Let's Keep It Simple

Scientific Paper
Title	Let's Keep It Simple
Read in full	Link to paper
Author(s)	Arnold G Gulko
Keywords	hydrogen atom, fine structure constant, electron structure, quantum mechanics, energy shell
Published	2008
No. of pages	11

Read the full paper here

Abstract

We exist in a particulate nature in which there are only two particles which possess significant mass at rest and long term independent stability. These are the electron and the proton. So when we consider our particulate nature from the perspective of the independently stable particles which abound around us, the nuclear zoo of particles in that nature can be simplified by focusing on only these two.

Overview

Arnold Gulko's paper is a compact statement of a programme he developed at length in The Vortex Theory, Revised (2006) and in Infinite Energy magazine. Its strategy is reduction: of all the particles catalogued by physics, only two have both significant rest mass and long-term independent stability, the electron and the proton; the simplest association of those two is the hydrogen atom; and so the whole of the particulate world can be tested against one question, whether we understand hydrogen. Gulko's answer is that we do not, and that the failure is not a gap but a foundational error.

The error, on his account, is the assumption that the electron is a structureless point. He argues that the electron must instead be a physically extended, two-sided object whose size is set by its energy content, and that the size of the hydrogen atom, the fine structure constant and the Rydberg energy all follow from that size once one supposes the two particles are held apart by a "double energy shell" of energy circulating between them. Where the mainstream sees a mathematically successful theory whose interpretive difficulties are secondary, Gulko sees calculations built on assumptions he considers demonstrably wrong: "when incorrect assumptions enable correct calculation we have chaos instead of science". His judgement on quantum mechanics is severe — it "may be useful as an engineering expedient, but it has destroyed physics as a science".

The argument

Why hydrogen is the test case

Rutherford's foil experiments forced the picture of a tiny massive nucleus with remote electrons, and immediately raised the spacing dilemma: since electrostatic attraction rises as the inverse square, the electron should collapse onto the proton, "making matter immensely dense and life impossible". Bohr answered by balancing orbital momentum against attraction, planet-fashion, which reproduced much of hydrogen's behaviour but was, Gulko says, "manifestly wrong", as Bohr himself came to accept. In Gulko's telling, quantum mechanics was then built on the further assumption that the thing not known — the electron's size and internal structure — did not matter.

The attack on the uncertainty principle

Gulko distinguishes Bohr's complementarity, which he treats as a statement about the difficulty of measuring conjugate variables, from Heisenberg's uncertainty principle, which he treats as an illegitimate promotion of that difficulty into a claim about "the constitution of that being measured". The twist gave Heisenberg "an alibi for his failure to comprehend the hydrogen atom", and physics accepted it because it needed the same alibi. If the principle were true, he argues, the fundamentals of nature would be unknowable, and physics would cease to be a quest to understand them.

The size of the electron and three ratios

Gulko's central move is to apply Planck's law to any isolated portion of energy, not only to photons. The electron's "energy radius" is then its Compton wavelength divided by 2π. Three consequences are offered:

• the average electron-proton spacing in hydrogen equals the energy radius squared divided by the classical charge radius;
• the energy radius divided by that spacing is the fine structure constant;
• the energy radius divided by the classical charge radius is 1/α.

In algebraic form these become his equation I, λ_ce/2π/a_o = α, where λ_ce is the electron's Compton wavelength and a_o the hydrogen radius. He remarks that "the ratio of one size to another is one of the simplest (and hence one of the strongest) mathematical relationships which can be established in physical reality", and that physics ignores these ratios because the electron has no size in quantum mechanics.

The two-sided electron and the double energy shell

Spin is read structurally. Because a measurable one-sided characteristic requires substantial size, and because a turned electron flips exactly half a turn and stops, the electron must be extended and two-sided — two connected portions of energy moving at light speed, "like a weather vane with one portion trailing behind the other", the total motion length being the Compton wavelength and each portion carrying half of it. Particles form when high-energy photons decay, so their constituent energy must move at c in a continuous closed path.

Hydrogen is then held together not by a balance of forces but by a physical connection: a double shell of energy circulating back and forth between electron and proton, whose length fixes the average separation. Since equation I ties α to the electron's size, the shell's energy must come from the electron — specifically from one of its two halves. To express this, Gulko multiplies numerator and denominator of equation I by π, obtaining equation II, λ_ce/2 divided by πa_o = α: half the electron's energy length divided by the length of a circle of radius a_o, that circle being the half-circle out to the proton plus the half-circle back.

