“The Toroidal Fine-Structure of the Electron” by Gene Gryziecki

Abstract

I. Introduction

The Bohr theory of the hydrogen atom, theorized by Niels Bohr (1885-1962), includes a negatively charged point-mass electron that travels in a circular orbit about a positively charged nucleus. In the atom’s lowest energy (or ground) state, the distance between the two particles is called the Bohr radius and is equal to 0.529 x 10-10 m. Since then, further investigation indicated that sometimes the electron behaves like a wave and sometimes like a particle [1]. Thus, the Bohr-Heisenberg model of the atom arose where the electron exists only as a cloud or fuzzy cavity about the nucleus and measurements are based upon the probability of a point particle being found at a certain location in the cloud. 

Recently, there has been some rather meticulous scientific research work by Dr. Paulo Correa and his team that has put forth a novel description of the electron as a torus ring, and a heuristic understanding of the Bohr radius and the Bohr-Heisenberg model of the atom. This paper is intended to provide an introduction to, and overview of, an important aspect of this work. 

II. Methods and Results

Building upon the work of Wilhelm Reich (1897-1957) and his research on gravitational pendulums, it became possible to decipher his formula for determining the functional equivalence between mass and length [2]. Reich’s work supported the idea that “atomic weights are gravitational functions that can be functionally replaced by pendulum lengths.” He selected pendulum lengths, in centimeters (cm), such that they were numerically equal to the gram-molar masses, and thus to the atomic weights, of various elements, while keeping the actual weight of the pendulum constant at 1 gram. For example, the length of gravitational pendulums for Hydrogen, Helium and Oxygen would be 1, 4 and 16 cm, respectively [3]. His process transforms “inertial mass into the rotary or pendular wavelength of the linear free fall motion” understood as weight [4]. 

In the case of the electron (the entirety of this paper applies to the electron and all reference values have been taken from a single source, CODATA 2018 [5]), this gravitational wavelength is resonant with the “wavelength of the energy circularized as mass-energy (see below) and on which the inertia of a state of rest is anchored as a reaction of that inert mass or of that mass-energy,” referred to as the mass-equivalent or amplitude [6] wavelength [7]. In fact, for the electron, these two wavelengths, gravitational and mass-equivalent, are numerically equal, and the wavelength of concern in this paper is the electron mass-equivalent wavelength. The equation for the mass to length transformation for the electron can be shown as: 

Length = λe = me NA 10-2 in meters      [2]   (1)

where λe is the mass-equivalent wavelength of the inert mass of the electron, me is the electron mass (in grams), and NA is Avogadro’s number: 

λe = (9.109 x 10-31 kg) (103 gm / 1kg) (6.022 x 1023 / mole) (10-2 ) (m) = 5.486 x 10-6 m   (2)

Using this tremendous insight and the famous equation for calculating rest energy or mass-energy, where energy E equals the product of mass m times the speed of light squared c2 , E = mc2 , one can determine a functional equivalent to the mass-energy of an electron using two physical quantities rather than three, incorporating length and time instead of mass, length, and time. Accordingly, 

E = mec2 =∫= λec2     (3)

with c designating the speed of light and the symbol =∫= indicating a functional transformation that involves both dimensional conversion and an equivalence between two different physical systems of measurement [8]:

E = (9.109 x 10-31 kg) (2.998 x 108 m s-1)2 = 8.187 x 10-14 Joules =∫= (5.486 x 10-6 m)(2.998 x 108 m s-1)2 = = 4.930 x 1011 m3 s-2     (4)

For electromagnetic (photon) energy consisting of oscillating electric and magnetic fields, where them aximum wave velocity is restricted to the speed of light, the well-known Compton electron wavelength (λce = 2.426x 10-12 m) can be used to determine the Compton electron frequency:

υce = c / λce = (2.998 x 108 m s-1) / (2.426 x 10-12 m) = 1.236 x 1020 s-1      (5)

When energy is quantized, it can be calculated by the product of Planck’s constant (h = 6.626 x 10-34 J s)and frequency. If the frequency happens to be the Compton electron frequency, then the result is equivalent to the mass-energy of the electron or to the low-energy limit of a gamma ray photon. Modern science shows this calculation as

