Classical Quantum Mechanics

[anton vrba]

Dear All, 

I have posted my preprint "Classically Quantised Vacuum Electrodynamics with Maximally Entangled Photon Pairs" on  Zenodo, you can download:

https://doi.org/10.5281/zenodo.23193740

I have added an executive summary at the front of the article, which gives the whole argument in two pages.

The article is essentially mathematical physics. In outline:

1. I identify a cyclic algebraic closure 𝔐 and show that the source-free Maxwell curl equations follow from it.
2. I use the closure to define a quantised vacuum. From the first relation of 𝔐, I derive the vacuum electromagnetic constants (ε₀, μ₀, the flux quanta and the action modulus) with the elementary charge as the only primitive.
3. Space and time are quantised through an elementary length and an elementary time.
4. I recast Maxwell's field equations in an excitation sector, from which Planck's relation E = hν follows.
5. I use 𝔐 to define the photon.
6. I assume a nil-residue universe: every additive conserved quantity sums to zero at every instant and under every partition. On this basis, Einstein's "spooky action at a distance" receives a classical, deterministic account. Entanglement correlations are reproduced without Bohr's probabilistic interpretation or measurement collapse, at the price of explicit nonlocality.
7. The article also proposes two experiments that could distinguish the model from orthodox quantum mechanics.

Please be as brutal in your critiques as I have been in mine.

Regards
Anton

[Parker Emmerson]

Anton,
I went through Part IV against your rubric (stated assumptions only, discard what fails) and against my PV-REC paper. Here is where it breaks.
1. Assumption 2.4 has two halves. First, every conserved total is "zero." Second, Eq. (5): a change in one region is matched by the opposite change in the rest of the universe, and "this balance holds identically and without temporal delay." The first half is idle for your argument: if a total is conserved at all, whatever its value, a change in one region is already matched by the opposite change elsewhere. All the work is done by the second half. Ordinary conservation pays for a change inside a region with flow through that region's boundary, at or below light speed. Eq. (5) pays for it instantly, anywhere. That is your nonlocality, and it enters as an assumption.
2. Proposition 11.1. When Alice's photon is polarised at angle αa, Eq. (5) sets Bob's photon to the same angle at that moment, and Malus's law at Bob gives E = cos 2(αa − αb). That is the textbook calculation where Alice's measurement projects Bob's photon. The summary says "without measurement collapse," but the step that produces the correlation is that projection, under the name of a ledger update.
3. "The order of polarisation events [is] taken in the rest frame of the source." In Section 11.2 the first reading lets Alice signal Bob faster than light: Bob's split moves from 1/2 : 1/2 to 3/4 : 1/4 when her half-wave plate goes in. If every such signal is instant in its own source's rest frame, two setups with sources moving relative to each other let an answer arrive before the question was sent. The model therefore needs one rest frame for the whole universe, and that belongs in Section 2 next to Assumptions 2.1 to 2.4.
4. Remark 11.4. The ledger predicts a CHSH violation from a single Type 0 or Type I crystal, and the paper says "This is not observed." Your rubric discards at that point. The paper keeps the ledger and brings in linear and circular "pilot waves," which first appear in that remark and sit outside Assumptions 2.1 to 2.4.
5. Section 11.2. A 3/4 : 1/4 split confirms the ledger; a 1/2 : 1/2 split means the link "is consumed," and "the classical approach" stays. Both results keep the model, so the run tests the consumption add-on only. You called my κ "an imposition out of the ignorance of not knowing." κ comes with a pre-registered statistic and a stated result that settles it. Please give the Figure 2 run and the single-crystal quarter-wave-plate run the same: name in advance the result that retires Assumption 2.4. The single-crystal run is the clean one: at equal analyser angles your model gives perfect correlation, and quantum mechanics gives outcomes that are independent of each other.
6. What PV-REC does with the same correlation. Each pair is one event fixed jointly by the source and the two analysers, the way Wheeler–Feynman radiation is fixed by emitter and absorber together. The joint probabilities are the singlet's (your ±cos 2(αa − αb)), and each station's own counts stay at 1/2 : 1/2 whatever the far analyser does. So Bob records 1/2 : 1/2 in your Figure 2, in every frame. Your "consumed link" alternative gives the same prediction. The correlation therefore needs only the conservation half of Assumption 2.4. The instant half adds the preferred frame and the signalling.
7. Your summary pays "the nonlocality that Bell's theorem demands." Bell's inequality is Boole's condition on tables where all four outcomes are fixed together for each source state, and the experiments show nature's tables above it. Reading that excess as instant action comes from Eq. (5). In PV-REC the same excess is a joint condition on each pair event.
Parker

