrba
Dear Bryan,
Thank you for the detailed reply. It helps clarify where the disconnect lies.
You state that your Classical Origin of Spin paper is purely classical and therefore not obligated to connect bivectors to electromagnetic theory or quantum observables. Taken in isolation, that would be a defensible position.
However, the difficulty is that you do not treat the work in isolation. Across this paper and others—including Spin Helicity and the Disproof of Bell’s Theorem—you explicitly claim resolution of quantum-mechanical phenomena: spin quantization, SU(2) structure, EPR correlations, Bell violations, parity, ZBW, g-factors, scattering, and more. Once those claims are made, the burden necessarily shifts to demonstrating how the classical bivector formalism reproduces or constrains the corresponding physical observables.
This is where the criticism applies. It is not that bivectors cannot be defined classically, nor that Clifford algebra is inappropriate. It is that the same mathematical object is repeatedly asked to play incompatible roles:
classical mechanical variable,
surrogate for quantum spin,
replacement for fermionic degrees of freedom,
explanatory basis for experimental quantum correlations.
Pointing out that one paper is “seminal” and another “applicational” does not resolve this, because the applicational papers rely on premises introduced earlier without the required bridges ever being made explicit.
So the issue is not that ChatGPT—or anyone else—“missed” parts of your work. It is that the work itself moves between domains while treating the transitions as self-evident. That is the apples-and-oranges problem: objections are declared out of scope only after cross-scope conclusions are asserted.
Given this, continued debate over finer details is unlikely to be productive for the group until the basic categorical questions are settled: what is classical, what is physical, what is observable, and what is merely geometric.
Regards,
Anton
Bryan Sanctuary
anton vrba
Dear Bryan,
We are clearly talking past one another, so I will try to close the loop in a precise and non-interpretive way.
Attached below is a structured summary of the issues identified in your work, split into two parts:
(1) The Classical Origin of Spin, and
(2) Spin Helicity and the Disproof of Bell’s Theorem.
The tables do not claim your work is “wrong,” nor do they dispute your intent. They simply list, point by point, where key claims rely on assumptions, heuristic limits, or category shifts that are not made explicit at the level required for the conclusions you later draw.
At this stage, repeating that “it is all in the paper” does not move the discussion forward. If it is indeed all there, then the appropriate next step would be to indicate—for each item—where the corresponding derivation, definition, or mapping is provided, or to clarify what I (and others) are misunderstanding.
Until those points are addressed explicitly, further debate risks remaining circular. That is what I mean by “talking past each other”—not a judgment of competence or intent, but a mismatch of what is being claimed versus what is being demonstrated.
Given that you say you are otherwise occupied, I suggest we pause the discussion here and return to it only if and when these specific points can be taken up directly. That would be the most productive use of everyone’s time.
Regards,
Anton
The Classical Origin of Spin: Vectors Versus Bivectors
| # | Assumption / Claim | Status | Failure / Gap |
|---|---|---|---|
| 1 | Electron spin is a classical bivector | Justified | Algebraically valid; physical mapping to measurement still heuristic |
| 2 | Double helix represents quantum limit | Partially justified | Consistent geometrically; lacks formal proof of half-integer spin periodicity |
| 3 | SU(2) symmetry emerges from Cl(2,2) | Partially justified | Plausible; full equivalence to quantum SU(2) not shown |
| 4 | Parity explained by bivector orientation | Partially justified | Coherent; connection to P, C, T operators not derived |
| 5 | Fermions = polarized blades of bosons | Partially justified | Algebraically possible; predictive/statistical consequences not derived |
| 6 | Poisson bracket dynamics reproduce spin motion | Justified algebraically | Does not directly yield quantum observables; requires “quantum limit” heuristic |
| 7 | Classical bivector model suffices for foundational mechanics | Conceptually justified | Predictive power for experimental outcomes not fully formalized |
Spin Helicity and the Disproof of Bell’s Theorem
| # | Assumption / Claim (Explicit or Implicit) | Status | Mathematical Gap / Failure |
|---|---|---|---|
| 1 | Bell’s theorem assumes spin must be scalar-valued | Incorrect | Bell assumes measurement outcomes are scalar-valued random variables, not that spin ontology is scalar. Ontology ≠ outcome. |
| 2 | Spin is fundamentally a bivector, not a scalar | Correct (ontological) | This does not affect Bell’s theorem, which applies to scalar detector outputs. Category error. |
| 3 | Bell’s use of scalar random variables is too restrictive | Incorrect | Scalar-valued random variables are required by Kolmogorov probability theory. Bell’s theorem is a probability theorem. |
| 4 | Bivector-valued hidden variables can replace scalar ones in Bell | Incorrect | Bell’s inequality is undefined for noncommutative algebra-valued random variables. The theorem’s domain is exited. |
| 5 | Bell’s factorization fails for bivectors | Misleading | Factorization fails because the model violates Bell locality, not because Bell is wrong. |
| 6 | Correlations can be computed using bivector products | Out of scope | Such correlations are not expectations in ( L^1(\Lambda) ); they are algebraic averages, not probabilistic ones. |
| 7 | The BiSM reproduces quantum correlations | Unproven | No scalar random variables ( A(a,\lambda), B(b,\lambda) \in {-1,+1} ) are derived without contextual projection. |
| 8 | Bell assumes fermions are fundamental | Incorrect | Bell assumes nothing about particle ontology. He assumes only random variables and probability measures. |
| 9 | Bell fails because spin is not quantized | Irrelevant | Bell’s theorem does not assume quantization or SU(2). It applies to any dichotomic outcomes. |
| 10 | The hidden variable ( \lambda ) can be a bivector with internal structure | Conditionally valid | Only if ( \lambda ) defines a Kolmogorov probability space. Sanctuary’s ( \lambda ) does not. |
| 11 | Measurement outcomes arise from bivector projections | Contextual | Outcome is a procedure, not a function ( A(a,\lambda) ). Bell forbids this. |
| 12 | Contextuality does not violate locality | Incorrect | Bell locality is factorization, not spacetime locality. Contextual dependence violates it. |
| 13 | A single global bivector can generate both outcomes | Invalid under Bell | This introduces shared algebraic structure → violates statistical independence. |
| 14 | Bell’s theorem is about physical reality | Incorrect | Bell’s theorem is about probability models, not ontology. |
| 15 | Violating Bell assumptions disproves Bell | False | Violating assumptions only means the theorem does not apply. This is not a refutation. |
| 16 | Noncommutativity invalidates Bell’s derivation | Incorrect | Bell’s derivation never uses commutativity of hidden variables—only scalar outcomes. |
| 17 | The BiSM restores realism | Ontological claim | Bell’s realism is statistical, not metaphysical. Categories are conflated. |
| 18 | Bell inequalities fail in the BiSM | Trivially true | Any theory outside Kolmogorov probability violates Bell inequalities by construction. |
| 19 | This shows Bell’s theorem is wrong | False | The theorem remains mathematically correct and intact. |
| 20 | Therefore Bell should be abandoned | Unsupported | No logical implication follows. Bell still constrains all scalar-outcome local models. |