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REVIEW 3 major objections 4 minor 36 references

From Faraday and Maxwell to Quantum Physics. The later story of the Electromagnetic Vector Potential

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This paper argues that the electromagnetic vector potential, not the fields themselves, is the thread that runs from Faraday through Maxwell to QED, and that its quantum nature is already visible in ordinary mobile phone receivers.

desk verdict A celebratory historical essay whose one concrete quantitative claim—mobile phones can count single photons—does not survive contact with the receiver noise floor; the rest is familiar history and clearly labeled speculation. read the letter →

arxiv 2509.04486 v1 pith:TMZIHQQ2 submitted 2025-08-31 physics.hist-ph hep-thquant-ph

Tuck Choy , Miguel Ortuno This is my paper · ORCID
classification physics.hist-phhep-thquant-ph
keywords electromagneticvectorpotentialquantumelectrodynamicsphotoncountingmobilephonereceiverLandau-Lifshitzlimitgaugeinvariancetoymodelofelectronhistorymechanics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tells the story of the electromagnetic vector potential as the connecting thread from Faraday's 'electro-tonic state' through Maxwell's equations to the quantized fields of QED. Its central historical claim is that the vector potential, not the E and B fields, is the fundamental quantum object, and that it forms a coupled 'duet' with the Dirac electron field that awaits a supersymmetric unification. The paper's concrete quantitative claim is that a 1.2 GHz signal of only about 0.25 µV/m—set by the Landau-Lifshitz one-photon-per-wavelength condition—already matches the sensitivity of ordinary mobile phone receivers. From this it concludes that single-photon counting experiments in QED can be done at home by modifying a phone.

What carries the argument

The central object is the electromagnetic vector potential A(r,t), read quantum-mechanically as the mode-expanded operator Â(r,t) whose Fourier coefficients are photon creation and annihilation operators. The argument's sharpest quantitative instrument is the Landau-Lifshitz quantum-regime condition (Eq. 6), E ≤ √(2ℏc) ν²/c² ≈ 0.25 F² µV/m, which is used to equate single-photon occupancy of a cubic wavelength with receiver sensitivity at 1.2 GHz; a companion strain formula (Eq. 7) extends the same logic to putative graviton detection.

What would settle it

Measure the noise floor of a standard 1.2 GHz phone receiver over its bandwidth at room temperature and compare with the single-photon energy: thermal noise kTB exceeds 8×10^-25 J per photon by orders of magnitude, so a receiver limited by that noise cannot resolve individual photons; alternatively, show that at -119 dBm the photon arrival rate is ~10^11 s^-1, so 'one photon per m³' does not equal 'one detectable photon per measurement interval'.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery it wants to establish is double: historically, the electromagnetic vector potential A(r,t) is the concept that survives from Faraday's electro-tonic state through Maxwell's electromagnetic momentum into the quantized QED operator Â(r,t), and it is inseparable from the Dirac spinor field ψ with which it forms a unified, as-yet-unknown supersymmetric structure. Practically, the paper claims that the quantum regime of the electromagnetic field is not remote: equating the electromagnetic energy density E²/4π with the Planck energy density hν/λ³ gives a field strength E ≈ 0.25 F² µV/m for frequency F in GHz, and at 1.2 GHz this is right at the -119 dBm sens

Load-bearing premise

The load-bearing premise is that the field strength at which one photon occupies a cubic wavelength is the same as the minimum signal a phone receiver can detect; this equates a quantum energy-density condition with a classical receiver's noise floor.

Editorial extensions

If this is right

  • If the sensitivity match in Eq. (6) holds, consumer GHz receivers are already single-photon detectors, and radio-frequency photon statistics (e.g., Poisson distributions) become observable with commodity hardware.
  • Kitchen-table QED becomes a real pedagogical option: students could detect the 21 cm hydrogen line and count microwave photons without a laboratory.
  • The historical thesis implies that the vector potential is not a gauge artifact but the primary physical field, meaning textbook statements that 'A is unobservable' are wrong and boundary or topological effects may produce observable consequences.
  • The electron-as-trapped-light toy model, if pursued, ties a g-factor of 2 and the fine-structure radius to pure electrodynamics, suggesting a classical precursor to a unified electron-photon description.
  • The graviton analog (Eq. 7) places single-graviton sensitivity at GHz frequencies far beyond present detectors, motivating new quantum-metrology technologies.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The mobile-phone claim likely overreaches: a radio receiver at -119 dBm sees roughly 10^11 photons per second in a typical bandwidth, and thermal noise at room temperature (kT/hν ~ 5000 per mode) means the energy threshold is set by noise, not by single-photon granularity; true photon counting would need a number-resolving detector and a cold front end.
  • The one-photon-per-cubic-wavelength criterion is better read as a sensitivity bound for coherent detection of faint sources (like Voyager 1) than as a photon-counting threshold, since energy density and photon arrival statistics are distinct quantities.
  • One testable extension: run Eq. (6) at other carrier frequencies (e.g., Wi-Fi at 2.4 GHz or GPS at 1.575 GHz) and compare with receiver noise figures; the claimed match is specific to 1.2 GHz and may not generalize.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper is a conference proceedings contribution that traces the history of the electromagnetic vector potential from Faraday and Maxwell through the quantization of the electromagnetic field, discusses gauge-invariant extensions of Maxwell's theory, claims that ordinary mobile phones can operate as single-photon QED detectors, presents a classical toy model for the electron's g-factor, and extends the same field-strength criterion to a proposed graviton-detection limit. The central advertised quantitative claim is that, at 1.2 GHz, the field strength corresponding to one photon per cubic wavelength (Eq. 6) is comparable to the sensitivity of a mobile phone receiver, so that a modified phone could count photons. The paper also makes a number of historical and pedagogical remarks about toy models and quotes from Heisenberg, Dirac, and Wigner.

