Electron Binding Energies in the Aether Physics Model

Scientific Paper
Title	Electron Binding Energies in the Aether Physics Model
Read in full	Link to paper
Author(s)	David W Thomson, Jim Bourassa
Keywords	Electron, Binding Energies, Aether
Published	2007
No. of pages	10

Read the full paper here

Abstract

Our previous papers and book explain the essentials of the Aether Physics Model in sufficient detail. In this paper, we show the Aether Physics Model's structure and logic for deriving a complete-periodic table ground state electron binding energy equation. There remains a very small arbitrarily induced quantity in the present formulation, but we are confident a physical quantity will soon replace it. This paper demonstrates the capacity for significant progress in understanding quantum structure and quantum mechanics using a completely new quantum paradigm.

Overview

David W. Thomson III and Jim D. Bourassa of the Quantum AetherDynamics Institute present what they describe as the first properly quantum-mechanical result of the Aether Physics Model (APM), a framework they had previously developed in the book Secrets of the Aether and in the conference paper A New Foundation for Physics. Where those earlier works quantified what the authors call "quantum structure", this paper attempts a quantum mechanics: a single closed-form expression that returns the ground-state (1s) Electron binding energy of every element from lithium to uranium, together with separate expressions for hydrogen and helium. The empirical comparison set is Gwyn Williams' compilation of electron binding energies, itself drawn mainly from Bearden and Burr's 1967 re-evaluation of X-ray atomic energy levels.

The departure from the mainstream account is total rather than incremental. Standard treatments of core-level binding energies — Koopmans' theorem, ΔSCF, many-body perturbation theory, coupled-cluster methods, density functional theory — are all variational or perturbative approximations to the many-electron Schrödinger problem, and the authors dismiss the whole family as "probabilistic". In their place the APM offers an explicitly discrete, deterministic scheme built on an "Aether unit" A_u (a quantum of rotating magnetic field with dimensions of kg·m³·sec⁻²·coul⁻² and value 1.419×10¹²), an "electron strong charge" e_emax² = 1.400×10⁻³⁷ coul², and a toroidal rather than point-like electron. Electrical quantities in the model are always expressed in "distributed charge", i.e. charge squared, and the authors are candid that this redefinition of dimensions is one reason the model has attracted little interest from physicists. They also warn the reader that the paper contains one frankly empirical ingredient — a linear factor in Z — which they hope will later be replaced by something physical. The closest companion on this wiki is Cynthia Whitney's Algebraic Chemistry, cited here as prior art in the same problem, and the authors thank her in the acknowledgements.

The argument

Energy as Aether acting through a strong charge

The chain begins from a claim made in the authors' earlier work that the Casimir Effect equation is a disguised form of the electron's strong-force equation. From that they define a "quantum energy" as the Aether unit imparting a strong force through the electron over one quantum length, taken to be the Compton wavelength λ_C = 2.426×10⁻¹² m:

enrg = e_emax² A_u / λ_C

and then observe that this equals m_ec². The identity holds numerically — 1.400×10⁻³⁷ × 1.419×10¹² ÷ 2.426×10⁻¹² = 8.19×10⁻¹⁴ J, the electron rest energy to four figures — but it is worth being clear that A_u is fixed by exactly this requirement, so the agreement is a calibration rather than an independent prediction. The authors' interpretive point is separate and philosophical: "mass is not matter and no physical meaning is attributed to velocity squared", so mc² is held to be an uninterpreted product in the Standard Model whereas the APM version has a stated mechanism behind it.

A short section on kinetic energy establishes a convention used throughout: every energy transaction has a source and a receiver, "cause and effect", so an electron that is either acting or acted upon accounts for only half the transaction. The binding-energy equation therefore carries a factor of one half.

The toroidal electron

Citing David McCutcheon's Ultrawave Theory, the authors note the relation 2π²r_eα₀ = λ_C², i.e. a torus whose minor radius is the classical electron radius r_e = 2.818×10⁻¹⁵ m and whose major radius is the Bohr radius α₀ = 5.292×10⁻¹¹ m has surface area equal to the square of the Compton wavelength. Together with h = m_eλ_C²F_q, this motivates modelling the electron as a flexible toroid whose radii may vary provided the quantum surface area is conserved. The ratio r_e/α₀ is the square of the Fine Structure Constant, α² = 5.325×10⁻⁵, and that ratio does most of the work in what follows.

Hydrogen and helium

For hydrogen the authors adopt the known relation E_1s = m_ec²α²/2 = 13.606 eV and reinterpret it in APM terms as (r_e/α₀) times the strong force of the electron over one quantum length. Hydrogen is treated as a special case because with a single electron there is no electron–electron strong-force binding.

