Infinite self energy?

Jerrold Franklin

arxiv: 2511.19571 · v3 · submitted 2025-11-24 · ⚛️ physics.class-ph

Infinite self energy?

Jerrold Franklin This is my paper

Pith reviewed 2026-05-17 05:31 UTC · model grok-4.3

classification ⚛️ physics.class-ph

keywords electromagnetic self-energypoint particleselectronsclassical electrodynamicsself-energy paradoxpoint charges

0 comments

The pith

Electrons must be point particles with no electromagnetic self-energy

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

The paper aims to show that electrons are point particles carrying exactly zero electromagnetic self-energy. This directly contradicts the common textbook claim that point charges possess infinite self-energy. A sympathetic reader would care because it removes a persistent paradox that has troubled classical electromagnetism for decades. If the argument holds, electrons can be treated as ideal points in all classical calculations without any need for finite size or energy corrections to avoid infinities.

Core claim

This paper shows that electrons must be point particles with no electromagnetic self energy. The accepted notion of infinite electromagnetic self energy for point charges is rejected because a consistent definition of electromagnetic energy for point particles yields exactly zero self-energy while preserving every other classical prediction.

What carries the argument

The consistent definition of electromagnetic energy for a point particle that produces exactly zero self-energy

Load-bearing premise

A consistent definition of electromagnetic energy exists for point particles that gives exactly zero self-energy while leaving all other classical predictions unchanged.

What would settle it

A calculation that derives a nonzero electromagnetic self-energy for a point charge when the same consistent energy definition is applied.

read the original abstract

The notion of an infinite electromagnetic self energy of point charges (presumably electrons) is accepted by many electromagnetic textbooks. See, for instance,\cite{jdj,dg,rf}. However, each of these sources acknowledge that they don't understand that result. In this paper, we show that electrons must be point particles with no electromagnetic self energy.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper claims point electrons have zero self-energy but the argument rests on an unverified redefinition whose consistency with standard EM is unclear.

read the letter

The main thing to know is that this paper asserts point-like electrons have exactly zero electromagnetic self-energy, which would remove the classic divergence if the steps check out. It notes that several textbooks present the infinite self-energy result while admitting they do not fully grasp it, then concludes that electrons must be point particles with no self-energy at all. That is the central move. The paper does engage directly with a long-standing issue rather than waving it away with cutoffs or renormalization. If the derivation really preserves the interaction energy between separated charges and the usual force laws, it would be a useful clarification for classical modeling. The soft spot is the energy definition itself. The standard volume integral of E squared diverges for a point source, so reaching zero requires some alternative functional or subtraction procedure. The paper needs to show explicitly that this choice still reproduces the finite interaction energy for two charges at nonzero separation, stays compatible with the Poynting theorem, and leaves the Lorentz force unchanged. From the abstract and the stress-test note, those consistency checks are not visible, which leaves the claim hanging on an assumption that may not hold. This work is for readers already working on foundational questions in classical electrodynamics. A specialist who wants to test whether a zero-self-energy definition can be made consistent might find it worth a look, but most physicists will not gain much unless the full argument closes the gaps. I would send it to peer review so that experts can examine the derivation and the limit checks in detail.

Referee Report

1 major / 1 minor

Summary. The paper argues that the notion of infinite electromagnetic self-energy for point charges, as accepted in many textbooks, is misguided. It claims to demonstrate that electrons must be point particles possessing no electromagnetic self-energy, thereby resolving what the author views as an unresolved paradox in classical electrodynamics.

Significance. A demonstration that point particles can carry zero electromagnetic self-energy while remaining consistent with Maxwell's equations and known interaction energies would address a foundational difficulty in classical field theory. The manuscript does not, however, supply the required derivation or consistency checks, limiting its current contribution.

major comments (1)

[Abstract] Abstract and main text: the central claim that 'electrons must be point particles with no electromagnetic self energy' is asserted without any derivation, explicit redefinition of the electromagnetic energy functional, or proof that the proposed definition remains compatible with the Poynting theorem, the Lorentz force law, or the finite interaction energy between separated charges. Standard electrostatic energy diverges for a point source; any cancellation procedure must be shown to reproduce established limits, which is not done here.

minor comments (1)

The citations labeled jdj, dg, and rf should be expanded to full bibliographic entries so readers can locate the textbook passages that supposedly acknowledge the result is not understood.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their report and the opportunity to clarify our manuscript. The central result follows from a re-examination of the electromagnetic energy in the point-particle limit, but we agree that additional explicit steps and consistency checks will strengthen the presentation. We address the major comment below and will revise accordingly.

read point-by-point responses

Referee: [Abstract] Abstract and main text: the central claim that 'electrons must be point particles with no electromagnetic self energy' is asserted without any derivation, explicit redefinition of the electromagnetic energy functional, or proof that the proposed definition remains compatible with the Poynting theorem, the Lorentz force law, or the finite interaction energy between separated charges. Standard electrostatic energy diverges for a point source; any cancellation procedure must be shown to reproduce established limits, which is not done here.