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[anton vrba]

... and to avoid such long conversations I have two experiments, both are go - nogo experiments that would settle the Copenhagen probabilistic interpretation versus a deterministic interpretation.  My interpretation is based on the physical foundations developed on the 30 pages that make up part I to III before we get to Part IV.  

[SMH Emamifar]

Anton, thank you for sharing your paper and explicitly inviting rigorous criticism.

I have examined *Classically Quantised Vacuum Electrodynamics with Maximally Entangled Photon Pairs*. I appreciate that it attempts a physical construction extending from electromagnetic geometry and vacuum excitation to photon structure, entanglement, and experimentally distinguishable predictions.

I would like to apply the same strict standard of physical necessity that we have discussed in this group: not merely whether a construction reproduces the correct mathematical result, but whether that result follows from the stated physical premises without inserting the decisive behavior at an intermediate step.

My concerns are as follows.

**1. From global conservation to a specific remote physical response**

Assumption 2.4 introduces the nil-residue universe, while Equation (5) requires complementary changes to balance without temporal delay.

I accept this as an explicitly stated physical assumption for purposes of examining the model. I am not rejecting instantaneous influence merely because it is nonlocal.

However, a global balance condition does not by itself specify which physical subsystem must provide the compensation.

If Alice changes the polarization of her photon, why must the compensating physical change occur specifically in Bob's photon?

Why could the balance not instead involve Alice's measuring apparatus, the surrounding electromagnetic fields, the source, or other degrees of freedom?

What dynamical equation selects Bob's photon as the compensating subsystem and uniquely determines the magnitude and orientation of its response?

This seems to be the first critical bridge between the universal assumption and the proposed physical mechanism.

**2. Are the field components in the pair ledger independently conserved quantities?**

In Proposition 11.1, the pair ledger includes conditions involving the electric and magnetic fields of the two photons, in addition to momentum and energy.

Conservation of energy, momentum, and angular momentum has a well-defined physical and mathematical meaning.

However, the electric and magnetic field vectors of spatially separated photons are not ordinarily conserved additive Noether charges.

What independent conservation law requires the particular combinations of photon field vectors appearing in your ledger to remain zero?

If these are additional constraints introduced by the model, I suggest they should be distinguished explicitly from established conservation laws.

The central question is whether these field constraints follow from the preceding electromagnetic dynamics or constitute additional pair-specific postulates.

**3. Does the Bell correlation follow from the dynamics or from the imposed polarization update?**

Proposition 11.1 obtains

E(αa, αb) = cos[2(αa − αb)]

using the polarization relationship maintained by the nil-residue ledger and the probabilities supplied by Malus' law.

I have no objection to the trigonometric calculation itself.

My concern is the physical step preceding it.

Once Bob's photon is assigned the polarization associated with Alice's first polarization event, Malus' law supplies the familiar angular dependence.

But which earlier field equation independently establishes that this particular polarization assignment must occur?

If the assignment is an additional physical rule, the correlation is correctly obtained conditionally, but it has not yet been independently derived from the preceding vacuum and photon dynamics.

**4. Determinism versus an event-level detection mechanism**

Section 12 acknowledges that the single-photon outcome probabilities are supplied by Malus' law together with unresolved creation-phase information, rather than derived event by event.

This distinction matters.

A deterministic underlying field representation is not automatically a deterministic account of individual detector outcomes.

