On the Space-Vortex Structure of the Electron

Scientific Paper
Title	On the Space-Vortex Structure of the Electron
Read in full	Link to paper
Author(s)	Paramahamsa Tewari
Keywords	Space, Vortex, Structure, Electron
Published	2005
No. of pages	22
Pages	221-242

Read the full paper here

Abstract

It was Rene Descartes, the French Mathematician and Philosopher who, perhaps for the first time in a scientific sense, assigned a reality to the medium of space as a property-less fluid-entity, already known at that time as ether. According to Descartes, large cosmic ether vortices existed throughout the universe. One such vortex carried the planets around the sun, and countless smaller vortices aggregated into different sizes of universal matter, filling the whole of space. He explained gravity by the pressure and impact of ether on bodies; and framed the principles of the inertial tendencies of matter for straight line motion based on the property of the fluidity of a space-substratum filled with ether vortices. The transmission of the then known magnetic forces and the force of gravity between the earth and the planetary bodies found explanations in Cartesian philosophy with physical contacts between the interacting entities mediated by the intervening ether. The theory of Descartes at that time was the most convincing natural philosophy and was based on a single dynamic ether as the only reality of the universe. The theory remained in acceptance for almost a century after publication of Newton's Principia...

Overview

This chapter, contributed to What is the Electron? (edited by Volodimir Simulik, Apeiron, Montreal, 2005), is Paramahamsa Tewari's condensed statement of a programme he developed at book length in Universal Principles of Space and Matter. Tewari, a career nuclear engineer and former Executive Director of India's Nuclear Power Corporation, sets out to derive the Electron's charge, Mass, Spin, magnetic moment, electrostatic field, gravitational field and Inertia from a single starting point: a vortex in a fluid medium of space that has no material properties whatever.

The historical framing is deliberate. Tewari places himself in the line running from Descartes through Faraday, Maxwell, Helmholtz, Kelvin and Larmor — the last of whom "concluded that the electron is a structure in the ether and that all matter consisted of electrons only". That programme collapsed around 1905 on two objections: vortex motion in an incompressible fluid dissipates as streamlines dilate outward, and an aether stiff enough to carry light at c would need an elasticity "near to that of steel". Tewari's claim is that both objections dissolve once the medium is stripped of every material attribute. His "space" is massless, densityless, incompressible, non-viscous and continuous — the dissipation problem is answered by a discontinuity at the vortex centre, and the elasticity problem does not arise because there is nothing material to be elastic. Where the mainstream account treats the electron as a structureless point with charge and mass as irreducible given quantities, Tewari treats charge and mass as derived — as integrals of a velocity field over a surface and a volume.

The argument

Postulates

Three postulates carry the whole paper. (1) Space throughout the universe is an eternally existing, nonmaterial, continuous, isotropic fluid substratum. (2) It has a limiting flow speed equal to c relative to the absolute vacuum, and a limiting angular velocity ω when circulating. (3) It is eternal and endowed with motion.

Breakdown of fluid space and the central void

In an ordinary viscous vortex, the inward pressure-gradient force balances the centrifugal force on a fluid element, both being proportional to the element's mass. In a massless vortex neither force exists. What remains is the radial outward acceleration field u²/r, which acts at diametrically opposite points on a streamline and "tends to create a tearing action to split open the continuous space". When the circulation speed reaches c and the velocity gradient reaches ω, space breaks down and a spherical void opens at the centre — "a field-less, energy-less and space-less volume of nothingness" of radius

r_e = c/ω.

The void's sphericity follows from the constancy of the velocity gradient: at a point P on the interface at polar angle θ, the tangential speed is ωr_esinθ over a radius r_esinθ, giving the same gradient ω everywhere, so the interface "rotates like a surface of a rigid spherical shell of negligible wall thickness". Its stability is a two-way feedback: shrinking raises ω above the postulated limit, so the void expands back; growing lowers the gradient below what can sustain the void, so it contracts back.

Charge, mass and the electron radius

Charge is defined from first principles as the surface integral of the tangential space velocity over the interface. Integrating dq = 2πcr_e²sin²θ dθ from 0 to π gives

q_e = 4πr_e²(cπ/4),

with dimensions L³/T — so that one CGSE unit is cm³/s. Mass is the corresponding volume integral of the circulation velocity within the void:

m_e = (4π/3)r_e³c, i.e. mass = void volume × c,

with dimensions L⁴/T, giving 1 gram ≈ 8.6 × 10⁶ cm⁴/s by two independent routes (one via the void content of a cubic centimetre of water, one directly from the electron mass). Putting the measured charge 4.8 × 10⁻¹⁰ CGSE into the charge equation yields r_e = 4 × 10⁻¹¹ cm — about 142 times larger than the classical electron radius of 2.82 × 10⁻¹³ cm. Tewari defends this by quoting Yankovsky's remark that modern electrodynamics implies "the electron has enormous dimensions, not 10⁻¹³ cm... but 10⁻¹¹ cm".

