STM-D-0657Paper2006Published and peer-reviewed

The Superposition Principle of Waves Not Fulfilled under M. W. Evans' O(3) Hypothesis

Erhard Wielandt

Abstract and summary · read the original at the source

In one page

Erhard Wielandt, a geophysicist at Stuttgart, takes two pages of algebra to test a specific proposal about light. Since 1992 Myron Evans had argued that every circularly polarised electromagnetic wave carries, besides its two ordinary transverse components, a third constant field pointing along the direction of travel — the B(3) or ghost field — and that the three are locked together by a cyclic relation he treated as a new law of electromagnetism. Wielandt asks whether that survives the most-checked property electromagnetic waves have: linear superposition, the principle that makes interference work. He adds two copies of the same wave shifted in phase by plus and minus alpha. The transverse parts add up to the original wave scaled by two times the cosine of alpha, as they must; the longitudinal part adds up to twice itself, unscaled. The two do not track, and the only value that keeps them consistent is the classical one, with no longitudinal field at all.

Why it matters hereChapter 10 is where this site takes longitudinal structure, scalar waves and the vector potential seriously, so it needs the constraint every such proposal has to clear stated exactly once and stated cleanly: whatever you add to a plane wave has to add the way waves add, because interference measures that directly. Chapter 1 gets a small model of the evidence ladder working — a claim, a two-page test with an unambiguous outcome, and a named measurement that decides it.

What it claims

01The hypothesis under test, stated in the author’s own terms. Evans writes a circularly polarised plane wave travelling along z in a complex circular basis, giving two transverse magnetic components carrying the phase factors for plus and minus the electromagnetic phase, and adds a third component that is a constant vector along the direction of propagation. The three satisfy cyclic relations in which each pair’s cross product returns the conjugate of the third, and the B Cyclic Theorem is the statement that every plane circularly polarised wave is accompanied by that longitudinal field.Section 1, M. W. Evans’ O(3) hypothesis; Equations [1.43] and [1.44]
Published and peer-reviewed
02The test is superposition, and the reason it is the right test is that superposition is one of the best-checked laws of electrodynamics: it is what interference measures, and its mathematical equivalent is the statement that electric and magnetic fields are vectors, which add.Abstract; Section 1, opening paragraphs
Settled physics
03The arithmetic. Wielandt introduces a coefficient that is one under the O(3) hypothesis and zero in classical electrodynamics, then superposes two waves whose phases are shifted by plus and minus alpha, with the cosine of alpha smaller than one. The two transverse components combine to give the original wave multiplied by twice the cosine of alpha. The longitudinal components, being constants, simply add to twice the coefficient times the original amplitude — with no cosine factor. Under the hypothesis the sum should have been accompanied by a longitudinal field scaled by that same cosine, so the two results disagree.Section 2, Checking the superposition property of the O(3) hypothesis; Equations (1) to (8)
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04The conclusion the algebra forces: only the classical value of the coefficient, zero, is compatible with the superposition principle. Wielandt states it as a single line — the cyclical O(3) hypothesis is incompatible with the superposition principle of waves.Section 2, closing statement
Published and peer-reviewed
05A corollary about wave packets, offered as a remark without detailed proof. The transverse components of a circularly polarised wave oscillate in space and time, so a Fourier sum of them can be arranged to cancel outside a chosen region — that is how one builds a localised packet. A longitudinal component that is a constant vector for every Fourier term cannot do that: summing constant vectors returns another constant vector. So under the hypothesis the longitudinal field of a wave packet must either vanish or fill the whole universe at all times, which amplifies an objection Akhlesh Lakhtakia had already raised in 1995.Section 2, Remark without detailed proof
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Read it · abstract

Abstract

In 1992 M.W. Evans proposed a so-called O(3) symmetry of electromagnetic fields by adding a constant longitudinal "ghost field" to the well-known transversal plane em waves. He considered this symmetry as a new law of electromagnetics. Later on, since 2002, this O(3) symmetry became the center of his Generally Covariant Unified Field Theory which he recently renamed as ECE Theory. One of the best-checked laws of electrodynamics is the principle of linear superposition of electromagnetic waves, manifesting itself in interference phenomena. Its mathematical equivalent is the representation of electric and magnetic fields as vectors. By considering the superposition of two phase-shifted waves we show that the superposition principle is incompatible with M.W. Evans' O(3) hypothesis.

Erhard Wielandt, Institute of Geophysics, Stuttgart University, Germany. Preprint arXiv:physics/0607262; published in Physica Scripta 74, 539–540 (2006).

(Abstract only — see the rights note above for why the full text is not reproduced here. The complete paper is five pages and the whole argument fits on the third of them; it is at the source.)

Why this sheet sits in chapter 10. The site’s interest is in what the potentials and the longitudinal degrees of freedom really carry, and the settled anchor for that chapter — the Aharonov–Bohm phase — is itself read off an interference pattern. So interference is the bench that answers both questions, and any proposal that adds a component to a plane wave has to say how that component behaves when two waves are added. The same question is the useful one to put to every alternative electrodynamics on this site. Wilhelm Weber’s force law, reviewed at /library/stm-bc8f1e5c8c, and Steffen Kühn’s Weber–Maxwell formulation at /library/stm-717b3fa832, are both put forward with that discipline: Kühn’s reproduces the standard closed-circuit results and is explicit about the one regime — open circuits — where his account and the textbook account part company, which is where an experiment can decide between them.

The way in

https://arxiv.org/abs/physics/0607262LICENCE. The preprint is arXiv:physics/0607262v1, posted 28 July 2006, and the arXiv record carries the assumed-1991-2003 distribution grant rather than a Creative Commons statement — checked on the arXiv abstract page on 2026-09-08. The version of record is Physica Scripta 74, 539 to 540 (2006), doi 10.1088/0031-8949/74/5/009, published by IOP; it predates SCOAP3 and carries no Creative Commons statement either. So this sheet holds the summary, the claims and the author’s own abstract and sends the reader to the source. The claims below are read against the complete five-page preprint and the locators use the paper’s own section and equation numbering. REGISTRY CORRECTION: the record reached the library with the author given as Gerhard W. Bruhn and the people slug gerhard-bruhn. The paper’s own title page names Erhard Wielandt of the Institute of Geophysics, Stuttgart University, as the sole author; Bruhn appears in the reference list, as the author of two of the earlier commentaries this paper builds on. The byline is corrected here and the people list is left empty until an erhard-wielandt entry exists in the site’s people index.

How to cite it

Erhard Wielandt (2006) The Superposition Principle of Waves Not Fulfilled under M. W. Evans' O(3) Hypothesis. doi:10.1088/0031-8949/74/5/009

Where it sits in the curriculum

Scalar waves and the field behind the fields The evidence ladder