1

Note

Date: June 19, 2011

Brief History of Elementary Charge by Dan Petru Danescu, e-mail: dpdanescu@yahoo.com

Keywords: elementary charge, elementary electric charge, electric charge, electron

charge, spin magnetic moment, spin motion, CP symmetry, CPT symmetry.

Contents:

1.Title page

2. Timeline.

14. References.

16. Appendix 1 Spin motion and 4 rotation.

17. Appendix 2 Interpretation of CPT symmetry.

18. Appendix 3 The average electron as a open sliding knot.

19. Appendix 4 The production of electron-positron pair

20. Appendix 5: A possible interpretation of fractional electric charges of quarks.

2

Timeline

● 1733 Charles Francois de Cisternay du Fay discovered the existence of two types of

electricity: “vitreous” and “resinous” (later known as “positive” and “negative” charge

respectively), [1].

● 1769 Benjamin Franklin arbitrarily associated the term “positive” (+) with vitreous

electricity and “negative” (-) with resinous electricity, [2].

● 1785 Charles Augustin de Coulomb discovered, with torsion balance, an inverse

relationship of the force between electric charges and the square of its distance, later

known as Coulomb’s law, [3], Fig.1.

F1,2 = k 2

21

r

QQ (1)

From (1) results the definition of charge unit in cgs system (F1,2 = 1 dyne; r = 1 cm; k=1;

Q1 = Q2 = 1Fr = 1statcoulomb = 1esu).

Fig.1 Coulomb’s torsion balance

3

● 1838 Richard Laming [4] introduced the concept of an indivisible amount of electric

charge to explain the chemical properties of atoms (hypothesized the existence of sub-

atomic particles of unit charge).

● 1843 Michael Faraday [5] discovered the law of conservation of electric charge. It is

written using vector calculation,

t

+ . J = 0 . (2)

● 1859-1873 According to Michael Faraday & James Clark Maxwell theory of field [6],

[7], in expression:

div D = 4

has character of auxiliary notation and the charge notion has character of auxiliary

term. In this context the interpretation of electric charge as a separate substance does not

have any significance. Charge interpretation as a knot-like on field lines [8] becomes very

important.

● 1876-7 Lord Kelvin suggested [9] that atom is composed of string knotted in various

configurations and Peter Guthrie Tait made first systematic study of knots [10].

“Crossing sign” in knot theory was associated with “right handed”and “left handed”

(Fig.2). Later, ± 1 algebric sign was adopted (Fig.2).

Left handed crossing Right handed crossing

Fig.2 Crossing sign

4

● 1891 George Johnstone Stoney proposed the term “electron” to describe the

fundamental unit of electrical charge [11]. This quantity of electricity was estimated to

3×10-11

esu by Professor Richarz.

● 1897 Discovery of electron in cathode rays by Joseph John Thomson. He measured the

mass-to-charge ratio of the cathode rays, [12],

e

me = 0.40 ÷ 0.54×10-7

g/emu (4)

independent of the nature of gas.

The “corpuscles” discovered by Thomson are identified with the “electron” proposed by

G.J. Stoney in 1891.

The inverse ratio, charge-to-mass, more known, is (actual value), [13]

em

e = -1.758 820 150×10

11 C/kg . (SI) (5)

or

em

e = -1.758 820 150×10

7 emu/g . (CGSem) (6)

or

em

e = -5.272 810 159×10

17 esu/g , (CGSes, CGS Gaussian) (7)

● 1911-1913 Robert Andrews Millikan measured the value of the elementary electric

charge ( The oil–drop experiment). The same time it was demonstrated the discrete nature

of electric charge [14], [15],

e = 4.777×10-10

esu (CGSes, CGS Gaussian) (8)

The modern value of the elementary electric charge is, [13],

e = 4.803 204 27×10-10

esu (CGSes, CGS Gaussian), (9)

e = 1.602 176 487×10-19

C (SI). (10)

● 1919-1923 Arthur Holly Compton [16] developed the concept of “thin flexible ring of

electricity” in connection with the electron structure. The radius of ring electron (or ring

of electricity) was estimated as about

5

rC ~ 2×10-10

cm. (11)

Later, in the Compton’s theory of the scattering of X-rays, [17], [18], a more precis

experiment, the Compton wavelength, C = 2.4×10-10

cm. , is aproximated equal to the

radius of the “ring of electricity”(rC ),

C ≈ rC (12)

Fig.3 “Thin flexible ring of electricity” (After A.H. Compton, implicit)

