Retardation in the Coulomb Potential

What this document is

"Retardation in the Coulomb Potential" is a short comment by Harold Aspden published in Physics Essays, volume 8, number 1, 1995. It replies to a challenge from a commenter named Allen, published in Physics Essays volume 6, page 614 (1993), and it summarizes Aspden's own earlier published analyses of how field energy is distributed in space between interacting charges. The piece is framed as a brief summary stimulated by Allen's challenge rather than as new experimental work. No experimental data are reported. The received date is given as 10 June 1993.

The reading-guide packet for this source supplies selected excerpts only. Two explicit "intervening text not supplied" breaks appear, and the semantic map records high limitation scores (0.93–0.94) across all three segments. The middle of the argument is unavailable, and this guide does not reconstruct it.

The retardation proposition

Aspden's proposition, offered in an earlier paper, is that there has to be retardation in the Coulomb interaction. When two electric charges move and their separation changes, the electrostatic interaction energy cannot adjust instantaneously.

His stated basis is geometric. As viewed from either charge, the spatial deployment of electrostatic field energy attributable to the interaction shows no net energy within a sphere of any radius up to the charge separation distance. From this he infers that if any of that energy transits through the seat of either charge — as action or reaction — then no part of the energy change can become part of the electrostatic potential until a time lapse of at least (charge separation ÷ speed of propagation).

He goes further and speculates that the retardation may be doubled: energy fed in through the seat of one charge must first reach a remote field zone before it can begin the equidistant journey between that zone and the other charge. He states plainly that the whole logic depends on whether the speed at which energy can travel is finite (retarded action) or infinite (instantaneous action).

Allen's counter-argument

Allen argues there is no delay and hence no retardation. His argument is that a spherical shell centered exactly between the instantaneous positions of the two charges, with radius equal to half their separation, marks the boundary between positive and negative interaction energy density. Equal and opposite energy increments can therefore be drawn by each charge in instantaneous synchrony.

Aspden notes that this argument relies on the assumption that the electrostatic field set up by a charge has no dependence on time — that the action is instantaneous. The disagreement is therefore not about the geometry but about the underlying premise: whether the field is time-dependent at all. Aspden frames the open question as whether an energy form that is not part of the electrostatic potential can travel through that field and, after the transit time, convert into electrostatic energy — and, in reverse, whether electrostatic energy shed by the remote field zone assumes a different form before passing through the electrostatic field to reach the seat of charge.

The field-energy distribution results

Two computational results are reported, and they are the most concrete content in the paper.

The zero-net-energy zone (1979). For two charges P and Q of like polarity, the sum of the interaction energy within a radius R equal to the charge separation distance is zero. Aspden notes that, given an energy gradient reducing as the inverse square of distance from the charge center, it may seem surprising that a similar curve applies to the electric field interaction energy. This is depicted as Fig. 2 in the paper, described as the Coulomb field energy distribution set up by a hollow sphere of charge of radius x, or equivalently by the mutual interaction of two like-polarity charges separated by distance x.

The Lorentz-force distribution (1980). The follow-up analysis, attributed mainly to coauthor Eagles, computed the energy distribution for the Lorentz electrodynamic force interaction. The reported finding: regardless of the directional criteria of the Lorentz force law — which requires the force between two moving charges to vary according to the orientations of their motions relative to each other and to their separation vector — the rigorous analysis leads to a linear form of energy distribution ranging up to the separation distance, and then a discontinuity in the general case as the distribution adjusts to a common inverse form at increasing distance. This is Fig. 3, showing the magnetic field energy distribution for (a) mutually parallel charge motion along the separation vector and (b) mutually parallel motion perpendicular to the separation vector. Case (a) is also said to apply to the gravitational field energy distribution.

Aspden calls the discontinuity a weakness inherent in the Lorentz interpretation, arguing it would be extraordinary if the energy distribution field could be anything other than continuous at that range from either charge. He concedes that a continuous transition may well apply when at least one charge is part of a continuous closed circuital current — which he identifies as the empirical basis of the law — but argues this gives no assurance that the field implications extend to two discrete charges in general motion. This is an internal tension in the paper: he asserts a distinction between closed-circuit and discrete-charge cases without resolving it empirically. He adds that relying on empirical findings confined to closed-circuit currents (including magnetic field sources) has abandoned the one link that could bridge conventional electromagnetism and the underlying quantum world of discrete charge centers.

The gravitational extension

Aspden extended the analysis to gravitation in another 1980 paper. He states that standard gravitational field theory should give a field energy distribution exactly similar to Fig. 1, with the qualification that gravitational interaction energy between two masses is negative, just as the Coulomb interaction would be between charges of opposite polarity.

He then states a principle: if the interaction energy tended to be as remote as possible from each reference body, the Fig. 2 case would apply; if the energy sought the closest proximity with each reference body, then the only distribution consistent with an inverse-square law of force would be a linear distribution over the separating distance. The excerpt breaks off mid-sentence here, and the intervening text is not supplied.

Radiation, the inversion radius and the inertia claim

The third segment turns to the classical theory of energy radiation from electric charge. Aspden argues that the Larmor derivation of the radiation formula overlooks the question of what causes the acceleration — "Let there be acceleration" is the usual starting point. In the standard picture, for each acceleration pulse the electric field lines are assumed to travel as if rigidly connected to the source charge, apart from a kink as the wave disturbance propagates at light speed; the extra field energy in that kink is the supposed radiated energy.