For helium and beyond, a geometric ingredient enters. The authors argue that half-Spin particles inhabiting a two-spin Aether cannot stack squarely, so bound toroidal electrons build up in a twisted pattern that shrinks the minor radius and grows the major radius in half-spin steps, (√(Z²+1) − 1)/2 and (√(Z²+1) + 1)/2. For Z = 2 these are 0.618 and 1.618 — the reciprocal and the value of the golden ratio, which the authors treat as a significant discovery. A further factor, the Z²-th root of 2, is introduced as an empirical description of how the Aether units deform as Z rises. Assembling these gives a 1s binding energy proportional to α², to the ratio of the two half-spin steps, to Z², and to e_emax²A_u/2λ_C. Evaluated at Z = 2 this returns 24.7212 eV against a measured 24.6 eV — an error of half a percent, and the arithmetic does reproduce to four figures.

Lithium to uranium and the linear adjustment

Applied unchanged to Z ≥ 3 the formula fails badly and systematically. Table 3 of the paper lists the unadjusted results: lithium 68.71 eV against 54.7 eV measured, neon 1122.06 against 870.2, iron 8525.36 against 7112. The discrepancy is large for light elements (about −20% for lithium through neon) and shrinks monotonically with Z, crossing zero near radon and reversing sign to +2.59% at uranium. The authors' response is to multiply the equation by the empirical factor (0.757 + 0.0028Z), noting that from sodium to uranium the variation is linear in the measured energies "indicating a simple physical explanation".

With that factor the fit becomes good. The paper works three cases in full: oxygen returns 534.5 eV against 543.1 eV measured, iron 7.077×10³ eV against 7112, and uranium 1.144×10⁵ eV against 115606. All three reproduce on recomputation, and all three land within roughly 1.6% of the tabulated measurement — a genuine improvement of an order of magnitude over the unadjusted equation.

The conclusion is measured. The authors call the equations "not exact, but very close", allow that the empirical data might be at fault but think it likelier that the Aether structure has aspects the equation does not yet capture, and present the result as evidence that a discrete model "devoid of probability functions and paradoxes" is viable.

Assessment

What is genuinely attractive here is the ambition and the transparency. A single expression that runs from lithium to uranium with two fitted constants and lands within a couple of percent of tabulated 1s levels across ninety elements is not nothing, and the authors do not hide the fitting: they print the unadjusted table alongside the adjusted one specifically so that readers can hunt for the missing physics. The worked examples are complete enough to be checked digit by digit, which is more than many papers in this literature offer, and on checking they are correct. The helium result, 24.72 eV against 24.6 eV measured with no adjustable factor at all, is the paper's strongest single number.

The difficulties are structural. First, the model is not one equation but three regimes — hydrogen by α²m_ec²/2, helium by the unadjusted golden-ratio expression, everything else by that expression times a linear factor. Applying the Z ≥ 3 formula to helium would give about 18.9 eV, well away from 24.6, so the regimes genuinely do not join. A framework advertised as deriving all ground states "from first principles" that needs a different rule for each of its first three cases has not yet earned that description. Second, the abstract's "very small arbitrarily induced quantity" understates the case considerably: the factor (0.757 + 0.0028Z) changes the answer by 24% at lithium, and it is not small but decisive. Third, the paper's own prose about the light elements is inverted — it says lithium through neon "calculate to eight tenths of their measured values", whereas Table 3 shows the calculations running about 25% high, with the measured values being eight tenths of the calculated ones. The number 0.8 is real; the direction stated is backwards.

Fourth, and most serious, the key inputs are not independent of the outputs. A_u is defined so that e_emax²A_u/λ_C equals m_ec²; the ratio r_e/α₀ is identically α² by the ordinary definitions of those radii; and h = m_eλ_C²F_q is likewise a rearrangement of the definition of the Compton wavelength. These are presented as discoveries of the model but are algebraic identities among standard constants. The hydrogen result in particular is the Bohr/Rydberg value rewritten, not rederived. Fifth, the Z²-th root of 2 is asserted as "empirically induced" with no derivation, and its numerical effect is negligible above Z ≈ 10 (2^1/676 = 1.001 for iron), so it cannot be tested by the fit that is supposed to support it.

There is also a mismatch between what is calculated and what is measured. The Bearden–Burr and Cardona–Ley values used for Z ≥ 3 are core-level binding energies measured in condensed matter by X-ray photoemission, referenced to the Fermi level and shifted by chemical environment and by solid-state relaxation; helium's 24.6 eV is a free-atom ionisation energy; hydrogen's 13.6 eV is another. A formula that fits all three sets with one linear factor is fitting quantities that are not the same physical observable, and part of the residual trend in Z is plausibly the trend of those experimental corrections rather than of any Aether structure. Against this, ordinary relativistic Dirac–Fock calculations reproduce the same 1s levels across the periodic table to a fraction of a percent without free parameters, and predict the fine structure and the L and M shells besides; the APM equation as it stands addresses only the 1s level and only its magnitude. Finally, the appeal to the golden ratio is coincidental in form: (√5 ± 1)/2 arises here simply because Z = 2 makes √(Z²+1) = √5, and no comparable numerological reading attaches to any other element.

Taken on its own terms, the paper is what it says it is — a first, partly fitted quantum-mechanical expression from a young framework, presented honestly with its residuals on display. It does not, however, yet demonstrate the superiority over the Standard Model that its conclusion claims.