The modern value of the Compton wavelength is [13],

C =cm

h

e

= 2.426 310 2175×10-10

cm. (13)

● 1920 Wolfgang Pauli introduced the elementary unit of magnetic moment,

interpretation in terms of the Bohr’s atom [19], [20]. From the classical expression for

magnetic moment = IA, and considering the effective current I = - e/T = - ev/2r,

which can be rewritten as I = - emevr/2mer, the magnetic moment result, = -(e/2me)L,

where angular momentum L, is quantified, conformable to Bohr-Sommerfeld theory, L

= =n (h/2), n = 1, 2, 3, …,n. A elementary unit of magnetic moment called the “Bohr

magneton” (for n = 1), is

B = c

1

em4

he

|| = 9.2110

-21 emu, (14)

or related to the mol,

B = c

1

em4

he

||N0 = 5548 Gauss.cm, (15)

6

N0 being the number of atoms or molecules per gram-atom, ( N0 = 6.061023

mol-1

) and

the 1/c factor being for conversion esu→emu, (Fig.4)

Fig.4 The charge and the vector model of Bohr’s magneton (implicit).

● 1924-1928 Wolfgang Pauli introduced the idea of “two-valued quantum degree of

freedom” associated with the electron, [21]. Samuel Goudsmit & George Ullenbeck [22],

postulated the electron spin. Paul Adrien Maurice Dirac [23], developed the electron spin

concept, (Fig.5).

Fig.5 The vector model of electron spin

S = 1)s(s = 2

3, s =

2

1 , (16)

7

s = - ge2m

eS ≈ - 3 B , (g ≈ 2, after Dirac) . (17)

Actual value of spin magnetic moment (s ) is

s ≈ 1.608 10-23

J/T (SI) (18)

s ≈ 4.821 10-10

esu (CGSes, CGS Gaussian*)) (19)

*) without 1/c factor of units transferred in torque relation.

● 1899-1905-1930 Hendrik Anton Lorentz, [24], [25] Albert Einstein, [26], and others:

The Lorentz transformations, the relativistic theory. The elementary electric charge is an

relativistically invariant,

e = e0 = const. (20)

Another particle characteristics are relativistically invariant (spin, S and magnetic

moment, s), other are relativistic (mass, me , energy, E and de Broglie wavelength )

S = S0 = const. , (21)

s = s0 = const. , (22)

me = me0 , (23)

E = E0 , (24)

= 0 , (25)

where

=2

c

v1

1

(26)

The property of charge invariance follows from the vanishing divergence of the charge-

current four – vector j

= (cp, j

), with ∂j

8

● 1928-1939 Paul Adrien Maurice Dirac [27] and Ernst Carl Gerlach Stueckelberg [28]

introduced the concept of “point charge electron” as a mathematical approximation. A

point charge (ideal charge) is a hypothetical charge located at a point in space. A point-

like charge electron was difficult to accept, because its magnetic moment presupposes an

area.

● 1931 Paul Adrien Maurice Dirac [29] predicted the existence of the positron.

● 1933 Carl David Anderson [30] discovered the positron (announced in 1932).

● 1936 Werner Heisenberg [31], introduced charge conjugation invariance (C), as a

symmetry operation connecting particle and antiparticle states.

● 1937-1939 H. Hellmann [32] – R. P. Feynman [33] defined the theorem where the

probability density of finding electron (later also named “quantum electron”[34], [35]) is

proportional to the charge density

||2 -e||

2 (27)

(Consequence: the electron or quantum electron is the charge)

● 1955 John A. Wheeler [36] proposed an idea about the relationship between electric

charge and the topology of a curved space-time. Later, Wheeler and Charles W. Misner

presented a model of electric charge (“charge without charge”) based on the topological

trapping of electric field [37].

● 1964-1995 Fractional electrical charges (2/3)e and (- 1/3)e for quarks and (-2/3)e and

(1/3)e for anti-quarks (Table 1 and 2).