Significance. If the main quantitative claim were correct, it would be remarkable: it would imply that the quantum regime of QED is accessible with off-the-shelf mobile phone receivers and that students could perform photon-counting experiments at home. The historical portions are competently assembled and some references, such as Pocklington's integral equation and Dirac's constraint quantization, are interesting and not commonly collected in one place. The authors also deserve credit for presenting the toy models with caveats ('food for thought', 'over simplified') and for reproducing primary historical exchanges. However, the load-bearing physical claim—that the Landau-Lifshitz field-strength scale is a detection threshold for a coherent radio receiver—is unsupported and in fact wrong. Correcting this would require substantial revision of Sections IV and VI; preserving the claim as stated is not possible. The toy-model derivation of g=2 is also circular. The paper therefore does not substantiate its advertised contribution.

major comments (3)
  1. [Section IV, Eq. (6)] The central claim that a modified mobile phone can count single photons conflates a field-strength scale for one photon per cubic wavelength with a receiver detection threshold. Eq. (6) estimates the electric field amplitude of a mode containing about one photon; it says nothing about whether a linear, coherent receiver can resolve that energy against its noise floor. At 1.2 GHz, hν≈8.3×10^-25 J, while -119 dBm is 1.26×10^-15 W, i.e. about 1.5×10^9 photons/s. At 300 K the thermal occupation is n̄≈kT/hν≈5×10^3, so even a 1 Hz bandwidth is flooded by ~5×10^3 hν/s of thermal noise; any practical receiver bandwidth (kHz–MHz) raises this by orders of magnitude. A phone front-end measures a continuous field, not photocounts, and single-photon microwave counting requires qubit-based detectors at millikelvin temperatures. Thus the 'keen hacker' photon-counting claim, and the derived GPS and 21-c
  2. [Section VI, Eq. (7)] The same conflation appears in the graviton-detection section. Eq. (7) is a dimensional-analysis scale for the strain of a single graviton per cubic wavelength, not a sensitivity threshold for an interferometric strain detector. Comparing H≈4.6×10^-39 F² km^-1 directly with LIGO's H~10^-22/km at 100–200 Hz does not establish any measurement capability: one must account for the interferometer response, classical and quantum noise, integration time, and signal bandwidth. The claims that GHz LIGO observatories would require 'quantum metrology, super-entangled state detectors' and could detect gravitons from primordial black holes or cosmic strings are speculative and unsupported by any quantitative detector model.
  3. [Section V, g-factor derivation] The derivation of g=2 from the spinning-cavity toy model is not self-contained. The text begins with the standard magnetic moment µ=eℏ/(2mc)s, which already corresponds to g=1, and then asserts that because the magnetic energy is 'only half' of the total energy mc², the mass should be halved, giving µ=eℏ/(mc)s, i.e. g=2. No derivation of the 'magnetic energy is half the rest energy' relation from the model is provided, so the argument is circular. The authors' stated caveats ('more creative thinking is needed', 'over simplified') are appropriate, but if the section is meant to substantiate Jennison's claim that the model gives g=2 exactly, a full calculation from the model's fields and stresses is needed.
minor comments (4)
  1. [Throughout] There are many typographical errors: 'Barestetskii' should be 'Berestetskii' [28]; 'Higg's' should be 'Higgs'; 'Jennsion' should be 'Jennison'; 'Eugnene Wigner' should be 'Eugene Wigner'; 'laboratoy' should be 'laboratory'; 'privilaged' should be 'privileged'. The equations in Section III, especially Eq. (4), have missing or malformed differential terms and should be carefully typeset.
  2. [Section I] The statement that 'Maxwell's theory is incomplete and that there are situations due to boundaries or topology that demand the vector potential must itself be gauge invariant' is too strong without a detailed citation and a precise definition. In standard electrodynamics, the vector potential is always gauge-dependent; the gauge-invariant objects are the fields and holonomies. If the authors intend a specific topological extension, it should be stated precisely.
  3. [Section II, Eq. (1)] The notation J=Λ(ψ)A is unexplained. The text says the current is J=eψ†γ^μψ, but the equation writes it as an operator Λ(ψ) acting on A. Clarify the definition of Λ and how this is equivalent to the standard Maxwell-Dirac system; otherwise the 'unified' equations are not self-contained.
  4. [Section IV] The phrase 'one photon per m3 sensitivity' is dimensionally a photon number density, not a detector sensitivity. If the authors wish to compare with the human eye or other detectors, they need to specify detection volume, integration time, and quantum efficiency. As written, the comparison is not meaningful.

