Gaussian Units vs. SI Units by Dan Petru Danescu,

Transcription

1 Note Date: May 6, 202 Gaussian Units vs. SI Units by Dan Petru Danescu, Keywords: Gaussian units, SI units, BIPM brochure, Maxwell equations, Lorentz force,,bohr magneton, fundamental physical constants. Contents:. Title page 2. Short presentation 3. Fig. (Electromagnetic wave and systems of units) 4. Table (Maxwell equations and evidence of moving wave with c velocity in Gaussian units) 5. Table 2 (Lorentz force and relativistic character of magnetism) 6. Table 3 (Fundamental physical constants. Comparison between SI and Gaussian units) 7. Appendix (An amendment to the Bohr magneton unit <in Gaussian system of units>)

2 Short presentation The International System of Units (SI) developed in the last century [], [2] has proved to be inadequate for theoretical physics. This was shown in some previous works [3], [4], [5], [6]. The most important works in theoretical physics developed by A. Einstein, N. Bohr, A.Sommerfeld, L. de Broglie, E. Schrodinger, M. Born, W. Pauli, P.A.M. Dirac, I. Tamm and others used the Gaussian units. In BIPM (Bureau International des Poids et Measures) brochure, 8th edition (2006) it is mentioned that: It has always recognized that CGS Gaussian system, in particular, has advantages in certain areas of physics, particulary in classical and relativistic electrodynamics (9th CGPM, 948, Resolution 6). In Fig., Table and Table 2 the contradictions of the International System (SI) and the advantages of the Gaussian system are schematically presented. Table 3 and Appendix shows a comparison of the fundamental physical constants in SI units and Gaussian units. Only in the Gaussian system of units we observe two groups of equal values of the electron charge and electron rest mass. Making the transition LTM Gaussian L (cm) we can write: e ± s 2 C cm [L] () m e 2( S /2) 2[ r.(e/2) 2 ] cm 3 [L] (2) the expression 2[ r.(e/2) 2 ] where r = (3/2)a 0, represents the double filiform volume generated by the movement of electric charge (double twist of spin) on the average radius of electronic cloud. The 2( S /2) expression is correlated with this double filiform volume. In conclusion: SI remains an industrial and practical system of units. For theoretical physics have used the Gaussian non-contradictory system of units. References [] Giorgi G., (902) Il sistema assoluta MKS. Atti dell associazione elettrotecnica italiana, vol VI, fasc.5. [2] Budeanu C.I., (956) Sistemul practic general de marimi si unitati, Ed. Acad. R.P.R. [3] Born M. (964) Die Relativitatstheorie Einsteins, Springer-Verlag. [4] Danescu D.P.,(978) Measuring units systems and the relativistic aspect of the electromagnetic phenomena, Studii şi Cercetări de Fizică,6, 30, pp [5] Danescu D.P., (978) The Fundamental Physical Constants of the Electron, Buletin de Fizică şi Chimie, Volumul 2, pp [6] Danescu D.P., (98) Considerations Regarding the Impedance Characteristic to the Vacuum, Buletinul Ştiinţific şi Tehnic al Institutului Politehnic "Traian Vuia",Timişoara, 26, (40), fascicola 2, pp

3 Representation of the electromagnetic wave. The E and H vectors vary synchronically, they are permanent perpendicular between them and they move together in the same direction, in vacuum, with c speed. The only correct system of units it is the Gaussian system, where we have in vacuum E = H. *) D.P. Dănescu, Consideraţii asupra impedanţei caracteristice a vidului (Considerations Regarding the Impedance Characteristic to the Vacuum), Buletinul Ştiinţific şi Tehnic al Institutului Politehnic "Traian Vuia",Timişoara, 26, (40), fascicola 2, pp (98). 3

4 Table Maxwell s equations and the evidence of moving wave with c velocity (in Gaussian units) In vacuum: = 0 ; J = 0 Name Gaussian units SI units Gauss law. D = 0. D = 0 Gauss law for magnetism. B = 0. B = 0 Maxwell-Faraday equation Ampere-Maxwell equation E = - c H = c B D B E = - D H = H. D =. B = 0 (absence of electric and magnetic sources); D - E B = c (moving wave with c velocity, in Gaussian units) 4

