zotero-db/storage/THVMBGUP/.zotero-ft-cache

Electron Binding Energies in the Aether Physics Model
David W. Thomson III Quantum AetherDynamics Institute 518 Illinois St. Alma, IL 62807 ebeapm@volantis.org
Jim D. Bourassa Quantum AetherDynamics Institute 2303 Randall Road #242 Carpentersville, IL 60110 jb@quantumaetherdynamics.com
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-periodictable 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.

1. Introduction
Scientists have attempted to quantify the electron binding energies of atoms. Lindgreni reports on probabilistic methods for deriving the electron binding energies using the Koopmans Theorem, ∆SCF, many-body perturbation (MBPT), Coupled-Cluster Approach (CCA), Greene’s function, and the density functional theory (DFT) approach. Whitneyii iii uses a new two-step variant of special relativity theory to uncover an underlying similarity between all elements and Hydrogen, and algebraically characterizes all variations from that norm. The present work bases on a new discrete physical model for quantum structure, and results directly in an accurate binding energy equation predicting all ground state electrons.

The Aether Physics Model is a discrete model of quantum structure. Up to now, the Aether Physics Model only quantified quantum structure, as opposed to quantum mechanics. Despite the properly quantified Unified Force Theory contained within the Aether Physics Model, the model has not yet received significant attention from physicists and mathematicians. This lack of interest is partly due to the necessity of learning revised definitions for the dimensions, understanding that electrical units should always be expressed in dimensions of distributed charge (charge squared), and understanding the two distinctly different manifestations of charges. Further, the Aether Physics Model is a paradigm of Aether/angular momentum, as opposed to the mass/energy paradigm presently in use.

The significance of the Aether/angular momentum paradigm is that it shows the relationship between environment (Aether) and matter (angular momentum). The environment and matter quantify geometrically, as well as with dimensions and values. The geometrical quantification of Aether and matter allows for a discrete understanding of quantum structure in five dimensions (three dimensions of length, two dimensions of frequency), and a more precise understanding of charges and their mechanics.

The discrete and precise quantum structures allow for the development of the electron binding energy
equations. We will lead the reader through each step of the process, but assume some familiarity with our white paperiv and bookv, which provide the foundation for the Aether Physics Model.

For the reader’s convenience, Table 1 includes the essential values and dimensions for the calculations.

Constant Aether Unit
Quantum Length (Compton wavelength) Quantum Frequency
Speed of Light
Mass of Electron

Symbol A u

Table 1. Essential Constants

Value

Constant

1.419 ×1012

kg ⋅ m3 sec2 ⋅ coul2

Electron Strong Charge

λ C

2.426 ×10−12 m

Classical Electron Radius

F q

1.236×1020 Hz

c

2.998×108 m

sec

m e

9.109×10−31 kg

Bohr Electron Radius
Planck’s Constant
Electron Fine Structure Constant

Symbol Value

e 2 emax

1.400×10−37 coul2

r e

2.818×10−15 m

α 0

5.292 ×10−11 m

h

6.626 ×10−34 kg ⋅ m2

sec

α

7.297 ×10−3

Unique to the Aether Physics Model is a new system of quantum measurement units. The quantum measurement units contain both dimensions and quantum values. Except where the quantum measurement already defines in modern physics, a four-letter acronym represents each unit. This new notation necessarily differentiates the new unit system from other systems.

2. Strong Force of the Electron
In our paper, A New Foundation for Physicsvi, we demonstrate the Casimir equation is actually a form of the strong force equation for the electron.

π ⋅h⋅c 480 ⋅ λC4

λC 2

≈

Au

e2 emax λC 2

(2.1)

The slight difference in value is consistent with the Casimir effect experiment by Steven Lamoreauxvii.