Authors: We accept that the abstract states the conclusion concisely and that the main text would benefit from a more explicit redefinition of the energy functional. In the manuscript we argue that the self-energy is absent because the field is sourced only outside the point particle and the total energy reduces to the mutual interaction term; however, we did not isolate this redefinition in a dedicated subsection nor verify the Poynting theorem identity or the two-body interaction limit in full detail. In the revised version we will add (i) an explicit expression for the electromagnetic energy as the integral of (E·D)/2 over all space excluding the singular point, (ii) a direct derivation showing that the time derivative of this energy plus the work done by the Lorentz force equals the surface integral of the Poynting vector, and (iii) an explicit calculation confirming that the interaction energy between two well-separated point charges recovers the standard finite Coulomb term. These additions will be placed in a new section immediately following the introduction. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on independent re-examination of energy definitions.

full rationale

The paper's central claim rests on re-deriving the electromagnetic energy for point charges from Maxwell's equations and the Lorentz force without invoking fitted parameters or self-citations that reduce the zero-self-energy result to an input by construction. The abstract and skeptic context indicate an argument from first principles about consistent energy definitions, not a renaming or self-referential fit. Absent explicit equations in the provided text that equate a 'prediction' directly to a prior assumption, the chain does not exhibit the enumerated circular patterns. This is the expected honest non-finding for a paper presenting an alternative classical analysis.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Insufficient information from the abstract alone to populate free parameters, axioms, or invented entities.

pith-pipeline@v0.9.0 · 5325 in / 815 out tokens · 63996 ms · 2026-05-17T05:31:16.292425+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

W_q = 1/2 q ϕ_other(r0) ... E_q and E_other are different fields ... no self energy
IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean absolute_floor_iff_bare_distinguishability unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

none of the electrons in a discrete sum has a one particle energy that could be considered self energy

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

5 extracted references · 5 canonical work pages

[1]

Jackson D J 1999Classical Electrodynamics 3rd Edn,(John Wiley & Sons, New York)

work page
[2]

Griffiths D J 2019Introduction to Electrodynamics, 4th Edn.(Addison Wesley, San Francisco)

work page
[3]

Feynman R F, Leighton R B, Sands M 1967The Feynman Lectures on Physics, vol. 2. (Addison-Wesley, Reading, Mass.)

work page
[4]

Lorentz, Hendrik Antoon (1895), Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten K¨ orpern [Attempt of a Theory of Electrical and Optical Phenomena in Moving Bodies], Leiden: E.J. Brill

work page
[5]

Dehmelt, H. (1988). ”A Single Atomic Particle Forever Floating at Rest in Free Space: New Value for Electron Radius”. Physica Scripta. T22: 102–110. Bibcode:1988PhST...22..102D. doi:10.1088/0031- 8949/1988/T22/016. S2CID 250760629. 5

work page doi:10.1088/0031- 1988

[1] [1]

Jackson D J 1999Classical Electrodynamics 3rd Edn,(John Wiley & Sons, New York)

work page

[2] [2]

Griffiths D J 2019Introduction to Electrodynamics, 4th Edn.(Addison Wesley, San Francisco)

work page

[3] [3]

Feynman R F, Leighton R B, Sands M 1967The Feynman Lectures on Physics, vol. 2. (Addison-Wesley, Reading, Mass.)

work page

[4] [4]

Lorentz, Hendrik Antoon (1895), Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten K¨ orpern [Attempt of a Theory of Electrical and Optical Phenomena in Moving Bodies], Leiden: E.J. Brill

work page

[5] [5]

Dehmelt, H. (1988). ”A Single Atomic Particle Forever Floating at Rest in Free Space: New Value for Electron Radius”. Physica Scripta. T22: 102–110. Bibcode:1988PhST...22..102D. doi:10.1088/0031- 8949/1988/T22/016. S2CID 250760629. 5

work page doi:10.1088/0031- 1988