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Electron Quantum SuperPhysics
Millennium Twain2019, Electron Quantum SuperPhysics
Electronic Parameters of the 2.8 Fermi Radius Electromagnetic Standing Wave Free Electron. Magnetic Flux, Flux Density, Voltage, Current, Charge, Inductance, Capacitance, Impedance, Velocity, Frequency, Wavelength, Permeability, Permittivity and Q-Factor
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Certain aspects of structure of electron
The values of four different fields related to electron: gravitational, circulation, electric, and magnetic, can be written with very similar formulas that bind them in pairs: gravitational-magnetic and circulation-electric. Moreover, the four integrals over these fields in space and time produce the electron-specific 'charges': circulation quantum, rest mass, magnetic flux quantum, and elementary charge, which also form pairs analogous with respect to their proposed structure: circulation quantum-elementary charge, and rest mass-magnetic flux quantum. A specific value of the gravitational constant is hypothesized and an extension to the SI system of units is proposed allowing for comparisons between its mechanical and electromagnetic units, as was the case in the CGS-Gaussian system of units. It is hypothesized that total rest energy of electron consists in equal parts of contributions from its gravitational and electromagnetic energies.
The Electron: New Theory and Experiment
American Journal of Physics, 1992
The Fermi edge singularity of spin polarized electrons
We study the absorption spectrum of a two-dimensional electron gas (2DEG) in a magnetic field. We find that that at low temperatures, when the 2DEG is spin polarized, the absorption spectra, which correspond to the creation of spin up or spin down electron, differ in magnitude, linewidth and filling factor dependence. We show that these differences can be explained as resulting from creation of a Mahan exciton in one case, and of a power law Fermi edge singularity in the other. The role of Coulomb interactions in the optical absorption spectrum of a Fermi sea of electrons has attracted interest for several decades. The response of the electron gas to the sudden creation of the hole attractive potential is manifested in a singularity at the photon energy for which an electron is excited to the Fermi level. This singularity, known as the Fermi edge singularity (FES), was first studied by Mahan [1, 2] in the context of the X-ray absorption edge of metals and the interband spectrum of degenerate semiconductors. Using a ladder diagram approach he was able to show that the absorption is singular at the threshold energy hω = E G + p 2 F /2µ, where E G is the gap energy, p F is the electron Fermi momentum, and µ is the electron-hole reduced mass. At higher energies, the absorption intensity decays as (ω− ω 0) −α , where α is a dimensionless coupling constant describing the interaction between the electrons and the deep hole created in the absorption process. An exact expression for the absorption spectrum was later derived by Combescot and Noziers [3, 4], and practically verified Mahan's predictions. A two-dimensional electron gas (2DEG) in modulation doped quantum wells has proven to be particularly convenient for observing and studying the FES. The ability to vary the electron density, n e , and the ratio between temperature and Fermi energy provides an important handle on the behavior of the singular-ity. Indeed, in the last two decades there has been a rich body of theoretical [5, 6, 7, 8] and experimental work [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] on various aspects of the singularity in this system. In particular , photoluminescence measurements have shown that the singularity persists when a magnetic field is applied [9, 18, 19]: the envelope of the Landau levels (LL) resembles the FES lineshape at zero magnetic field [8]. The role of the spin degree of freedom was, however, commonly assumed to be limited to the degeneracy in the density of states. Yet, it is plausible to expect that the 2DEG spin polarization would affect the FES in a profound way: electron-electron scattering, which plays a key role in the singularity [2], is strongly suppressed when the spin of the photo-excited electron is opposite to that of the Fermi sea electrons. In this paper we study the absorption spectrum of a high mobility 2DEG in a magnetic field. Our main finding is that at low temperatures, when the 2DEG is spin polarized, the absorption spectra which correspond to the creation of a | ↓> or | ↑> electron differ in magnitude , linewidth and filling factor dependence. We show that