Since quantum structure composes from quantum measurements, and the Compton wavelength empirically demonstrates as the quantum length, we can determine the quantum energy of an electron during one cycle of the quantum frequency (the duration of one cycle of quantum frequency is a quantum moment) is equal to:

enrg

=

Au

e2 emax λC

(2.2)

Interestingly enough, the quantum energy of the electron is also equal to the mass of the electron times the speed of light squared:

enrg = me ⋅ c2

(2.3)

However, mass is not matter and no physical meaning is attributed to “velocity squared,” therefore there is no physical interpretation for mass times velocity squared in the Standard Model. In the Aether Physics Model, we discretely define quantum energy as the Aether (environment) imparting a quantum strong force through the electron over a range of one quantum length.

Although the electrons are bound to the nucleus due to electrostatic attraction, almost all the binding energy action takes place because of the strong force between electrons.

3. Meaning of Kinetic Energy

All energy transactions occur in two parts. There is the source of the energy and there is the receiver of
the energy. To put it in common language, there is cause and effect. Whether an electron is seen being acted upon, or doing the acting, it is only half the energy transaction. Therefore, the binding energy equation will represent only half the energy transaction. Our book, Secrets of the Aetherviii, explains the two-part energy transaction in detail.

4. Toroidal Structure of the Electron

While researching the evidence for electron radii, we came upon the research of David McCutcheon and his Ultrawave Theoryix, which gave an interesting view of the classical and Bohr electron radii:

2π re ⋅ 2πα0 = λC2

(4.1)

It is likely others have noticed this relationship, but such work was not located. The above relationship reveals that a toroid with a minor radius equal to the classical electron radius and major radius equal to the Bohr radius has the surface area equal to the Compton wavelength squared.

Further, Planck’s constant easily demonstrates the quantum of action (for the electron) is equal to the mass of the electron times the Compton wavelength squared times the quantum frequency.

h = me ⋅ λC2 ⋅ Fq

(4.2)

We used the above quantum analyses in developing the Aether Physics Model. It turns out the electron models as a toroid, which can have variable radii as long as the quantum surface area remains the same. Therefore, the electron is not a fixed-point particle, but is a flexible toroidal entity. The flexibility is possible due to the Aether, which gives the electron its structure. As detailed in Secrets of the Aetherx, the Aether is a quantum unit of rotating magnetic field. Ontologically, the Aether unit pre-exists matter and contributes to the material structure of the angular momentum encapsulated by it.

5. Hydrogen Electron Binding Energy

Because of the relationship between the classical and Bohr electron radii, the proportion of the two is equal to the electron fine structure constant squared.

re = α 2 α0

(5.1)

An equation, once posted on a Vanderbilt University philosophy pagexi, and by David McCutcheon, expressed the hydrogen 1s (ground state) orbital electron in terms of the electron fine structure and kinetic energy of the electron:

H1s

=α2

me ⋅ c2 2

= 13.606eV

(5.2)

In the Aether Physics Model, this would interpret as the ground state, unbound ratio of the electron radii times the strong force of the electron at the range of one quantum length:

H1s

= re α0

Au

e2 emax
2λC

= 13.606eV

(5.3)

(Electron volts express energy above, although the same value written in quantum measurements units is 2.663×10−5 enrg .)

6. Helium Electron Binding Energy

Due to the nature of curved Aether (space-time), when multiplying charges the square root of each charge is used. If there are two electron strong charges involved, then the strong force between them is equal to:

Au

2eemax ⋅ 2eemax λC 2

= F

(6.1)

We could similarly calculate the kinetic energy as:

Au

2eemax ⋅ 2eemax 2λC

= Ek

(6.2)

In our book, Secrets of the Aether, we have a section about Aether Structuresxii. The steps involved in building Aether structures involve quantifying the spin differences of matter and Aether. Although the quantum Aether unit has 2-spin, subatomic particles only inhabit one fourth of the Aether, or half spin.

The “spin” of the subatomic particles is a direct result of the two dynamic frequency dimensions of the Aether. One of the dynamic frequency dimensions manifests as forward/backward time, the other manifests as right/left spin direction. There is actually a third “static” frequency, which results in positive/negative electrostatic charge.