The quarks idea was independently proposed by Murray Gell-Mann [38] and George

Zweig [39]. Quarks were introduced of an ordering scheme for hadrons

9

Table 1

Qurks

Name Charge Spin Mass Theoretized Discovered

Up (u) + e

3

2

2

1

1.5 MeV/c2 Murray Gell-Mann (1964),

[38]

George Zweig (1964), [39],

[40]

SLAC (1968)

Down (d) - e

3

1

2

1

4.0 MeV/c2 Murray Gell-Mann (1964)

George Zweig (1964)

SLAC (1968)

Strange (s) - e

3

1

2

1

80 MeV/c2 Murray Gell-Mann (1964)

George Zweig (1964)

SLAC (1968)

Charm (c) + e

3

2

2

1

1.3 GeV/c2 Schledom Glashow (1970),

[41]

John Iliopoulos

Luciano Maiani

SLAC &

BNL (1974)

Bottom (b) - e

3

1

2

1

4.2 GeV/c2 Makao Kobayashi (1973),

[42]

Toshihide Maskawa

Fermilab

(1977)

Top (t) + e

3

2

2

1

173 GeV/c2 Makao Kobayashi (1973)

Toshihide Maskawa

Fermilab

(1995)

SLAC: Stanford Linear Accelerator Center

BNL: Brookhaven National Laboratory

Table 2

Antiqurks

Name Charge Spin Mass

Anti - up ( u ) - e

3

2

2

1

1.5 MeV/c2

Anti - down ( d ) + e

3

1

2

1

4.0 MeV/c2

Anti - strange ( s ) + e

3

1

2

1

80 MeV/c2

Anti - charm ( c ) - e

3

2

2

1

1.3 GeV/c2

Anti - bottom ( b ) + e

3

1

2

1

4.2 GeV/c2

Anti - top ( t ) - e

3

2

2

1

173 GeV/c2

10

See: A possible interpretation of fractional electrical charges of quarks (Appendix 5)

● 1972 Based on Faraday’s and Maxwell’s idea (probably) , Andrei Sakharov developed

the concept of the knot-like charge and he named it “base”[43]

Fig.6 Topological structure of elementary charge (in connection with trefoil knots and cinquefoil

knots) after A. D. Sakharov

● 1977-2002 Dan Petru Danescu defined “the topological structure of elementary electric

charge in connection with the elastic overhand knot (idealized) with minimum energy”

and the fundamental physical constants [44], [45], [46], [47], [48], (Fig.7).

In Gaussian units [48], (LTM dimensions) “electrical constants group” were identified:

|e±| ≈ 4.810

-10 esu;

|s| ≈ 4.810-10

esu;

2C ≈ 4.810-10

cm.

(|s| = gem2

e|S| ≈ 3

em2

e= 3 B , without 1/c factor of units, transferred in torque

relation and g ≈ 2, after Dirac).

In 1-dimensional (geometric) system of units, by transition LTM Gaussian → L, where:

[r, , e, ]= L; [t] = L2; [m, S, h, ] =L

3; [v, c ] =L

-1; [, , G ]= L

-2 ,

we have,

|s| ≈ |e±| ≈ 2C ≈ 4.8 10

-10 cm . (28)

These equalities can be interpreted.

11

Fig.7 The interpretation of elementary electric charge and spin magnetic moment using the

idealized elastic overhand knot with minimum energy. The charge is associated with crossing

sign: a) Convention of crossing sign after P.G. Tait and other; b) Interpretation of the relationship

(28); c) The proposed notation for the elementary electric charge.

In connection with the electric charge interpretation see:

Appendix 1 Spin motion and 4 rotation;

Appendix 2 Interpretation of CPT symmetry;

Appendix 3 The average electron as a open sliding knot.;

Appendix 4 The production of electron-positron pair

Appendix 5 A possible interpretation of fractional electrical charges of quarks.

12

● 1978 Dan Petru Danescu defined the” Elementary electric charge in connection with

kinematic inversion” [45].

From (28) relations and C = h/mec, |s| ≈ 3 eh/4me , in 1-dimensional system of units,

by transition LTM Gaussian →L (cm) result

2C ≈ |e±| ≈

c3

8π = const. (invariant) (29)

The interpretation of relation (29) it is shown in Fig.8 and Fig.9.

The geometric inversion of straight line in a C1 circle, the tangent case (A=A’), (Fig.8a)

imply:

OA . OA’ = OM . OM’ = const. = K (30)

Kinematic inversion of filament AL = , with negligible diameter, in a loop C1 (Fig.8b):

r1 = O1A = 1 cm (arbitrary) → Scale 1/1 (31)

OA’ =

Δ (32)

OA .