Aspden says he recognized the need for another charge interacting with the accelerated charge to account for the acceleration, and asked what happens to that kink field component as the wave disturbance passes through the field of the other charge. He criticizes the approximation that once the wave carrying radiated energy is initiated it travels outward until it is too far from the source to affect the remote wave-zone calculation, and is then simply lost as radiation.

Studying the interaction energy close to the accelerated point charge, together with the self-energy, he reports finding an inversion radius at which no energy travels outwards or inwards from the charge. He regards this as relevant because, in his reading, the Poynting vector theory assumes that energy is radiated by an accelerated electron rather than proving it.

He anticipates the appeal to radio transmission and counters it: energy radiation by the concerted acceleration of many billions of electrons is no proof that each individual electron is a self-radiator. The Larmor formula is proportional to the square of the total charge accelerated, and he argues that (nq)² is hardly to be distinguished from n(n−1)q² once the assumed self-radiation energy n(q)² of n electrons is removed. Radio transmitters, he notes, involve billions of electrons oscillating together.

He cites as clear evidence of non-radiation the fact that single electrons moving in atoms, with their "Pauli exclusion" passport, do not radiate their energy. He says this is consistent with the quantum hypothesis, but that historically, because the seat of the Coulomb interaction energy was not studied, physics missed the fact that an electron will contrive to preserve itself by not radiating its intrinsic energy.

The central claim follows: when he determined the boundary radius of the inversion (zero energy transfer) condition, it was found to depend on a unique relationship between the assumed rate of acceleration f, the sum total E of the self-energy of its electric field, and the speed of propagation c of the wave disturbance. He asserts that the zero energy radiation condition is nothing other than the raison d'être for the very existence of the inertial property, with mass M as the connection linking f, E and c, so that the electron's self-conservation is a causal foundation for E = Mc².

This is a strong claim presented without independent verification. It also sits in tension with standard classical electrodynamics, where the Larmor formula and Poynting-vector treatment of radiation are standard results — though Aspden's point about bound atomic electrons not radiating aligns with quantum treatments.

The "chicken and egg" framing

Aspden closes with a rhetorical summary. A standard textbook derivation (the excerpt breaks off here) leads to a generic electrodynamic law that includes, as a different special case — where two like charges move in parallel directions — the inverse-square action directed along the line linking the charges that we associate with gravitation. He then writes that physics has gone adrift on the "chicken and egg" question, trying unsuccessfully to get Lorentz (the chicken) to lay a variety of eggs including gravitation, without realizing the need for an alternative: several chickens (Neumann potentials) cooperating to determine a general law of electrodynamics that lays different eggs in different circumstances (Lorentz force and gravitation). He adds that physics has gone adrift further in not resolving the conflict between energy radiation and quantum processes by taking notice of the flaw he identifies in the Larmor theory.

This framing is colorful but not load-bearing for the technical claims. The substantive content is the field-energy distribution analysis and the inversion-radius argument.

Claims versus computations

The source text's evidence is a journal comment summarizing the author's own prior work. It is worth separating the two kinds of statement it contains:

• Presented as rigorous computation: the zero net interaction energy within a sphere of radius equal to the charge separation (1979); the linear-then-discontinuous energy distribution for the Lorentz force interaction, attributed mainly to Eagles (1980).
• Presented as author claims, not independently validated: the necessity of retardation in the Coulomb interaction; the speculation that retardation may be doubled; the inversion radius and its link to inertial mass; the derivation of E = Mc² from the zero-energy-transfer condition; the reading of the Larmor formula as unproven for a single electron.

The acknowledgment thanks Dr. Panarella, the editor of Physics Essays, for the opportunity to comment on Allen's paper, and thanks Allen for questioning the earlier comments. It also thanks a referee who "stressed a number of points that warranted mention" — points that are not enumerated in the supplied text.

Coverage gaps

• Two explicit "intervening text not supplied" breaks: one in segment 1 (between the discussion of the energy form and the inverse-square gradient) and one in segment 2 (in the gravitational discussion, and again before the textbook-derivation summary).
• The referee's points are acknowledged but not listed.
• The 1979 and 1980 papers by Aspden (and Eagles) are referenced but not supplied; the 1993 Allen comment is referenced but not supplied.
• The full argument's middle sections are unavailable, so this guide does not attempt to reconstruct them.

Where to read next

• The 1979 paper on the electrostatic field energy distribution (referenced, not supplied).
• The 1980 paper with Eagles on the Lorentz-force energy distribution (referenced, not supplied).
• The 1980 paper on gravitational action (referenced, not supplied).
• Allen, Physics Essays 6, 614 (1993) — the comment that occasioned this reply.

Related pages in this wiki

This source sits alongside the other Aspden packets: (Power From Magnetism and the Potter debate), (over-unity motor design), (Modern Aether Science, 1972), (Aether Science Papers, 1996) and the cyclotron-resonance packet. Where those extend the Aspden corpus into motor and energy-extraction claims, this one extends it into electrodynamic foundations — retardation, radiation and inertia. The critique of Lorentz and the appeal to a deeper electrodynamic substrate also connect to laws-of-nature-critique, aether-cosmology-claim and vacuum-reaction-field-claim, and to the broader alternative-physics thread running through the Kozyrev and morphic-resonance dossiers.