these differences can be explained as resulting from the creation of a Mahan exciton [1] in one case, and of a power law FES [2] in the other. Measuring the absorption spectrum of a single GaAs quantum well (QW) at low temperatures has always been a difficult task. Here we introduce a new technique for measuring the absorption spectrum of a single QW, using very weak white light in a reflection geometry. The idea is growing a cavity structure in which the QW is located at an anti-node of a standing wave formed by the optical field. The structure consists of a Bragg reflector, made of 20 pairs of λ/4 layers of AlAs and Al 0.3 Ga 0.70 As (λ = 800 nm), with its top layer is at a distance of 3λ/2 from the surface. The Bragg reflector and the sample surface form a microcavity with a broad stop-band, in which all wavelengths are back reflected (R ∼ 1). A modulation-doped GaAs QW, which is 20 nm wide and is embedded in Al 0.38 Ga 0.62 As barriers, is grown in the middle of the cavity, at a distance of 3λ/4 from the Bragg mirror and the surface. Figure 1 shows the calculated re-flectivity spectra, assuming typical excitonic parameters of a GaAs QW. The broad stop-band is seen to extend from 1.47 to 1.63 eV, with a deep notch at the exciton energy , ∼ 1.538 eV. We find that the exciton lineshape is very sensitive to the location of the QW within the cavity , and one can get a Lorentzian or dispersive lineshape by varying it [21]. The inset shows a reflectivity measurement of an optimized sample with a single modulation-doped QW at B = 9 T. It can be seen that the reflectivity at the lowest LL energy is ∼ 0.3, corresponding to an order of magnitude enhancement relative to the single pass absorption. The whole structure is grown on an n + layer that serves as a back gate. The wafer was processed to form a mesa structure, with ohmic contacts to the QW and to the back gate, such that n e can be tuned in the range (0.4 − 3) × 10 11 cm −2. The measured electron mobility is ∼ 1 × 10 6 cm 2 V −1 s −1. We used a tungsten halogen lamp to illuminate the sample, and selected a spectral range of 20 nm, centered around the heavy hole
Fundamental Atom-Molecular Engineering. Part 1. Model of Electron
viXra, 2014
The present chapter investigates electron. It is shown that electron has an intricate internal structure which determines both static and dynamic properties of the electron itself and important parameters of te condensed matter. Stationary “cold” electron (≤0.1eV) is modeled by a thin elastic ring called ector having diameter which is 137,036 times larger Bohr’s radius of hydrogen which consists of specific form of magnetic field. On the basis of the ector model the size, mass, charge, electromagnetic mass, spin and magnetic moment of electron are described. The model of “cold” ring electron in a condensed matter explains from new perspective critical parameters of phase transitions “metal-semiconductor” (Winner’s crystallization) and low temperature and high temperature superconductivity. Ring electron spirals into a void torus as compared to steady moving “hot” electrons (>>0.1эВ). The size of the torus depends on its kinetic energy which makes it possible to describe change...
Theory of the Anomalous Magnetic Moment of the Electron
Atoms, 2019
The anomalous magnetic moment of the electron a e measured in a Penning trap occupies a unique position among high precision measurements of physical constants in the sense that it can be compared directly with the theoretical calculation based on the renormalized quantum electrodynamics (QED) to high orders of perturbation expansion in the fine structure constant α, with an effective parameter α/π. Both numerical and analytic evaluations of a e up to (α/π) 4 are firmly established. The coefficient of (α/π) 5 has been obtained recently by an extensive numerical integration. The contributions of hadronic and weak interactions have also been estimated. The sum of all these terms leads to a e (theory) = 1 159 652 181.606 (11)(12)(229) × 10 −12 , where the first two uncertainties are from the tenth-order QED term and the hadronic term, respectively. The third and largest uncertainty comes from the current best value of the fine-structure constant derived from the cesium recoil measurement: α −1 (Cs) = 137.035 999 046 (27). The discrepancy between a e (theory) and a e ((experiment)) is 2.4σ. Assuming that the standard model is valid so that a e (theory) = a e (experiment) holds, we obtain α −1 (a e) = 137.035 999 1496 (13)(14)(330), which is nearly as accurate as α −1 (Cs). The uncertainties are from the tenth-order QED term, hadronic term, and the best measurement of a e , in this order.