Δ = 2

2 cm

2 (33)

t = 1s:

OA .

v = 2

2 cm

2 /s (34)

Or

OA . v = 4 cm2 /s (35)

Kinematic inversion of an elastic straight filament (ℓ), in a overhand knot with

minimum energy (C1) which moves with c velocity (v = c ≈ 3×1010

cm/s), (Fig.9):

OA . 2

3c ≈ 4 cm

2 /s (36)

In a 1-dimensional system of units, result:

13

OA = c3

8π ≈ 4.8×10

-10cm ( ≈2C ≈ |e

±| ) (37)

The scale resulted, for C1 , is : 1/ 2.4×10-10

a) b)

Fig.8 Transition from geometric inversion a) of a straight line () in a circle to the

physics inversion b) of a filament (ℓ) with negligible diameter in a loop (C1).

14

a) b)

Fig.9. From geometric inversion of the straight line in a circle to the kinematic inversion a

elastic filament with negligible diameter in a idealized overhand knot which moves to

v = c velocity (after D.P.Danescu): a) The positive charge; b) The negative charge.

15

References [1] du Fay, “Two Kinds of Electrical Fluid: Vitreous and Resinous” Vol.38, Phil. Trans.

Roy. Soc. (1734).

[2] B. Franklin, “Experiments and Observations on Electricity, London, David Henry

ed. (1769).

[3] C. A. de Coulomb, Premier Memoire sur l’Electricite et le Magnetism, Histoire de

l’Academie Royale des Sciences 569-577 (1785).

[4] R. Laming, On the Primary Forces of Electricity. Location (1838).

[5] M. Faraday, Experimental Researches in Electricity, Vol.II, Richard and John Edward

Taylor, (1844).

[6] M. Faraday, Experimental Researches in Chemistry and Physics (1859).

[7] J.C.Maxwell, Treatise on Electricity and Magnetism, Clarendon Press (1873).

[8] I.E. Tamm, Osnova teori electricestva, Gosudarctvenoe Izdatelstvo, Moskva (1954).

[9] Lord Kelvin (W. Thomson), On vortex atoms, Proc.Roy.Soc. Ed., 6, 94-105 (1867).

[10] P.G. Tait, On Knots I, Trans. Roy. Soc., Edimburgh 28, 145-190 (1876-7).

[11] G.J. Stoney, Of the “Electron” or Atom of Electricity, Philosophical Magazine,

Series 5, Vol.38, pp.418-420 (1894).

[12] J.J. Thomson, Cathode Rays, Philosophical Magazine, 44, 293 (1897).

[13] CODATA, Recommended Values of the Fundamental Physical Constants (2006).

[14] R.A. Millikan, The Isolation of an Ion a Precision Measurement of its Charge and

the Correction of Stoke’s Law, Phys. Rev.XXXII, 349 (1911).

[15] R.A. Millikan, On the Elementary Electric Charge and the Avogadro Constant, Phys.

Rev. II, 2, p.109 (1913).

[16] A.H. Compton, The Size and Shape of the Electron, Phys. Rev. 14, 247-259 (1919).

[17] A.H. Compton, A Quantum Theory of the Scattering of X-Rays by Light Elements,

Phys. Rev. 21, 483-502 (1923).

[18] A.H. Compton, The Spectrum of Scattered X-Rays, Phys. Rev. 22, 409, (1923).

[19] N. Bohr, On the Constitution of Atoms and Molecules (Part I), Phylosophical

Magazine, 26, 1-25 (1913).

[20] W. Pauli, Talk entitled “Quantentheorie und Magneton” at Bad Nauheim, on the

occasion on the 86 th Naturforseherversammlung, September 1920.

[21] W. Pauli, The question of the theoretical meaning of the satellite of some

spectralline and their impact on the magnetic fields, Naturwissenschaften, 12, 741

(1924).

[22] S. Goudsmit and G. Uhlenbeck, Naturwissenschaften, 13, 953 (1925), Nature 117,

264 (1926).

[23] P.A. M. Dirac The Quantum Theory of the Electron, Proc. Roy. Soc. London, A117,

610 (1929); A118 351 (1928).

[24] A.H.Lorentz, Simplified Theory of Electrical and Optical Phenomena in Moving

Systems, Proc. Acad. Science Amsterdam 1, 427-442 (1899).

[25] A.H. Lorentz, Electromagnetic Phenomena in a System Moving with any Velocity

Smaller than that of Light, Proc. Acad. Science Amsterdam, 6, 809=831 (1904).

[26] A. Einstein, Zur Electrodynamic bewegter Korper, Annalen der Physik, 17, 891-921

(1905).

[27] P.A.M. Dirac, The Quantum Theory of the Electron, Proc. Roy. Soc. London A117,

610 (1928).

16

[28] E.K.G. Stueckelberg, A New Model of the Point Charge Electron and of Other

Elementary Particles, Nature, 144, 118 (1939).

