Turning Back to Coulomb's Law as a Basis for Electromagnetism
| Scientific Paper | |
|---|---|
| Title | Turning Back to Coulomb's Law as a Basis for Electromagnetism |
| Read in full | Link to paper |
| Author(s) | Jan Olof Jonson |
| Keywords | Coulomb's law, Electromagnetism, electromagnetic theory, electromagnetic fields, electromagnetic field |
| Published | 2008 |
| Journal | Proceedings of the NPA |
| Volume | 5 |
| Number | 1 |
| No. of pages | 13 |
| Pages | 113-118 |
Read the full paper here
Abstract
Successful falsifications of today's electromagnetic theory pave the way for a 'back to the basics' approach through turning back to coulomb's law as a basis for electromagnetism. In this paper a number of apparently disparate discoveries within electromagnetism and related subjects are brought together into a coherent context. The intent is to gain momentum for a new electromagnetic field theory, based upon Coulomb's original force law of 1785. Throughout the paper it is repeatedly given support to the assumption that Coulomb's law is able to give credit to phenomena, which have thus far been explained using either new or completing laws. The first -and simultaneously most crucial - issue is that of the potential functions used in order to derive the electromagnetic fields used today, often called the Lienard-Wiechert potentials. Referring to an earlier paper it is shown that these potentials have regrettably been fallaciously derived. The issue is crucial, since if the potentials are false, the rest of the electromagnetic theory must accordingly be rejected, due to its formal dependence of the former. Reference is also being made to earlier results with Ampere's bridge, refuting the Lorentz force, simultaneously giving credit to Coulomb's law. Also electromagnetic induction can be explained using Coulomb's law instead of the 'Induction law'. The fourth issue is that of 'photons'. Using again Coulomb's law, it is possible to classically explain the "wave-particle paradox". A fifth issue is that of gravity. It is discussed, whether gravity might be able to explain as an electromagnetic effect.
Overview
This is Jan Olof Jonson's 2008 contribution to the NPA conference, a thirteen-page programmatic paper that gathers a decade of his own earlier work into a single manifesto. Its thesis is stated without hedging: Coulomb's law of 1785, applied with retarded action, is sufficient for the whole of classical electromagnetism, and the superstructure built on top of it — the Liénard–Wiechert potentials, Maxwell's equations as a derived system, the Lorentz force, the induction law, the Poynting vector, and the photon as a wave–particle hybrid — should be discarded. The paper does not attempt to prove each of these points afresh; it summarises five previously published attacks and argues that together they oblige a return to electrostatics.
The strategy is explicitly Popperian in temper. Jonson opens by saying that "to be motivated to search for a new theory it is often convenient to see some cases of falsification of the currently, widely accepted theories", and the paper is organised as a chain: break the foundation (the retarded potentials), then show that each effect the foundation was supposed to explain can be recovered from retarded Coulomb attraction alone. He restricts himself to the classical regime, setting relativistic and quantum questions aside as "the task for articles to come". Notably, the departure is not from the results of electromagnetism but from its derivation: Jonson concedes that Maxwell's equations correctly relate the fields to one another, while insisting that what they relate is meaningless.
The argument
Breaking the chain: the Liénard–Wiechert potentials
The retarded potentials are, Jonson says, the logical start of a proof chain running potentials → fields → Maxwell's equations → wave equations, so an error at the first step voids everything downstream. He distinguishes his own objection from J. P. Wesley's. Wesley had argued that it is illegitimate to treat the retarded time inside the delta function as itself a function of the source–field distance, replacing δ(t − t′ − |r − r′|/c) by δ(t′ − t(R)). Jonson rejects this: because the geometry makes the propagation distance vary from element to element, the delay must vary with it, and "these matters of fact makes the Liénard-Wiechert approach correct."
His own charge is different and geometric. Analysing Feynman's derivation, he holds that Feynman assigns a single constant retarded time to each charge element into which a conductor is divided, whereas the retarded time varies continuously along the element because the distance to the field point does. The consequence he claims is "a partial 'double counting' of charge elements of the conductor" — a mathematical rather than a physical error. From this he concludes that "such a fundamental fault within the very basis of the theory must require the rejection of the whole theory."