Quantum Wave Mechanics Ch 20 Origin of the Electron Fine Structure Constant
Quantum Wave Mechanics 4th ed., 2022
The fine structure constant alpha (= 0.0072973552... ~ 1/137) is a dimensionless quantity described as a fundamental physical constant characterizing the strength of the electromagnetic interaction. Introduced by Sommerfeld in 1916 to describe the spacing of splitting of spectral lines in multi-electron atoms in terms of electric charge, speed of light and Planck;s constant, the alpha constant represents a relativistic correction to the Bohr theory of the energy level of an electron. The fine structure constant alpha has numerous interpretations including ratio scaling of tangential velocity v to velocity of light c, electromagnetic force to max. force at Compton radius, impedance of free space to electron impedance, Bohr radius to Compton radius, classical electron radius to Compton radius, Compton radius to electromagnetic radius, etc. The inverse fine structure constant 1/alpha (= 137.035999...) is associated with scaling in mass ratios while the reduced fine structure constant alpha/2pi (= 0.0011614...) is associated with scaling in angular velocity and energy ratios. The electron charge to mass ratio e/m in mechanical units has the value 1.758820088E11 rad/sec. This angular velocity is quite small in comparison to the Compton angular frequency of 7.76343E20 rad/sec and is interpreted as a precession frequency. The whirl no q equals the inverse fine structure constant. This slight precession arises as a result of imbalance of electrostatic and magnetostatic energy which creates a torsion defect (loop closure failure) with a precession angle (topological charge) of 0.04458 rad (2,62 deg). This topological charge provides an explanation for origin of electric charge of the electron. This precession also results in wave function interference impeding flow of energy, hence providing an explanation of the origin of electron mass which heretofore has likewise been a mystery. A derivation of the fine structure constant and gyromagnetic spin ratio is presented with calculated values of physical properties of the electron corresponding to observed experimental values.
Electron Quantum SuperPhysics …
Humility, mortification, embarrassment — nostalgia, pride, understanding —
perhaps not enough words to even begin to describe my (electric, magnetic?)
re-journeying through “The Undiscovered Physics” these last weeks while I
worked through my new models of the SuperPlasma SuperFilaments of SGRA*
and ‘Neutron’ (Alpha Particle?) Stars — and our Sun. And started from scratch
re-illustrating the Volts, Teslas, Amperes, Ohms, Meters (per) Seconds —
Farads, Henrys — and did I say ‘Webers’? — of the Electron, Proton, Neutron
and Nuclei — and so on up the proverbial Electromagnetic Wave and Plasma
Filament and SuperPositional SuperFilament ladder …
[See the subsequent Oct31 2020 Publication of the Quantum SuperPhysics:]
https://tinyurl.com/TwainProton, and https://tinyurl.com/TwainProtonPDF
Talk about ‘Ancient Texts’, the World Wide Web hadn’t even been imagined yet,
and Googling was still a decade away — and a Wikipedia was unimaginable, in
the darkest days of 1989 when I began focusing in earnest on the question of
“The Electron” — with all the power that pen-and-paper gave me, and the
dozens of libraries and the search-computers at Stanford University.
Truth mattered a hundred-times more than humility, pretense, conformity —
but that certainly didn’t stop me from throwing away my first book two years
later when I realized just how ‘debased’ it was, ‘derivative’ from institutional
physics, ‘descended’ from the church of corporate science. It was another two
years before I was able to bring together “The Electron” and share it worldwide
(by post), with my new and growing global network of dissident and alternative
physicists, a hundred-strong.
An integration of a century of (the scarcest) of models of the topology of the
Electron — yet with which, thanks to that century of work I was able to stand
upon — the first to discard all the materialist dogma they were based upon, and
to show the experiential foundation of creation (of mass, energy, charge,
space and time) from the Electromagnetic Wave, in the conception, the
embodiment, indeed the sensation, of the Electron.
Which model, today, I will begin to update by two-and-a-half decades, by reillustrating and adding the AstroElectronic circuit parameterizations Charge,
Voltage, Magnetic Flux, Velocity, Wavelength, Period, Current, Impedance,
Inductance, Capacitance (and Permeability & Permittivity!) And then extend to
the superluminal Proton topology, the subluminal Plasma Filament structure of
the Sun, and the Superluminal SuperPlasma SuperFilament of a ‘Black
Dwarf’ (‘Neutron Star’), and, indeed, of Sagittarius A*.