Energy is transferred to the shell in increments; more returns than leaves, so a surplus accumulates at the electron and is released at stationary states, producing the spectrum. The doublet structure of a spectral line arises because the release "may include one more or one less energy increment". As corroboration Gulko notes that the Rydberg formula obtains the total energy of formation by halving the electron's energy and multiplying by α² — the same factor of one half and the same α that his shell picture requires. He closes by claiming the model explains the large size of atoms, and why a ground-state atom radiates nothing: the electron "is being carried and is not itself moving", so its changing distance and direction from the proton have no dynamical importance.

Assessment

The paper is clear about its own method — "science is based on projection from observation, the projection being checked by mathematical correlation" — and the questions it presses are real ones. Why the ground state does not radiate, why atoms are of the size they are, and what physical content the fine structure constant carries are all legitimate, and the insistence that a model be visualisable is a defensible methodological preference rather than a mistake.

The numerical relations are CORRECT, and worth setting out because they are the paper's evidence. The reduced Compton wavelength is ℏ/m_ec = 3.8616 × 10⁻¹³ m; the classical electron radius is 2.8179 × 10⁻¹⁵ m; their ratio is 137.04, that is 1/α. Squaring the first and dividing by the second gives 5.292 × 10⁻¹¹ m, the Bohr radius to four figures. The first divided by the Bohr radius is 7.297 × 10⁻³ = α. Equation II checks too: (2.4263 × 10⁻¹²/2)/(π × 5.2918 × 10⁻¹¹) = 7.297 × 10⁻³. And ½α²m_ec² = 13.606 eV, the Rydberg energy.

But these are not independent facts requiring explanation; they are one identity written four ways. In the standard framework α is defined as e²/4πε₀ℏc, and the three lengths are r_e = α²a₀ = αℏ/m_ec by construction, each obtained from the next by one factor of α. Textbooks derive them in a line. So the claim that "physics today cannot explain how the fine structure constant comes into existence" conflates two very different things: why α has the numerical value 1/137, which is genuinely unexplained, and why these particular length ratios are powers of α, which is elementary. The paper's evidence bears only on the second. Equation II is weaker still: multiplying numerator and denominator by π changes nothing whatever, so it cannot corroborate the half-electron picture; the physical content — that the circulating length is πa_o and the source is half the Compton wavelength — is supplied by the interpretation, not by the algebra. The same applies to the Rydberg "corroboration": the factor of a half in ½α²m_ec² comes from the virial theorem, and reading it as the electron's two halves is an association, not a derivation.

One load-bearing empirical claim is simply wrong. Gulko defines the fine structure constant as the wavelength difference of a doublet divided by the longer wavelength, and says "it does not matter which line in a spectrum one examines or which element whose spectrum is selected, the above ratio is always the same". It is not. Fine-structure splitting scales as α²Z⁴/n³ relative to the binding energy, so the fractional splitting varies enormously: the sodium D lines are separated by 0.6 nm at 589 nm, a ratio of about 1.0 × 10⁻³, while hydrogen's Hα fine structure is roughly 0.014 nm at 656 nm, about 2 × 10⁻⁵. Neither is α = 7.30 × 10⁻³, and they differ from each other by a factor of fifty. Nor is every line a doublet; many-electron spectra show singlets, triplets and larger multiplets according to the coupling. The paper's account of what the fine structure constant is therefore does not survive contact with a spectroscopic table, and the shell mechanism built to explain the doublet spacing is explaining a regularity that does not exist.

The structural claims conflict with direct measurement. That the electron must be large because it has a measurable spin does not follow — spin is an intrinsic angular momentum with no classical size requirement — and the extended electron is excluded experimentally: high-energy electron-positron scattering bounds any electron substructure below about 10⁻¹⁸ m, some three orders of magnitude smaller than the classical radius and five below the reduced Compton wavelength, while QED predicts the electron magnetic moment on the point-Dirac-particle assumption to twelve significant figures in agreement with measurement. The statement that "particles form when high energy photons decay" also mis-states pair production, which requires a nucleus or second photon to conserve momentum and yields an electron and a positron rather than either alone. Historically, the paper attributes quantum mechanics to "Bohr and E. Heisenberg" — the initial is W., for Werner — and has Bohr formulating it in response to his own failure, whereas matrix mechanics was Heisenberg's 1925 work and wave mechanics Schrodinger's.

Finally, the model is not carried far enough to be tested. Nothing in the double shell yields the n² scaling of excited-state radii, the 1/n² term energies that the Rydberg formula actually encodes, the angular momentum quantum number, the Lamb shift, hyperfine structure, or any many-electron atom — and the paper's own opening complaint, that physics cannot correlate the chemical properties of the elements with their nuclei, is left exactly where it was found. What is offered is a picture of hydrogen that reproduces, by construction, the one length ratio it started from.

See also

• Arnold G Gulko
• Hydrogen Atom
• Fine Structure Constant
• Electron
• Uncertainty Principle
• Quantum mechanics
• Niels Bohr
• Compton Effect
• Category:Vortex Theory