Derived quantities

From the same two integrals Tewari reads off the intrinsic angular momentum L_e = (4/5)m_ecr_e and the magnetic moment μ_e = (3/4)q_ecr_e. The creation energy of the void — the energy released if the interface collapsed — integrates to

E = (4/5)m_ec²,

which he presents as recovering "an equation discovered by Einstein (and others)" while supplying the physical reason c appears in it: it is "the actual maximum possible space-circulation in the structure of fundamental matter". Because the void has a finite minimum radius, the electrostatic self-energy integral has a lower limit r_e rather than zero and comes out finite, (π/10)m_ec²; the remainder, about (1/2)m_ec², is identified as gravitational potential stored in space. The electric field E = −c²r_e²sin²θ/2r² is shown to have the inverse-square, charge-proportional form of Coulomb's Law; the vacuum permittivity comes out as ε₀ = π/2c and, via c = 1/√(μ₀ε₀), the permeability as μ₀ = 2/πc. Attraction and repulsion are given a hydrodynamic reading: superposed velocity fields between an electron and a Positron raise u, which by ur = constant lowers r and draws them together.

Light, nuclei and the photoelectric effect

Annihilation is the collapse of two superimposed voids. The interiors being energy-less can emit nothing; what is emitted is the de-energising of the surrounding medium as the electrostatic and gravitational potentials it carried are erased. A single spherical shell of radial width r_e propagates outward at c — and "the spherical shell produced due to the dying of potentials... is the fundamental phenomenon known as light". Frequency, on this view, is not a property of a single shell but a count of shells per unit time.

Nuclear structure is built from a "primary unit" of two electrons and two positrons, electrically neutral overall. A Neutron is 919 such pairs, radius 12r_e; its instability under rotation is offered as the mechanism of beta decay and the ~15-minute half-life. A Proton is a neutron enclosed in a space vortex, whose charge works out to 12q_e. Requiring the hydrogen atom's electron and proton magnetic moments to cancel fixes the orbital velocity at v_orb = 0.69c at a radius of 24r_e ≈ 10⁻⁹ cm. Finally, for an average atom Tewari computes the inward acceleration field on the outermost orbital electron as 1.44 × 10²⁴ cm/s²; setting a light shell's opposing field c²/λ equal to it gives a threshold λ = 6.25 × 10⁻⁴ cm (0.48 × 10¹⁴ Hz, against ~5 × 10¹⁴ Hz for sodium) and a released kinetic energy of 7.2 × 10⁻¹¹ erg against a measured ~8 × 10⁻¹¹ erg. His conclusion is that light does not give the photoelectron its energy at all: "Light simply disturbs the stability of the forces under which an electron is stable in its orbit."

Assessment

What is genuinely distinctive here is the direction of derivation. Nearly every aether-electron model asserts a structure and then fits parameters; Tewari instead defines charge and mass as integrals of one field and lets the numerical values fall out. The dimensional consequences — charge as L³/T, mass as L⁴/T, permittivity and permeability both inverse in c — are unusual, self-consistent within the scheme, and checkable, and Tewari does check them: the gram conversion is obtained twice by different routes agreeing to within 2 per cent, and the ε₀ = π/2c result is verified by recomputing Coulomb's constant and getting 0.73 where 1 is wanted. The finite self-energy is a real advantage over the point charge, and the paper is candid about the machinery it uses, marking clearly which results are imported from the 2002 book rather than derived here.

The difficulties are substantial. The postulates are doing heavy and unexamined work: a fluid that is massless, densityless and non-viscous has no dynamical equations, so the "acceleration field" that tears space open is asserted rather than derived, and no equation of motion for the medium is ever written down. The definitions of charge and mass as surface and volume integrals of velocity are stipulated "from first principles", not obtained from anything; once stipulated, the subsequent algebra follows, but the algebra is not evidence for the stipulation. The numerical agreements are also weaker than they look. The derived electron radius is 142 times the classical radius, and the defence is a single 1968 quotation rather than a measurement; the actual bound is that electron scattering shows no structure down to about 10⁻¹⁸ cm, seven orders of magnitude below Tewari's interface, which the paper does not address. The proton charge comes out as 12q_e, flatly contradicting the measured proton-electron charge equality, which is experimentally established to better than one part in 10²¹; Tewari does not flag the conflict. The hydrogen orbital radius of ~10⁻⁹ cm is about twenty times the Bohr radius, and an orbital electron at 0.69c would radiate. The photoelectric numbers are the paper's best empirical showing, but the threshold frequency is off by an order of magnitude and the kinetic energy is matched only after choosing an orbital radius by assumption — Tewari says as much.

There are internal tensions too. The mass-energy result is (4/5)m_ec², not m_ec²; the paper presents this as recovering Einstein's equation while the factor 4/5 goes unremarked. Mass is said to be constant up to c because the void volume is constant, yet relativistic mass increase is then reinstated as "the reaction of the fluid space against the central interface", with the derivation deferred to the book. The account of light as a single shell of width r_e gives annihilation radiation a wavelength of 4 × 10⁻¹¹ cm — the measured 511 keV annihilation line has a wavelength of about 2.4 × 10⁻¹⁰ cm — and the concession that "the concept of frequency is not applicable" leaves the Planck relation, and with it the whole of atomic spectroscopy, without a footing. Read as what it is — a self-consistent kinematic scheme in which one velocity field is made to yield the constants of electromagnetism — the paper is an ambitious and unusually disciplined piece of aether modelling. Read as a competitor to Quantum Electrodynamics, it has not yet engaged the measurements that would decide between them.