The Charge of an Electron is defined, derived, determined by physics tradition to
be - (minus, negative) 1.6 x 10^-19 Coulombs. The electron mass-energy is
511,000 eV, or Electron-Volts, or 511,000 Volts per charge. And, conveniently
enough, an electron is the very DEFINITION of a single charge -- thus it is
charged to 511,000 Volts! [Questions immediately arise, and will complicate or
resolve matters soon, as to whether we mean peak voltage, or peak-to-peak,
and, yes, the periodicy, the frequency, of the ‘alternating’ current.]
Which are ‘both’ (suspiciously, tentatively, happily) answered by assuming the
‘classical’ electron radius of 2.8 x 10^-15 meters (2.8 Fermi). Further that
Velocity = 3 x 10^8 meters/sec = Wavelength (λ) times Frequency (F) = 2πr x F;
meaning Frequency = Velocity/Wavelength = Vel/λ = (3 x 10^8 meters/sec)
divided by (2π x 2.8 x 10^-15 meters/cycle). Thus F = 1.7 x 10^22 cycles/sec
or Hertz. And, as I = Current = Amperes = Coulombs/Sec, then I= (1.6 x 10^-19
Coulombs/cycle) x (1.7 x 10^22 cycles/sec) = 2,720 Amps. The solution for the
Impedance Z, of 188 Ω, is left to the student.
Which brings us to the solutions for Magnetic Permeability (μ), Electric
Permittivity (ε), Inductance (L), Capacitance (C), and Magnetic Flux (Φ) and
Magnetic Flux Density (B).
Let’s start with Capacitance (C). Blundering ahead we try Capacitance =
Farads equals the amount of Charge in Coulombs produced per Volt.
Capacitance = Charge (Q)/Voltage (E).
C = (1.6 x 10^-19 Coulombs/cycle) divided by (511,000 volts) = 3.1 x 10^-25
Farads. Checking units; Volts = kg-meters^2 ÷ coul-secs^2. Capacitance =
Farads = coul^2-sec^2 ÷ kg-meters^2. (1.6 x 10^-19 Coulombs/cycle) divided
by (kg-meters^2 ÷ coul-secs^2) = (coul^2-sec^2 ÷ kg-meters^2) per cycle =
Coulombs per Volts-Cycle = Farads. Check!
Let’s try an alternate route for calculating Capacitance. The Electric Permittivity
(ε) of ‘free space’ is traditionally set at 8.85 x 10^-12 Farads/Meter.
Taking ε and multiplying by an electron radius of 2.8 x 10^-15 meters gives
us 2.5 x 10^-26 Farads. A VERY good answer, only off by about a factor of ten.
I then assumed that the topological, and hence numerical, corrections would be
found as a combination of factors of two (2) and π (3.14). The difference
between the two values of Capacitance are 31/2.5 = 12.4. Once — after the
days of exploring, testing and retesting many differing approaches to
determining electron Capacitance — once, after I was happiest with these two
models and their solutions, the factor of 12.4 was seen obviously to be
factorable by π and 2. Specifically 2 x 2 x π! And since I had already been
questioning the veracity of using 511,000 (peak) Volts in contrast to 1,022,000
(peak-to-peak) Volts, and of using Radius r rather than Wavelength 2πr — it only
took me a couple of minutes to decide to divide by an additional 2 in the first
Capacitance equation, and multiply by an additional 2π in the second
Capacitance equation — which, bringing the first down by 2, and the second up
by 2π, thus brought them each to the same answer: 1.6 x 10^-25 Farads!
And now for Inductance (L). By definition, conception, Magnetic (or Electric)
Induction is the Magnetic Flux (or Electric Field) produced by a changing
current. That is L = Henrys = Webers Φ / Amp (I) = Volt-Secs/Amp = Voltage E
divided by dI/dT. Or E = L (dI/dT). Solving for L = Volt-Secs/Amp we get
(1,022,000 Volts times 5.9 x 10^23 seconds) divided by 2720 Amps. Alternately
we could divide by the Frequency F = 1.7 x 10^-22 Hz which is the inverse of
the period in seconds. Either way we get 2.2 x 10^-20 Henrys.