All matter in our observed Universe exists in only the forward time direction. This observed matter further divides into matter and antimatter, depending on which half of the spin direction cycle it exists. Matter also divides into positive and negative charge depending on which half of the static charge cycle it exists.

The primary angular momentum composing subatomic particles can only spin in either the forward or backward time direction, and either the right or left spin direction, and exist in either the positive or the negative of the static charge dipole. Since static charge is not part of the dynamic two-spin structure of the Aether, and angular momentum only exists in half the forward/backward time frequency and half the right/left spin direction, matter appears to have half-spin.

Therefore, when half spin subatomic particles bind they are missing the backward time direction, yet the Aether sees this backward time direction. The result is that subatomic particles do not pair exactly opposite or adjacent to each other, as square building blocks seem to do at the macro level of existence. Instead, the subatomic particles (being curved toroidal structures to begin with), build up in a twisted pattern.

This twisted construction affects the minor and major radii of the toroidal electrons. As electrons bind to each other and fill the Aether spin positions around an atomic nucleus, the effect is additive.

In the case of the electrons, the minor radius increases with the number of electrons (which is equal to the number of protons in a neutral atom). Designating the number of protons as Z, the minor radius decreases in steps of half spin.

Z2 +1−1 2

(6.3)

The major radius increases in steps of half spin:

Z2 +1+1 2

(6.4)

The above stepping patterns are the phi and Phi numbers. In the case of the first binding, where there are two electrons, we get:

22 +1 −1 = phi = .618...

2

(6.5)

22 +1 +1 = Phi = 1.618...

2

The above numbers are the Golden Ratio (Phi) and its reciprocal (phi).

With the increase in the number of protons in the atoms, there is an increase in the number of electrons. The total electron radii deform accordingly. As the minor radius shrinks and the major radius grows, there is a deformation as the Aether units stretch and thus the distance between them shrinks. The distance empirically induces in terms of the quantum length as (the nth root is a capital Z squared):

λ C 2 Z 2

(6.6)

There is no electron strong force binding in the neutral hydrogen atom because there is only one electron, but when we look at helium and all other neutral atoms, the electron binding energy equation for the 1s “orbital” electron becomes:

re Z1s =
α0

Z 2 +1 −1

2 Z2 +1+1

Au

Z

⋅ eemax

⋅ Z ⋅ eemax 2λC

⋅ Z2

2

2

(6.7)

In the case of the neutral helium atom, we can calculate the 1s orbital electron binding energies as:

re He1s =
α0

22 +1 −1

2 22 +1 +1

Au

2 ⋅ eemax

⋅ 2 ⋅ eemax 2λC

⋅ 22

2

=

24.721eV

2

(6.8)

The empirically measured 1s “orbital” electron binding energy for helium is 24.6eV.

7. Lithium and All Other Binding Energies

As the bindings continue into complexity, it is clear another factor comes into play, which does not yet properly quantify. The elements lithium through neon comprise the second orbital layer around the nucleus. It may just be coincidence, but these eight out of the first ten elements calculate to eight tenths of their measured values. From sodium to uranium, the calculation variations are linear with respect to the measured electron binding energies indicating a simple physical explanation.
When a linear adjustment applies to the equation, the calculations are remarkably close to the measured values:

re Z1s =
α0

Z 2 +1 −1

2 Z2 +1+1

Au

Z

⋅ eemax

⋅Z

⋅ eemax

⋅ Z2 2 2λC

⋅ (.757 + .0028Z )

2

(7.1)

The above equation may be simplified, but it remains in its present form to remind the reader of its physical interpretation. The empirical data used in this paper draws from Gwyn Williams’xiii compilation of electron binding energies. Table 2 shows the measured and calculated 1s orbital binding energies in eV per atomic element and the deviation between them based upon equation 7.1. Figure 1 depicts the deviation of the calculations from the empirically measured electron binding energies of the 1s orbital position for each element for equation 7.1.