E = hυce = (6.626 x 10-34 J s) (1.236 x 1020 s-1) = 8.187 x 10-14 Joules       (6)

matching the results of the E = mec2 calculation shown above in equation (4).Now, it also becomes apparent that a functionally equivalent Planck’s constant h, in meter and second unitsof measure, can be determined by rearranging the above equation as

h = E / υce = (4.930 x 1011 m3 s-2) / (1.236 x 1020 s-1) = 3.990 x 10-9 m3 s-1        (7)

Our limited understanding of charge has confused the issue of the fine-structure of the mass-energy of amass-bearing charge more than necessary. If we go back to James Maxwell’s (1831-79) theory, charge, or as he stated, “a [fundamental] quantity of electricity”, could be represented using three physical quantities and dimensions, as [9]

q = M0.5 L1.5 T-1(M = mass, L = length, T = time)         (8)

This is in agreement with the physical quantities for charge in the Electrostatic System of Units (ESU) [10],and also as proposed in the work of Harold Aspden (1927-2011) [11]. If the mass to length transformation is appliedto this definition of charge it can be seen that the property of charge is equivalent to a function of linear momentum that is treated as being massfree -

q = M0.5 L1.5 T-1 =∫= L2 T-1 = pe       (9)

- where pe symbolizes charge, with massfree dimensionality, as an electric linear momentum vector function [11].Charge is a special type of linear momentum function that can be expressed inertially or electromagnetically in mass dependent systems of units (as q or e, see below) or electrically in the meters and seconds massfree system of unit sas pe [11]. As shown below in equations (15) and (17), this linear momentum charge function is inherent to the mass-energy of the electron and every massbound charge. The functional equivalences of charge in three different systems of units (ESUs, Coulombs, and meters squared per seconds) are

“q = 4.830 x 10-10 ESU =∫= e = 1.611 x 10-19 C =∫= pe = 13.970 m2 s-1” [12]         (10)

In addition to being expressed in joules, per equation (4) above, the electron mass-energy can also beexpressed as charge, represented by “e,” multiplied by voltage, found to be equal to 510,998.950 electron volts (eV),per Codata 2018:

E = mec2 = (e)(511kV) = hυce =∫= (pe) (h / pe)(υce       (11)

The Duane-Hunt Law states that the maximum frequency of X-rays emitted from a tube, resulting from electrons that being accelerated by an applied voltage strike a metal anode, is proportional to the applied voltage and is quantized by Planck’s quantum of action h, per the equation:

υmax = Ve / h = K / h        (12)

where υmax is the maximum frequency, V is the voltage applied to the tube, e is charge, and K is equal to the kinetic energy of the accelerated electron. Notice that if the terms are rearranged to solve for energy and if the maximum frequency happens to be the Compton electron frequency (υce), then the kinetic energy would have the same magnitude as the mass-energy of the electron:

K = hυce = Ve = E = (e)(511kV) =∫= pe (h / pe) υce       (13)

In the meter and second system of units, the term (h/pe) has the physical dimensionality of length which is expressed in meters and is a wavelength. Under the above condition, this wavelength may be determined for the electric equivalent of the electron mass-energy as the quantum of action h divided by the quantum of charge pe; it is, therefore, a constant:

λx = h / pe = (3.990 x 10-9 m3 s-1) / (13.970 m2 s-1) = 2.856 x 10-10 m (14)

Expanding the electron mass-energy equation to include both inertial and electric linear momentum functions results in

E = mec2 = pAec = hυce =∫= λec2 = peWx = hυce (15)

where pAe is the (photo)inertial linear momentum mec, pe is the electric linear momentum, and Wx is the electric wave function corresponding to the intrinsic voltage (511kV) of the electron mass-energy. The function Wx is called“the voltage equivalent electric wave speed of the electron mass-energy” [13] and it can be directly expressed by its equivalent electromagnetic form as a function of the Compton frequency and the Duane-Hunt wavelength – thus, asa function of two constants:

511kV =∫= Wx = λx υce = (2.856 x 10-10 m) (1.236 x 1020 s-1) = 3.529 x 1010 m s-1     (16)

This confirms that

E = 511keV =∫= λec2 = peWx = 4.930 x 1011m3 s-2 = (13.970 m2 s-1) (3.529 x 1010 m s-1) = 4.930 x 1011 m3 s-2 (17)

and it expands the electron mass-energy expression to include Wx and its constituents. It results in

E = mec2 = pAec = hυce =∫= λec2 = peWx = λeWkWx = λeWk (λxυce)    (18)

Note that the Compton electron frequency υce of the electromagnetic equivalent of the electron mass energy, pAec = hυce, is shared with the actual electric structure of that mass-energy (Wx = λxυce) [14].Equation (18) requires another wave speed function, namely Wk, which is the magnetic wave speed characteristic of the electron charge. As shown by that equation, there is a fundamental equivalence of c2 = WkWx.The product of these two wave functions, Wk and Wx, represents a superimposition, where the two separate wave functions are superimposed nearly perpendicularly to one another. Since c and Wx are known, it is a simple matter to solve for

Wk: Wk = c2 / Wx = (2.998 x 108 m s-1)2 / (3.529 x 1010 m s-1) = 2.547 x 106 m s-1   (19)

Besides being intrinsic to the electric equivalent of the electron mass-energy, the wave speed Wk is actuallythe magnetic wave speed “intrinsic to the elementary charge of the electron” [15]:

pe = λeWk   (20)

Rearranging the above terms permits the confirmation of the value of Wk. An interesting sidebar to the mainpurpose of this paper is an insight into the meaning of the charge to mass ratio. It can be seen below that this ratio results in a wave speed that is exactly equal to Wk, the magnetic wave speed intrinsic to charge [6, 15]:

Wk = pe / λe = (13.970 m2 s-1) / (5.486 x 10-6 m) = 2.547 x 106 m s-1   (21)

This can be verified by performing the transformation process on the 2018 Codata value of the electroncharge to mass ratio of 1.758 x 1011 C / kg, as follows. Rearranging a portion of equation 10 and substituting theCodata 2018 value for the electron charge “e” gives

pe / e = (13.97 m2 s-1) / (1.602 x 10-19 C) = 8.72 x 1019 m2 s-1 C-1  (21A)

and from equation (1)

1kg =∫= 1kg (103gm / 1kg)(6.022 x 1023 / mole)(10-2 m gm-1) = 6.02 x 1024 m (21B)

then,

1.758 x 1011 C m-1 =∫= [(1.758 x 1011C) (8.72 x 1019 m2 s-1 C-1)] / (6.02 x 1024 m) = 2.546 x 10 6 m s-1  (21C)

showing the enduring value of the process and confirmation of the value of the charge to mass ratio and thus of the magnetic wave speed intrinsic to charge, Wk, per equation 21.Returning to the Electrostatic System of Units of charge as mentioned above in equation (9) and repeated here for reference,

q = M0.5 L1.5 T-1 =∫= L2 T-1 = pe (9)

squaring both sides

q2 = ML3T-2 =∫= L4T-2 = pe2     (22)

and solving for M results in

M = q2 / L3T-2 =∫= pe2 / L3T-2 = L   (23)

Whereas, as we have seen from equation 21, the electron mass is part not only of the mass-energy of the electron, but of its very charge structure (pe = λeWk), it can also be obtained from dimensional equation 22 (and the squared superimposition of charges) by invoking the proportionality of the fine structure constant, if the term (L3T-2) is made to equal the electron mass-energy

λe = (100 α-1) pe2 / E = (Wx / Wk) pe2 / E    (24)

But in the absence of such a proportionality invocation, what results is the very wavelength characteristic of the electron's magnetic wave function Wk:

 λh = pe2 / E = (13.970 m2 s-1)2 / (4.930 x 1011 m3 s-2) = 3.958 x 10-10 m     (25)