Can the model specify a physical detection rule mapping the photon state, its unresolved phase, the analyzer setting, and the detector interaction into one definite recorded outcome?

Can it then derive the required ensemble probabilities from an independently justified phase distribution?

Without this step, the construction may establish deterministic field parameters while retaining an assumed statistical measurement rule.

**5. The single-crystal difficulty and the proposed carrying field**

Remark 11.4 explicitly acknowledges that unrestricted application of Proposition 11.2 predicts a Bell-CHSH violation for single Type 0 or Type I crystal sources where such a violation is not observed.

The proposed resolution introduces a carrying-field condition restricting when the pair ledger can be rebalanced.

That may be a legitimate hypothesis, but I would like to know whether this condition is derived independently from Parts I–III.

Can the theory determine, before consulting the observed correlations, which optical arrangements support the carrying field and which do not?

If this selection is introduced only after the original prediction fails, its independent physical justification and falsification conditions become essential.

**6. What precisely do the two proposed experiments falsify?**

I welcome both proposed experiments, particularly because they produce explicit differences from orthodox quantum predictions.

For the circularized single-crystal experiment, the proposed distinction between S = 0 and |S| = 2√2 is clear under the stated source assumptions.

For the second experiment, the predicted change in Bob's unconditional local statistics from 1/2 : 1/2 to 3/4 : 1/4 would be particularly significant.

However, Section 11.2 also allows a null result to mean that Alice's beam displacer has consumed the relevant pair connection, rather than falsifying the broader classical framework.

What independent equation determines whether the connection survives the beam displacer?

Can the survival criterion be specified before the experiment, without selecting it according to the observed outcome?

I am not insisting that one null experiment must falsify every component of a broad theoretical program. I am asking which precise hypothesis would be falsified and which would remain viable.

**7. Spacetime implementation and frame dependence**

The analysis orders polarization events in the rest frame of the source, while the proposed second experiment permits controllable superluminal signaling under one interpretation.

If the physical update is instantaneous in that frame, what transformation law governs the same process between relatively moving experimental systems?

Is the source rest frame merely a computational convention, or is it physically privileged for the nonlocal interaction?

This question seems especially important because the paper acknowledges that Lorentz covariance has not yet been established.

A complete physical account would need a definite rule for the causal ordering and physical ownership of the remote update.

**My central question**

These concerns converge on one issue:

Given the cyclic Maxwellian closure, the excitation-sector photon model, and the nil-residue assumption, what independently specified dynamical law necessarily produces the particular remote polarization response required by Proposition 11.1 and Proposition 11.2?

I am not assuming that nonlocality, instantaneous interaction, or determinism is impossible. I am asking whether the specific proposed mechanism is mathematically forced by the model's physical laws, rather than selected because it reproduces the intended correlation.

I would welcome a derivation identifying the precise equation and assumptions that establish this connection.

If that derivation is already present and I have missed it, I would be pleased to examine it and withdraw the corresponding criticism.

I believe the question is important because the paper attempts something more ambitious than reproducing a Bell correlation: it proposes a concrete physical explanation.

That ambition deserves an equally concrete test of the proposed mechanism.

Best regards,

SMH

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[anton vrba]

Dear SMH,

Thank you for a careful and fair reading with thoughtfully crafted comments.  I will try and answer as directly as I can. 

Beginning with 

**SMH's central question**

What I present is a complete theory beginning with a quantised spacial volume l_o^3, that allows a quantised reading of Maxwell's theory, which allows constructing a photon model.  Using that model I find unique parametrisations of that model under the nil-residue assumption to explain entanglement.  Thus, there is no independent dynamical law, derived from the closure or the excitation sector, that produces the remote polarisation response. The response follows from the nil-residue assumption applied to the pair ledger. The paper’s claim is conditional: given the assumption and the ledger, the correlations follow, and the mechanism makes predictions that differ from orthodox quantum mechanics. Parts I–III supply the physics in terms of Maxwell's field equations in the  excitation sector, which leads to the photon parameters on which the ledger is evaluated. They do not supply the ledger itself. 