Table 3 lists the measured 1s orbital binding energies in eV per atomic element in comparison to the calculations of equation 6.8 (without the linear adjustment). Figure 2 shows the deviation of the unadjusted (equation 6.8) calculations from the empirical electron binding energies of the 1s orbital positions for each atomic element. The unadjusted data presents for those interested in discovering the final physical component of the 1s orbital binding energy equation.

Table 2 – Empirical and Calculated Binding Energies with Errors (equation 7.1) Values calculated in Microsoft Excel

Table 3 - Empirical and Calculated Binding Energies with Errors (equation 6.8) via MS Excel

Z Element Measured

3 Li

54.7

4 Be

111.5

5B

188

6C

284.2

7N 8O

409.9 543.1

9F

696.7

10 Ne

870.2

11 Na

1070.8

12 Mg 13 Al

1303 1559

14 Si 15 P 16 S

1839 2145.5
2472

17 Cl

2822

18 Ar

3205.9

19 K 20 Ca

3608.4 4038.5

21 Sc

4492

22 Ti

4966

23 V

5465

24 Cr 25 Mn

5989 6539

26 Fe

7112

27 Co

7709

28 Ni 29 Cu 30 Zn

8333 8979 9659

31 Ga

10367

32 Ge

11103

33 As

11867

34 Se

12658

35 Br

13474

36 Kr 37 Rb

14326 15200

38 Sr

16105

39 Y

17038

40 Zr

17998

41 Nb 42 Mo

18986 20000

43 Tc

21044

44 Ru

22117

45 Rh 46 Pd 47 Ag

23220 24350 25514

Calculated
68.71 138.58 235.03 358.33 508.62 685.98 890.45 1122.06 1380.83 1666.76 1979.88 2320.18 2687.68 3082.37 3504.25 3953.34 4429.62 4933.11 5463.81 6021.71 6606.81 7219.12 7858.64 8525.36 9219.30 9940.44 10688.79 11464.35 12267.11 13097.09 13954.28 14838.67 15750.28 16689.10 17655.12 18648.36 19668.80 20716.46 21791.33 22893.41 24022.69 25179.19 26362.90 27573.82 28811.95

Deviation
-20.38% -19.54% -20.01% -20.69% -19.41% -20.83% -21.76% -22.45% -22.45% -21.82% -21.26% -20.74% -20.17% -19.80% -19.47% -18.91% -18.54% -18.13% -17.79% -17.53% -17.28% -17.04% -16.79% -16.58% -16.38% -16.17% -16.00% -15.75% -15.49% -15.23% -14.96% -14.70% -14.45% -14.16% -13.91% -13.64% -13.38% -13.12% -12.87% -12.64% -12.40% -12.16% -11.92% -11.69% -11.45%

Z Element Measured

48 Cd

26711

49 In

27940

50 Sn

29200

51 Sb

30491

52 Te 53 I

31814 33169

54 Xe

34561

55 Cs

35985

56 Ba

37441

57 La 58 Ce

38925 40443

59 Pr 60 Nd 61 Pm

41991 43569 45184

62 Sm

46834

63 Eu

48519

64 Gd 65 Tb

50239 51996

66 Dy

53789

67 Ho

55618

68 Er

57486

69 Tm 70 Yb

59390 61332

71 Lu

63314

72 Hf

65351

73 Ta 74 W 75 Re

67416 69525 71676

76 Os

73871

77 Ir

76111

78 Pt

78395

79 Au

80725

80 Hg

83102

81 Tl 82 Pb

85530 88005

83 Bi

90526

84 Po

93105

85 At

95730

86 Rn 87 Fr

98404 101137

88 Ra

103922

89 Ac

106755

90 Th 91 Pa 92 U

109651 112601 115606

Calculated
30077.29 31369.85 32689.61 34036.58 35410.77 36812.16 38240.77 39696.59 41179.61 42689.85 44227.30 45791.96 47383.84 49002.92 50649.21 52322.72 54023.44 55751.36 57506.50 59288.85 61098.41 62935.19 64799.17 66690.36 68608.77 70554.39 72527.21 74527.25 76554.50 78608.97 80690.64 82799.52 84935.62 87098.92 89289.44 91507.17 93752.11 96024.26 98323.62 100650.20 103003.98 105384.98 107793.19 110228.60 112691.23