We can double-check this by using the Magnetic Permeability formula. L
= μ x2πr. Magnetic Permeability of free space μ = 1.26 x 10^-6 Henrys/Meter.
Multiplying μ by 2π and 2.8 x 10^-15 meters we get 2.2 x 10^-20
Henrys! Check. Students, please verify the units of both formulas; kg, meters,
coulombs, seconds. [And find and call me out, for any typos or outright errors I
made in ANY of the derivations above, or in those to come!]
And now for Magnetic Flux!
Taking a step back from our quantitative description of the Circuit, Velocity
Field, Experiential Topo-Manifold of the Electron — we need to come back to
the understanding and perspective that Voltage, Magnetism, Charge, Polarity,
Spin, Frequency, Wavelength, Period, Current, Inductance, Capacitance,
Impedance, Permeability and Permittivity are all Qualitative Realities,
Physicalities, Concepts. And are all aspects of ONE ElectroMagnetic Topological
Manifold of Attraction/Repulsion, Spin/Orientation, Acceleration/Deceleration,
Rarefaction/Compression, Centrifugal Expansion, Centripetal Contraction, RedShift/Blue-Shift that we experience in everything we do, in every action, touch,
interaction we carry out or sense. The Frequency-Field, Frequency-Space. In
this ‘sense’, neither Voltage nor Magnetism exist. Certainly not by themselves.
And not statically!
The dynamic Electron illustration above — Magnetic North Up, out of page — is
taken from my 1995 “Proof of Metric Relativity” and begins to give an
impression of the universal Electromagnetic Topological Manifold. In this case
illustrating the simplest (mean, free, average) Electron Lissajous Standing
Electromagnetic Wave topology of a Circle, where the Sinusoidal Frequency in
the X direction is equal to that in the Y direction. Where the ratio of the two
frequencies, N = One. Imagine you are able to stand anywhere on the black
circle, which describes the CCW trajectory of the Electromagnetic Wave orbit
or circuit of the Electron. Say you start on the right side, where the negative
voltage vector is at full strength, and pointing out to the left of the blue ellipsoid.
As you progress CCW around the Electron orbit the magnitude of the negative
voltage vector arrow (in the XY plane) will reduce and will also spin out of the
plane as will the inner-directed positive voltage vector arrow. Until reaching the
top of the Circle the two directions of the Vector will be wholly out of the page,
at the same time the voltage reaches Zero.
For the next 90 degrees of the Circuit the Voltage arrows will be the negatives of
the first 90 degrees, as they increase from Zero to 511,000 Volts. And so the
cycle repeats during the next 180 degrees. The net result? A negative Voltage
or Charge is always presented OUTSIDE the Electron orbit or circle, and
positive on the inside. Preserving the integrity or resonance of the two
Electromagnetic Waves, and the stability and charge of the ‘negatively charged’
Right-Hand parity Electron.
And, not to forget, Magnetic Flux! And let’s approach it from some DIFFERENT,
INSIGHTFUL, REVEALING directions!!
Several approaches: Magnetic Flux Density (B) = kg/coul-sec = Volts x (secs/
meters^2) = 511,000 ÷ (1.7 x 10^22 Hz aka cycles/sec), and all divided by π x
2.8 x 10^-15 meters x 2.8 x 10^-15 meters. As Volts = kg-meters^2 ÷ coulsecs^2, all the meters cancel, and one of the seconds terms cancels, leaving
12,200 x 10^8 kg/coul-sec = 1.22 x 10^12 kg/coul-sec aka Teslas!
Magnetic Flux (Φ) = kg-meters^2 ÷ coul-secs = Volts x seconds =
511,000 ÷ (1.7 x 10^22 Hz aka cycles/sec) = 300,600 x 10^-22 = 3.01 x 10^-17
Webers.