5 Table 2 The systems of units and Lorentz force System of units Electrostatic CGS (CGSesu) Electromagnetic CGS (CGSemu) Gaussian CGS Lorentz-Heaviside CGS International System of Units (SI) Lorentz force relations F = q[e + (v B)] F = q[e + (v B)] v F = q[e + ( B)] c v F = q[e + ( B)] c F = q[e + (v B)] Remark: Only in Gaussian CGS and Lorentz-Heaviside CGS systems of units, relativistic aspect of magnetism can be observed (the v/c factor) 5

6 Table 3 Fundamental physical constants of electron. Comparison between SI and Gaussian units (202) The starting point of this table is CODATA recommended Values of the Fundamental Physical Constants-2006, by Peter J. Mohr, Barry N. Taylor, and David B. Newell. Opportunity of used Gaussian units shown in [-3]. An amendment to Bohr magneton measure unit was developed in [3]. This amendment consist in transfer of /c factor of units in torque relation imply the change of unit emu esu. Importance of double Compton wavelength result in description of symmetry phenomena [4]. Quantity, symbol SI units Gaussian units speed of light in vacuum (c, c 0 ) m s cm s - magnetic constant (vacuum permeability), ( 0 ) N A -2 electric constant (vacuum permittivity), ( 0 ) F m - characteristic impedance of vacuum (Z 0 ) Compton wavelength ( C ) (33) 0-2 m (33) 0-0 cm electron g-factor (g) (5) (5) Bohr magneton ( B ) (23) 0-26 JT (69) 0-0 esu electron magnetic moment ( e) (23) 0-26 JT (69) 0-0 esu spin magnetic moment [ s = g (e/2m e )S] (40) 0-23 JT (2) 0-0 esu electron charge (e) (40) 0-9 C (2) 0-0 esu double Compton wavelength (2 C ) (67) 0-2 m (67) 0-0 cm fine-structure constant ( ) (50) (50) 0-3 inverse fine-structure constant ( ) (94) (94) Bohr radius (a 0 ) (36) 0-0 m (36) 0-8 cm Bohr speed ( c, v 0 ) (4) 0 6 m s (4) 0 8 cm s - average radius of electron cloud (s), (53) 0-0 m (53) 0-8 cm r =3a 0 /2 Planck constant (h) (33) 0-34 J s (33) 0-27 erg s Planck constant, reduced (ћ) (53) 0-34 J s (53) 0-27 erg s spin angular momentum (S = 3 /2) (45) 0-35 J s (45) 0-28 erg s electron rest mass (me) (45) 0-3 kg (45) 0-28 g Newtonian constant of gravitation (G) (67) 0 - m 3 kg - s (67) 0-8 cm 3 g - s -2 classical electron radius (re, r 0 ) (58) 0-5 m (58) 0-3 cm Thomson cross section ( e) (27) 0-28 m (27) 0-24 cm 2 Rydberg constant (R ) (73) m (73) 0 5 cm - [] D.P.Dănescu, Systems of measure units and relativistic aspect of electromagnetic phenomena, St. Cerc. Fizică, 6, 30 (978). [2] D.P.Dănescu, The fundamental physical constants of electron, Buletin de Fizică şi Chimie, Vol. 2, 70 (978). [3] D.P.Dănescu, Consideration of characteristic impedance of vacuum, Buletinul Ştiinţific şi Tehnic al Institutului Politehnic"Traian Vuia",Timişoara, 26, (40), fascicola 2, (98). [4] D.P.Dănescu, The symmetry of Compton effect and 2 C constant, Revista de Fizică şi Chimie, Vol. 36, Nr (200). 6

7 APPENDIX An amendment to the Bohr magneton unit (in Gaussian system of units) Comparison of the current element and the magnetic moment follows = idl (The current element) df = c idl B (The Laplace force) = ida (The magnetic moment) d = c ida B (The torque) The quantities = idl and = ida, introduced by definition, have geometric and electrokinetic nature not electrodynamic nature. They are without /c factor of units, transferred in the force respectively in the torque expression. Consequence: I. The Bohr magneton is B = B = c e = emu; 2m e II. The spin magnetic moment is s = g and not s = g c e 2m e e = esu, and not 2m e e 2m e S = emu. S = esu, 7

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