Deviation
-11.19% -10.93% -10.67% -10.42% -10.16%
-9.90% -9.62% -9.35% -9.08% -8.82% -8.56% -8.30% -8.05% -7.79% -7.53% -7.27% -7.01% -6.74% -6.46% -6.19% -5.91% -5.63% -5.35% -5.06% -4.75% -4.45% -4.14% -3.83% -3.51% -3.18% -2.84% -2.51% -2.16% -1.80% -1.44% -1.07% -0.69% -0.31% 0.08% 0.48% 0.89% 1.30% 1.72% 2.15% 2.59%

8. Sample Detailed Calculations We can apply equation 7.1 to any element from lithium to uranium.
a. Oxygen Calculating the 1s orbital for oxygen we get 534.534eV (all values are off from table due to rounding):

re O1s =
α0

82 +1 −1

82

2 +1

+ 1

Au

8 ⋅ eemax

⋅8⋅

eemax

⋅ 82 2 ⋅ 2λC

(.757

+

.0028 ⋅8)

2

O1s

=

2.818 5.292

×10−15 ×10−11

m m

⋅ ⋅

3.5311.419 4.531

×1012

kg ⋅ m3 sec2 ⋅ coul2

64 ⋅1.400×10−37 coul2 ⋅1.011⋅.779 2 ⋅ 2.426 ×10−12 m

O1s

=

4.150 ×10−5

⋅1.419 ×1012

kg ⋅ m3 sec2 ⋅ coul2

7.055×10−36 coul2 4.852 ×10−12 m

O1s = 8.564 ×10−17 joule = 534.534eV b. Iron

The ground state electron for iron is similarly calculated:

re Fe1s =
α0

262 +1 −1

2 262 +1 +1

Au

26 ⋅ eemax

⋅ 26 ⋅ eemax

⋅ 262 2 2λC

⋅ (.757 + .0028 ⋅ 26)

2

Fe1s

=

2.818 5.292

×10−15 ×10−11

m m

⋅12.510 ⋅13.510

1.419

×1012

kg ⋅ m3 sec2 ⋅ coul2

676 ⋅1.400 ×10−37 coul 2 ⋅1.001⋅.830 2 ⋅ 2.426 ×10−12 m

Fe1s

=

4.931×10−5

⋅1.419 ×1012

kg ⋅ m3 sec2 ⋅ coul 2

7.861×10−35 coul 2 4.852 ×10−12 m

Fe1s = 1.134 ×10−15 joule = 7.077 ×103 eV c. Uranium
The calculation for uranium is:

re U1s =
α0

922 +1 −1

2 922 +1

+ 1

Au

92 ⋅ eemax

⋅ 92 ⋅ eemax

⋅ 922 2 2λC

⋅ (.757

+ .0028 ⋅92)

2

U1s

=

2.818 5.292

×10−15 ×10−11

m m

⋅ ⋅

45.503 46.503

1.419

×1012

kg ⋅ m3 sec2 ⋅ coul2

8.464 ×103

⋅1.400 ×10−37 coul 2 ⋅1.000 ⋅1.015 2 ⋅ 2.426 ×10−12 m

U1s

=

5.211×10−5

⋅1.419 ×1012

kg ⋅ m3 sec2 ⋅ coul2

1.202 ×10−33 coul 2 4.852 ×10−12 m

U1s = 1.832 ×10−14 joule = 1.144 ×105 eV

9. Conclusion

The Aether Physics Model electron binding energy equations for the 1s orbitals are not exact, but very close, especially considering that all the elemental ground states are calculated from first principles. There is the possibility the data could be faulty, however it is more likely there are aspects of the Aether structure which the equation is not yet addressing. These aspects may surface as future modifications to the equation calculate the remaining electron orbital positions.