Magnetic Flux Density (B) = the ratio kg/coul divided by seconds. (B) = the
ratio kg/coul divided by seconds. The equivalence ratio of kilograms to
coulombs differs for the electron and proton. One coulomb = 6.24 x 10^18
charges. Charges being either protons or electrons. As the average electron has
a mass of 9.11 x 10^-31 kg, when multiplied by 6.24 x 10^18 electrons/coulomb
we get 56.8 x 10^-13 kg/coul. [Similarly for the proton, mass = 1.67 x 10^-27
kg, we get 10.4 10^-9 kg/coul.] Thus we can solve for B by taking the electron
kg/coul ratio of 56.8 x 10^-13 and multiplying it by 1.7 x 10^22 cycles/sec to get
96.6 x 10^9 kg-coul/sec or 9.7 x 10^10 Teslas. [Note that this is a factor of 12.6
(4π)smaller than our earlier derivation of 1.22 x 10^12 Teslas.]
The final approach to deriving B is to use the traditional single-loop circuit
equation B = μI/2R, where μ is Magnetic Permeability of free space = 1.26 x
10^-6 Henrys/Meter, and I, the electron current we derived earlier as 2720
Amps, and 2R is the Diameter of the electron ring = 2.8 x 10^-15 meters.
[Correction, Diameter equals two times the radius = 2 x 2.8 x 10^-15 meters.]
Thus we, again, get Magnetic Flux Density (B) = 1224 x 10^9 = 1.22 x 10^12
Teslas! [Not again? Divide by 2? B = 6.1 x 10^11 Teslas?]
To Recap: We illustrated our model of the Electron as a one or two frequency
4D Lissajous Standing (Self-Connected) Electromagnetic Wave. No point
charge or charges involved. And the ‘lines’ do not depict any physical reality,
except a visual representation of the (dynamic, not static) voltage ‘peaks’ of the
Electromagnetic Frequency Field or Space or Vortex plenum everywhere around,
inside, and outside it. [Imagine a topo map of the Electromagnetic Field of
continuously varying frequency, wavelength, velocity, and electronic
parameters.]
The numbers we assumed or derived were:
•
Electron Radius R = 2.8 x 10^-15 meters (2.8 Fermi)
•
Electron Velocity V = 3 x 10^8 meters/sec
•
Electron Frequency F = 1.7 x 10^22 cycles/sec or Hertz
Electron Charge Q = -1.6 x 10^-19 Coulombs
•
Electron Mass M = 9.11 x 10^-31 kg
•
•
Electron Voltage E ranges between ± 511,000 Volts
Internal Electron Current I = 2,720 Amps
•
Electron Impedance Z = 188 Ω (Ohms)
•
•
•
•
•
•
•
•
•
Electron Circuit Resistance = 0 (Zero)
Electron Q-Factor = ∞ (Infinite)
Electric Permittivity(ε) of Electron =8.85 x 10^-12 Farads/Meter
Electron Self-Capacitance C = 1.6 x 10^-25 Farads
Magnetic Permeability (μ) of Electron = 1.26 x 10^-6 Henrys/Meter
Electron Self-Inductance L = 2.2 x 10^-20 Henrys
Electron Magnetic Flux(Φ)=3.01 x 10^-17 Webers
Electron Magnetic Flux Density B = 1.22 x 10^12 Teslas
More articles in process, soon to be shared, illustrating the Totality & Universality
of our Electromagnetic Ocean of Experience, the Unbounded Wave Chorus/
Cascade of every Cosmic ripple, surge, swell, breaker and tsunami – this
Songline of every Voice, each ‘Note’ and all ‘Octaves’ of nature – a Fourier
Superposition of the whole bandwidth of our observed Rainbow Spectrum
at every Astrophysical Scale – all Wavelengths, every Frequency – from the
Sub-Femtometer proton fine-structure to the Super-Kilo-Yottameter aggregation
of every SuperGalaxy SuperFilament.
Full Histories Archived in these Groups:
https://www.facebook.com/SoverAnia
https://www.facebook.com/groups/SGRAstar
https://www.facebook.com/groups/QuantumSuperphysics
https://www.facebook.com/groups/HaltonArp
https://www.facebook.com/groups/SiriusSol
Millennium Twain, 2019
https://twitter.com/MillenniumTwain
https://twitter.com/QuantumTwain
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