This immediately allows the determination of the magnetic wave function frequency [6] specifically characteristic of the electron:

υk = Wk / λh = (2.547 x 106 m s-1) / (3.958 x 10-10 m) = 6.433 x 1015 s-1    (26)

This analytical methodology leads to a totally new and strictly electric expression of the electron mass energy, where basic components and their functions define its fine structure:

E = mec2 =∫= λec2 = peWx = λeWkWx = λe (λhυk) (λxυce) = (5.486 x 10-6 m) [(3.958 x 10-10 m)(6.433 x 1015 s-1)]x [(2.856 x 10-10 m) (1.236 x 1020 s-1)] = 4.930 x 1011 m3 s-2     (27)

Evidently, the wave functions Wk and Wx are not electromagnetic, since the Wx wave speed exceeds the speed of light [6]. In effect, it describes the wave speed of the flux in each of the rings of a torus, just as themagnetic wave speed describes the equatorial velocity of the rings with respect to the center of the torus. As such,the radii of the two circular wavelengths are calculated in the normal manner:

r = λ / 2π (28)

rh = λh / 2π = (3.958 x 10-10 m) / 6.283 = 6.30 x 10-11 m   (29)

rx = λx / 2π = (2.856 x 10-10 m) / 6.283 = 4.456 x 10-11 m   (30)

resulting in the fine geometry of the electron mass-energy torus:

E = mec2 =∫= λec2 = peWx = λeWkWx = λe (2πrhυk) (2πrxυce)   (31)

The structure of the electron mass-energy, broken down this way into its basic constituents, presents itselfas a flux of electric energy shaped as a torus due to the superimposed wavefunctions Wk and Wx. When thegeometric mean of the two wavefunction radii is calculated, the result is the Bohr radius which compares favorablywith the CODATA 2018 value of 0.529 x 10-10 m:

(rhrx)0.5 = [(6.30 x 10-11 m) (4.456 x 10-11 m)]0.5 = 0.535 x 10-10 m    (32)

The implication is that the Bohr radius is not really the radius of a spherical cavity, or of a quasi-sphericalcloud where a point-mass may locate once the probability wave collapses, but merely the geometric mean of thetwo radii of the electron mass-energy torus. The latter has the "normal" volume given by [6]:

V = 2π2rhrx2    (33)

III. Conclusions

The proposed model is a much more satisfactory and rigorous description of the electron and explanationof the phenomenological nature of the Bohr radius. Rather than leading a nebulous existence as a supposed particle, wave, cloud, cavity, or “point particle in a cloud of probable locations”, it is best understood as a “precisetoroidal volumetric flux structure” of electric energy resulting from two longitudinal waves being superimposed uponand trapped with each other, “that occupies the location of the entire ‘cloud’ [16].

”The torus model also rejoins the problematics of "the ring electron" originally proposed in 1915 by AlfredParson [17], and taken up during 1917-1921 by others, in particular by Arthur Compton [18, 19] and H. Stanley Allen[20]. However, unlike the ring electron model, the model proposed by the Correas does not invoke for the electron avortical ring structure, but rather that of a closed torus composed by a large number of continuous rings. The two models share many of the features that overcome the present-day conceptualization and treatment of the electron. Loss of energy by radiation of the closed-loop mass-energy is done away simply by assuming rotation of a ringshaped charge, and the virtually impossible complications raised by independent orbitals required to explain diamagnetic atoms melt away, given that it is the electron mass-energy itself that has a diamagnetic moment [6].Likewise, paramagnetism and X-ray diffraction patterns are explained by the tilting of the toroidal ring, confirming the contention of the above three physicists that the elementary magnet is not the atom, but the electron itself. The magnetic susceptibility of paramagnetic substances flows directly from the electron retaining its magnetic propertiesat low temperatures. Asymmetric scatter of X-radiation is explained by the striking of distinct loops of the torus.Runge's rule that abstrusely related variable magnetic effects to the ratio e/m [20] is replaced by the elegant andeloquent result of equations 21, 25 and 26:

Wk = λhυk = pe / λe =∫= e / me    (34)