Circularity Check

0 steps flagged · score 2.0 of 10

No load-bearing circularity; the central estimates come from external formulas and the only self-citations are peripheral.

full rationale

The paper's central quantitative claims are not circular. Equation (6) is presented as an externally derived Landau–Lifshitz scale obtained by equating electromagnetic energy density with hν/λ³; the mobile-phone photon-counting suggestion compares that scale to a known receiver sensitivity rather than fitting the receiver sensitivity to force a conclusion. The g=2 discussion is a heuristic toy-model calculation based on an assumed energy partition, not a fitted parameter renamed as a prediction. The self-citations that appear ([13], [33]) are side remarks about pedagogy and cosmology and are not load-bearing for the main claims. Concerns about thermal noise, photon rates, and the difference between field-amplitude detection and photocounting at GHz frequencies are physical correctness risks, not circularity. Overall, no derivation reduces by construction to its own inputs; the score of 2 reflects only the presence of minor non-load-bearing self-citations.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The paper rests on standard QED references, the Jennison toy model (external), and speculative extensions from Barrett. No free parameters are fitted to data; the estimates use known constants. The main contributions are narrative and order-of-magnitude calculations, not new derivations.

assumptions (4)
  • standard math The Landau-Lifshitz quantum field limit (Eq 6) determines the field strength at which quantum effects become relevant for a given frequency.
    The paper takes this formula from Landau and Lifshitz (ref [28]) and uses it to make the mobile phone claim.
  • ad hoc to paper A traveling electromagnetic wave trapped in a rotating cavity can model an electron with g-factor 2 (Jennison's toy model).
    Adopted from Jennison [25,26] and used in Section V to derive the electron's magnetic moment.
  • domain assumption Maxwell theory is incomplete and requires the vector potential to be gauge invariant via a compensating field (Eq 5), leading to topological charges.
    Stated in Section III, but not derived; the paper refers to Barrett [21] for details.
  • ad hoc to paper The gravitational strain quantum limit (Eq 7) derived by dimensional analysis can be compared with LIGO-style detectors to assess graviton detection.
    This is a speculative analogy in Section VI, without a detector model or signal calculation.

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Cite this review

Pith. "Pith review of From Faraday and Maxwell to Quantum Physics. The later story of the Electromagnetic Vector Potential." pith.science (2026). https://pith.science/paper/TMZIHQQ2

@misc{pith2026250904486,
  author       = {Pith},
  title        = {Pith review of: From Faraday and Maxwell to Quantum Physics. The later story of the Electromagnetic Vector Potential},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TMZIHQQ2}},
  note         = {Machine review of arXiv:2509.04486}
}
abstract

With the advent of quantum mechanics by Heisenberg in 1925 exactly a century ago, the quantization of the electromagnetic field became an important goal for our founding fathers, whom we are here to celebrate. It was realized very soon that a consistent picture of quantum electrodynamics (QED) requires the quantization of not just the electromagnetic field ${\bf A}({\bf r},t)$, but the electron field ${\bf \psi}({\bf r},t)$ as well. The electron field is now a Dirac spinor field and it becomes a major partner for the vector potential. Together these two fields form a duet which yearns for a unification which is not often emphasized in text books, but no one knows how to do this yet. The underlying structure appears to be a super-symmetric one where bosons and fermions live comfortably as a single field that could by some yet unknown process produce QED. This area is still at the forefront of current research with names like Super-symmetric Quantum Electrodynamics (SQED), strings and others. Ironically for a variety of reasons, the number of fields in SQED has to be increased and not decreased, defying the objective of an economical unification. Furthermore it is now known that Maxwell's theory is incomplete and that there are situations due to boundaries or topology that demand the vector potential must itself be gauge invariant. (This paper is dedicated to the celebration of 100 years of quantum mechanics, on the anniversary of Heisenberg's founding paper on the subject in July 1925, delivered by Miguel Ortu\~no at the IQSA 2025 Conference at Tropea in Calabria, Italy from 30 June to 4th July 2025. The proceedings will be published as a celebratory volume by World Scientific Publications, Singapore in 2026).

Figures

Figures reproduced from arXiv: 2509.04486 by the authors.

Figure 1
Figure 1. Milliwatt WSPR transceiver built using a raspberry Pi Zero [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. WSPR 1mW transmissions, highlighted is transmission from Texas to Western Australia [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Reproduced from Electronics World http://www.electronicsworld.co.uk with permission[26] [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Reproduced from Electronics World http://www.electronicsworld.co.uk with permission[26] [PITH_FULL_IMAGE:figures/full_fig_p016_4.png]

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Reference graph

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