The Lorentz force and Ampère's bridge
Since the Lorentz force is usually presented without recourse to potentials, it is treated separately. Jonson cites the classic Ampère's-bridge experiments (Moyssides) and Wesley's analysis of them as a critical experiment the magnetic force law fails, and points to his own 1997 Chinese Journal of Physics paper deriving the force between two currents from Coulomb's law alone. The mechanism is a differential retardation effect: the conduction electrons move relative to the fixed positive ions, so the retarded electrostatic force each population exerts on a neighbouring current differs slightly, and the residue is what is normally called the magnetic force. He claims the advantage that his expression "succeeds in predicting the spatial behaviour of the force between the currents, whereas the Lorentz force does not."
Induction, and the claim that direct current is impossible
The most unusual section argues that DC is a fiction. A battery, like a capacitor, is discharged by the current it drives; with Q = CV and I = C dV/dt combined with Ohm's law I = V/R, one obtains dV/dt + V/RC = 0 and hence V = V0 exp(−t/RC). Ohm's law is then not fundamental but a by-product of the exponential's self-similarity under differentiation: "the reason for the constant relation between current and voltage is the fact that by differentiating an exponential function, that same exponential function appears again, times a constant."
For the transformer, Jonson uses the continuity equation for charge together with his Coulomb-derived electric field to obtain a secondary current
- I2 = −ε0εr(A/L) ∂V2/∂t
whose prefactor he notes "corresponds to a capacitance", modelling the secondary as a voltage generator with a series capacitor (Fig. 2). With ∂V2/∂t ~ −∂I1/∂t, V1 = L1∂I1/∂t and V2 = R·I2, he arrives at V2 ~ V1, "just as expected" — the point being that this was reached "using basically Coulomb electrostatics". He grants that "it remains a huge work to determine coupling constants in order to achieve numerically correct values."
The photon without a magnetic field
The Poynting vector is dismissed as a casualty of the first section. In its place, Jonson's earlier papers treat what is called a photon as "a very rapid jump within an otherwise zero electric field due to a neutral atom", produced by the de-excitation of an orbiting electron between two shells. He carries over the two-conductor result — the force between current elements written with cos θ cos ψ and a 1/R2 dependence — by treating an electron bound to a nucleus as equivalent to a conduction current, "the important point of interest [being] the assumption of equivalence of currents". The atoms that the pulsed field touches serve as receiving "antennas". The claimed achievement is that the model reproduces the 1/R2 far-field energy dependence of the Poynting vector, satisfying the requirement that a refutation supply an alternative. Two further claims follow: the electric field "is shown to be aligned with the movement of the photon", and "neither a magnetic field is needed."
Gravity from quark dipoles
The last technical section is offered tentatively. Since neutrons are neutral, an electric account of gravity looks excluded — unless one recalls that they contain fractionally charged quarks (ddu against the proton's uud). Jonson suggests that assemblies of neutrons could adopt "a dipole structuring, as the negative edge of one neutron will feel attached by the positive edge of its closest neighbour" (Fig. 3). He immediately raises the objection himself: static dipole fields fall off as 1/R3, gravity as 1/R2. His proposed escape is that an oscillating dipole radiates with an energy dependence ~1/R2, so if the quarks inside the neutron undergo continuous acceleration there would be "an originally electric force upon other neutral particles, a force that has thus far been denominated for 'gravitational'". He notes that the concept of gravity "is [not] unambiguous, which is shown by the on-going debate concerning dark matter", and closes the section by saying it is "absolutely too early to either support or refute" the model.