Well beyond what the ring electron model could provide, the Correa model of the electron torus addressesother features still. In effect, the number of toroidal loops is directly obtained by the relation that accounts for boththe composite nature of the mass of the electron and the proportionality role played by the reciprocal of the finestructure constant – whose actual value is thereby revised [21] – in the topogeometry of the electron:

No. loops = λe / λx = α-2 = 19,205.9 = (138.5853745)2    (35)

The very fact that the number of loops is very nearly an integer may suggest that it is simply 19,206 or,instead, that the fractional value actually indicates a kink in the toroidal structure (the shorter loop), one that mayhave phenomenologically induced existing physics into believing that the electron is a point-mass engaged in orbital motion, since the kink will rotate with the magnetic wave speed of the torus. Communication from the Correassuggested they incline to the latter case, as if the torus contained a beat – in perfect agreement with Allen's notion ofa pulse travelling around the ring-shaped electron as a "small hump" [20].While the energy stored in the rotating torus is in a non-radiating form, absorption of kinetic energy by thetorus will, under specific conditions (collision, field deceleration), originate radiating energy in the form of photonsemitted 1:1 by the loops, such that Planck's radiation law stands explained by

K = α-2 (hυp)    (36)

where υp is the frequency of the emitted photons

This suggests that the real measure of angular momentum is simply

h / 2π = perx    (37)

Further development of the toroidal model of the electron has led the Correas to analyze dynamic changesin the radial dimensions of the toroidal loops and the magnetic wave speed [6]. It permitted identification of thephotoinertial (a.k.a. "spin state") configuration as a limiting one, where the angular momentum conforms to Compton's notion of a wavelength maximum, the Compton wavelength

 λce: h / 2π = pAe (λce / 2π) = pAero    (38)

where ro is the radius of the wavelength of the wave speed of the flux in each of the rings of the electron torus while in the (photo)inertial configuration.

Such limit is reached when pair annihilation occurs. The same approach also permitted a full understanding of the anomalous gyromagnetic ratio and the Landé factor [6].

Unlike the present explanation for orbital jumps, the torus model of the electron indicates that elastic variation in its volumetric and winding features is not to be assimilated to the fine structure of added kinetic energy. Addition of extra energy does not accelerate the ring rotation – as the ring model held – since the magnetic wavespeed of the torus is a conserved characteristic. It is only the loop flux that accelerates to a maximum fixed by the electron mass-energy itself.  So-called orbital jumps, then, merely abide by equation 36, as successive kinetic energy states result in emission of resonant photon frequencies. Likewise, the Zeeman effect first observed in 1896 stems from the same resonant process being split by an applied magnetic field.

All the consequences of the Correa model of the electron torus cannot possibly be discussed in the scope of the present paper. They range widely, from a better understanding of thermoelectric effects and the quantum nature of the temperature scale, to a thorough revision of Louis de Broglie’s (1892-1987) theory of matter/particle waves, a totally new treatment of the fine structure of nucleons and, most importantly, the discovery of massfree (ambipolar) electricity in induction devices, ambipolar plasmas and nuclear fusion. This complex dramatic breakthrough has been ignored for nearly two decades just as the work that started it all 75 years ago - Reich’s mass to length transformation technique.

For those further interested in this earth-shaking science, in-depth learning can only be accomplished by reading the monographs, books and other publications generated by the Correas and their research associates (Dr.Gene Mallove, Dr. Malgosia Askanas, Dr. Harold Aspden, to name a few) at the Aurora Biophysics Research Institute. The Correas have provided various proof of concept machines based on their research – demonstrating the utility and correctness of the theories - some of which may be commercialized. Descriptions of these technologies can be found at www.aetherenergy.com. The monographs, meticulously describing the experiments, thought processes and conclusions can be found at www.aetherometry.com.

Acknowledgements

The author would like to thank Dr. Paulo Correa, Alexandra Correa and Dr. Malgosia Askanas, for theirsuggestions and support.This research did not receive any grant from funding agencies in the public, commercial, or not-for-profitsectors.The author declares no competing interests.

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