**1. From global conservation to a specific remote physical response**

Equation (4) is already complementary if A doubles then A* also doubles, which is equation (5). And balancing with the environment leads to loss of entanglement and to phenomena like https://en.wikipedia.org/wiki/Entanglement_swapping or https://en.wikipedia.org/wiki/Quantum_teleportation or https://en.wikipedia.org/wiki/Greenberger%E2%80%93Horne%E2%80%93Zeilinger_state.  You also ask what dynamical equations, It is a phase change no energy is involved think https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect  

**2. Are the field components in the pair ledger independently conserved quantities?**

Emmy Noether states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law. So if  for two photons, lets take the calcium 2 photon cascade, energy is balanced with the atom, and the 2 photons combined have zero linear and angular momentum, then the fields at creation must also add to zero, if not then that would leave a residue field  on the atom and it has a frequency thus it has energy too, thus breaking the conservation laws.

**3. Does the Bell correlation follow from the dynamics or from the imposed polarization update?**

The Bell correlation are obtained that Bob's photon in-flight adjust to Alice's photon if its state is altered to maintain a nil-residue  ledger balance. How can it change polarisation state is the magic that requires answering. What is missing is a section on vector potentials that could aid in understanding.   Using the results of  theorem  7.2 and we write  (𝜖 B × E) l_o^4 =  (𝜖 φ × ψ) =h, here φ and ψ are the magnetic and electric flux, And the interaction  (𝜖 φ × A_E) , where A_E is the vector electric potential of others.  (𝜖 φ × A_E) has  units momentum, this impulse changes the phase, no energy is involved.

I agree that the correlation is obtained conditionally. What the ledger supplies is the update: co-rotation is the only closure, and this is computed, not chosen. Malus’ law then gives cos2(α_a − α_b). No field equation from Parts I–III independently forces the update; it is forced by the condition that the ledger sets, which rests on the Assumption 2.4, the outstanding task is to identify the physics behind, which what we lack in knowledge in classical field mechanics needs to be developed.

**4. Determinism versus an event-level detection mechanism**

The claim of determinism applies to the fields and to the ensemble statistics they generate. Individual outcomes are not predictable within the present description: they depend on the creation phase, which is unresolved, and possibly on the state of the apparatus, neither of which the model yet specifies. I therefore make no claim that individual events are determined by the model as it stands. Equally, I do not concede that they are fundamentally random; the paper’s position is that the unpredictability reflects unresolved information, not indeterminism in nature. The step that would turn this position into a derivation, a detection rule mapping phase, setting and apparatus to a single outcome, is at present hidden from us.

**5. The single-crystal difficulty and the proposed carrying field**

The hypothesis was introduced in response to the observed absence of single-crystal violations. It is derived from observing the conditions required to establish polarisation entanglement and that (𝜖 φ × A_E) provides a momentum inpulse that changes phase, rotational phase can only be achieved if the carrying fields allow it.   What it does do is commit in advance: it names the configurations that should support rebalancing (two-crystal combinations, Type II cone intersections), and it predicts a correlation for circularised single-crystal pairs where orthodox quantum mechanics predicts none. A null result there refutes the hypothesis.

**6. What precisely do the two proposed experiments falsify?**

Both experiments test the Copenhagen interpretation in proposing experiments that cannot be explained by the orthodox thinking. Plainly put it tests if the formulation of quantum mechanics is correct.  

**7. Spacetime implementation and frame dependence**

In the present formulation the source rest frame is physically privileged, not a computational convenience. The model therefore carries a preferred frame for the nonlocal update, as Bohmian mechanics does. No transformation law to other frames is given, and Lorentz covariance remains open, as the paper says.

------ Original Message ------

From "SMH Emamifar" <smhema...@gmail.com>

To "anton vrba" <anto...@gmail.com>

Cc "Bell Inequalities and quantum foundations" <Bell_quantum...@googlegroups.com>

Date 10/9/2026 10:53:38 AM

Subject Re: [Bell_quantum_foundations] Classical Quantum Mechanics