[29] P.A.M. Dirac, Quantised Singularities in the Electromagnetic Field, Proc. Roy. Soc.

London, A 133, 60-72 (1931).

[30] C.D. Anderson, The positive electron, Phys. Rev. 43, 491 (1933).

[31] W. Heisenberg and H. Euler, Forgerungen aus der Diracschen Theorie des Positrons,

Zeitschr. Phys. 98, 714-732 (1936).

[32] H. Hellmann, in Einfuehrung in die Quantenchemie, Deuticke, Leipzig, pp.285

(1937).

[33] R.P. Feynman, Forces in Molecules, Phys. Rev. 56, 340 (1939).

[34] D. Ivanenco, A. Sokolov, Klasicescaia teoria polia, Gosudarctvenoe izdatelstvo,

Moskva (1951).

[35] A. Messiah, Mecanique quantique, Dunod, Paris (1964).

[36] J.A. Wheeler, Physical Review, 97, 511-536 (1955).

[37] C.W. Misner and J.A. Wheeler,Classical physics as geometry.Gravitation,

electromagnetism, uncuantized charge and mass as properties of curved empty space.

Annales of Physics, vol.2, no.6, pp.525-603 (1957).

[38] M. Gell-Mann, A Schematic Model of Barions and Mesons, Physics Letters (3),

214-215 (1964)

[39] G. Zweig, An SU (3) Model for Strong Interaction Symmetry and its Breaking,

CERN Report No.8181/Th 8412 (1964).

[40] G. Zweig, An SU (3) Model for Strong Interaction Symmetry and its Breaking,

CERN Report No.8419/Th 8412 (1964).

[41] S.L. Glashow, J. Iliopoulos, L. Maiani, Weak Interactions with Lepton-hadron

Symmetry, Physical Review D2, 1285-1292 (1970).

[42] M. Kobayashi, T. Maskawa, CP Violation in the Renormalizable Theory of Weak

Interaction, Progress of Theoretical Physics 49 (2): 652-657 (1973).

[43] A.D. Sakharov, Topological Structure of Elementary Charges and CPT-Symmetry,

In Problems of Theoretical Physics (A Memorial Volume to Igor E. Tamm), Nauka,

Moscow (1972).

[44] D.P. Danescu, Spin of the Electron Interpreted as a Revolution and Translation

Motion. Elementary Electric Charge Structure and CPT Symmetry, Preprint IFA –

Bucureşti nr. 19 / 25 apr. (1977), pp 1-35.

[45] D.P. Danescu,.Transformation by Inversion. Applications, Gazeta Matematică, Anul

LXXXIII, nr.3, (1978), pp 97-101.

[46] D.P.Danescu, The Compton Effect and the Structure of Electric Charge.

Epistemological Implications, Revista Învăţămîntului Superior "FORUM", 11,

(1979), pp. 85-92.

[47] D.P. Danescu, An Interpretation of the Fine-structure Constant, Buletin de Fizică şi

Chimie, Volumul 12-13, (1988-1989), pp.20-35.

[48] D.P. Danescu, On the Quantum Electron, Revista de Fizică şi Chimie, Volumul 36,

Nr. 4-5-6, aprilie-mai-iunie (2001), pp.15-23.

[49] D.P. Danescu, Considerations Regarding the Characteristic Impedance to the

Vacuum, Buletinul Ştiinţific şi Tehnic al Institutului Politehnic "Traian Vuia",

Timişoara, 26, (40), fascicola 2, 1981, pp.37-40.

17

Appendix 1

Spin motion and 4 rotation

Illustration of the radial spin motion, as an internal double twist, starting from trefoil

knot:

a) The spin motion with 4 internal rotations in the case of trefoil knot.

b) The spin motion with 4 rotations in the case of elastic overhand knot (open trefoil

knot) identified with extended quantum electron (charge). Vector s projection on the 0z

axis (rotational component) is permanently zsμ ≈ -B .

Copyright © 2011 Dan Petru Danescu. All rights reserved

18

Appendix 2

Elementary electric charge and CPT symmetry

Elementary electric charges structure: a), b). CPT symmetry: c), d), e) sequences. In this

case: r → -r (x,y,z →-x, -y, -z) ; e+ → e

- ; Sz → -Sz ;

zs → z

s .

19

Appendix 3

20

Appendix 4

Production electron-positron pairs

Copyright © 2011 Dan Petru Dănescu. All rights reserved

21

Appendix 5

A possible interpretation of fractional electric charges of quarks