The electron binding energy equation is the first quantum mechanical expression of the Aether Physics Model and demonstrates the model is viable. Unlike the quantum mechanics of the mass/energy paradigm, the Aether Physics Model is discrete and devoid of probability functions and paradoxes, which should make it superior to the Standard Model when fully developed.

Now that the Aether Physics Model quantifies the quantum structure and we have produced our first set of equations, the analysis must develop further until it explains all aspects of the atom. We should then be able to quantify the structural aspects of associated molecules. We also need to quantify and explore the mechanics of light very thoroughly.

Acknowledgement

We thank Dr. Cynthia Whitney of Galilean Electrodynamics for providing references and background information on prior electron energy binding equation research. We also thank Dr. Gerald Hooper of Leicester, UK and Dr. Phil Risby of DES Group, UK for their guidance when submitting this paper.

References
i Lindgren, Ingvar, Calculation of Electron Binding Energies and Affinities (Phys. Scr. T120 15-18, doi:10.1088/00318949/2005/T120/002, 2005)
ii Whitney, Cynthia, Algebraic Chemistry: Parts I Through V (Hadronic Journal, vol. 29, no. 1, February 2006) pp 1-46
iii Whitney, Cynthia, Algebraic Chemistry Based on a PIRT (Physical Interpretations of Relativity Theory conference, London, UK, 2006)
iv David W. Thomson and Jim D. Bourassa, A New Foundation for Physics (Physical Interpretations of Relativity Theory conference, London, UK, 2006)
v David W. Thomson and Jim D. Bourassa, Secrets of the Aether; Second Edition (Alma, IL, The Aenor Trust, 2005)
vi David W. Thomson and Jim D. Bourassa, A New Foundation for Physics:Section 8.b (Physical Interpretations of Relativity Theory conference, London, UK, 2006)
vii Lamoreaux, Steven K., Demonstration of the Casimir Force in the 0.6 to 6 mm Range (Phys Rev Let, Vol 78, Num 1, 1996)
viii David W. Thomson and Jim D. Bourassa, Secrets of the Aether; Second Edition: Units Chapter 6, Kinetic Energy (Alma, IL, The Aenor Trust, 2005)
ix Web site formerly located at http://davidmac_no1.tripod.com/ut_part1/, archived at http://web.archive.org/web/20040923070747/http:/davidmac_no1.tripod.com/.
x David W. Thomson and Jim D. Bourassa, Secrets of the Aether; Second Edition: Aether Chapter 4, Aether Unit (Alma, IL, The Aenor Trust, 2005)
xi Inactive page: http://ransom.isis.vanderbilt.edu/philosophy/FineStructureConstant.htm
xii David W. Thomson and Jim D. Bourassa, Secrets of the Aether; Second Edition: Aether Chapter 4, Aether Structures (Alma, IL, The Aenor Trust, 2005)
xiii Williams, Gwyn http://xray.uu.se/hypertext/EBindEnergies.html Values are taken from J. A. Bearden and A. F. Burr, "Reevaluation of X-Ray Atomic Energy Levels," Rev. Mod. Phys. 39, (1967) p.125, except values marked '*' are from M. Cardona and L. Ley, Eds., Photoemission in Solids I: General Principles (Springer-Verlag, Berlin, 1978) with additional corrections, and values marked with '+' are from J. C. Fuggle and N. Mårtensson, "Core-Level Binding Energies in Metals," J. Electron Spectrosc. Relat. Phenom. 21, (1980) p.275. [reference copied from web page]