Assessment
The paper has a genuine methodological virtue that is rare in this literature: Jonson does not accept every criticism of orthodoxy that happens to point his way. He examines Wesley's objection to the retarded potentials in detail and rejects it, on the correct ground that the retarded time must depend on the source–field separation because the geometry makes that separation vary. He is also explicit that a refutation incurs a debt — "it is the normal scientific practice not only to refute a theory; an alternative must also be provided" — and he pays at least part of it, in the sense that his derivation of the inter-current force from retarded Coulomb attraction is a real calculation with a published referee record. The retarded-electrostatics programme he is working in has a respectable ancestry (Weber, Ampère, Ritz), and the observation that magnetic effects can be recast as relativistic-order corrections to Coulomb attraction is not itself controversial; it is standard in the treatment of the current-carrying wire in a moving frame.
The difficulties begin with the paper's central logical move. Even granting that Feynman's textbook derivation contains a geometric slip, it does not follow that "the whole theory must be abandoned". The Liénard–Wiechert potentials can be obtained by several independent routes — direct solution of the inhomogeneous wave equation by Green's function, or Lorentz transformation of the static Coulomb potential of a uniformly moving charge — none of which passes through the step Jonson criticises. A flawed presentation of a result is not a flawed result, and the paper never addresses the alternative derivations. The same over-reach runs through the paper: the Poynting vector is discarded not by argument but by inheritance from section 2.
Several steps are asserted rather than derived. The transformer calculation is the clearest case. Jonson claims that the standard induction law gets the primary–secondary phase relation wrong "more exactly 90 degrees!", but the chain he actually presents — I2 ~ −∂I1/∂t, V1 = L1∂I1/∂t, V2 = RI2, hence V2 ~ V1 — is precisely the relation Faraday's law gives for an unloaded transformer, since the standard result is also emf2 ∝ dI1/dt. His own worked example therefore does not discriminate between the two theories; it reproduces the orthodox answer and then claims the orthodox answer is wrong by a quarter cycle. He also concedes that the coupling constants are undetermined, which means the model as presented cannot be checked numerically against a transformer at all.
The paper's own arithmetic is loose in places. In section 4.1.1 the current is written I = C dV/dt with a positive sign, but the differential equation that follows, dV/dt + V/RC = 0, requires I = −C dV/dt — with the sign as printed, Ohm's law would give the exponentially growing solution V = V0exp(+t/RC). The decay result is correct physics, so this is a transcription slip rather than a conceptual one, but it sits in a section whose whole point is that a sign or a factor has been mishandled by everyone else. The internal cross-references are also scrambled throughout ("differentiating (1)" for (4), "using (2) and (3)" for (5) and (6), "the homogeneous equation (4)" for (7)), and the reference list does not match the text citations — Feynman is cited as [3] in the text but appears as [6] in the list, while [3] and [4] in the list are bare "ibid" entries. One reference still carries the author's editorial note "check page numbering!!!", confirming that the version archived here is the "March 8 version" draft rather than a finished proceedings paper.
Two claims run into direct experimental conflict. First, the photon model requires the electric field to be "aligned with the movement of the photon" and dispenses with the magnetic field entirely. A longitudinal electric field carries no polarization transverse to the beam, yet transverse polarization of light is among the most robustly measured properties in optics — Malus's law for crossed polarizers, the vanishing of the reflected parallel component at Brewster's angle, and the polarization of scattered sunlight all measure it directly, and none of them is compatible with a purely longitudinal field. The paper does not mention polarization anywhere. Second, the gravity proposal requires neutrons to possess an electric dipole moment large enough to bind matter. The neutron electric dipole moment has been searched for since the 1950s and is bounded to below roughly 10−26 e·cm — one of the tightest null results in physics, and many orders of magnitude too small for the mechanism proposed. There is a further category confusion in the escape from the 1/R3 problem: the 1/R2 of an oscillating dipole is the falloff of radiated power flux, not of a static binding force, and radiation pressure between two emitters is repulsive rather than attractive. Matching a power-law exponent is not the same as producing a force. To his credit, Jonson flags this section as speculative and declines to draw conclusions from it.
The honest summary is that the paper is a research programme announced rather than a result demonstrated. Its strongest section is the one it does not re-derive here — the 1997 Coulomb derivation of the force between currents — and its weakest are the ones added to make the programme comprehensive. Readers wanting to evaluate the case should go to the individual papers cited; this document is best read as their table of contents.