Note Date: May 03, 2011 The International System of Units (SI) A Handicapping System for Theoretical Physics by Dan Petru Danescu, e-mail: dpdanescu@yahoo.com Key works: SI units, Gaussian units, BIPM brochure, Maxwell equations, Lorentz force Contents: 1. Introduction 2. Fig.1 (Electromagnetic wave and systems of units) 3. Table 1 (Maxwell equations and evidence of moving wave with c velocity in Gaussian units) 4. Table 2 (Lorentz force and relativistic character of magnetism) 5. Table 3 (Fundamental physical constants. Comparison between SI and Gaussian Units) 11Note. SI handicap 1
Introduction The International System of Units (SI) developed in the last century [1], [2] has proved to be inadequate for theoretical physics. This was shown in some previous works [3], [4], [5]. 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, 1948, Resolution 6). In Fig.1, Table 1 and Table 2 the contradictions of the International System (SI) and the advantages of the Gaussian system are schematically presented. Table 3 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 ± µ s 2λ C 4.8 10-10 cm [L] (1) m e 2( S /2) 2[ r 1.(e/2) 2 ] 9.1 10-28 cm 3 [L] (2) the expression 2[ r 1.(e/2) 2 ] where r 1 = (3/2)a 0, represents the double (round trip) filiform volume generated by the movement of electric charge on the average radius of electronic cloud. The 2( S /2) expression is correlated with this double filiform volume. References [1] Giorgi G., (1902) Il sistema assoluta MKS. Atti dell associazione elettrotecnica italiana, vol VI, fasc.5 [2] Budeanu C.I., (1956) Sistemul practic general de marimi si unitati, Ed. Acad. R.P.R. [3] Danescu D.P.,(1978) Measuring units systems and the relativistic aspect of the electromagnetic phenomena, Studii şi Cercetări de Fizică,6, 30, pp.559-571. [4] Danescu D.P., (1978) The Fundamental Physical Constants of the Electron, Buletin de Fizică şi Chimie, Volumul 2, pp.170-173. [5] Danescu D.P., (1981) Considerations Regarding the Impedance Characteristic to the Vacuum, Buletinul Ştiinţific şi Tehnic al Institutului Politehnic "Traian Vuia",Timişoara, 26, (40), fascicola 2, pp.37-40. 2
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.37-40 (1981). 3
Table 1 Maxwell s equations and the evidence of moving wave with c velocity (in Gaussian units) In vacuum: ρ = 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 1 B E = - c 1 D H = c E = - H = B D. D =. B = 0 (absence of electric and magnetic sources); 1 H D - 1 E B = c (moving wave with c velocity, in Gaussian units) 4
Table 2 The systems of units and Lorentz force System of units Electrostatic CGS (CGSesu) Electromagnetic CGS (CGSemu) Gaussian CGS Lorentz-Heaviside CGS Internationa 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
Table 3 Fundamental physical constants of electron. Comparison between SI and Gaussian units (2011) by Dan Petru Dănescu, e-mail: dpdanescu@yahoo.com. 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 [1-3]. An amendment to Bohr magneton measure unit was developed in [3]. This amendment consist in transfer of 1/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 ) 2.997 924 58 10 8 m s -1 2.997 924 58 10 10 cm s -1 magnetic constant (vacuum permeability), (µ 0 ) 12.566 370 614... 10-7 N A -2 1 electric constant (vacuum permittivity), (ε 0 ) 8.854 187 817... 10-12 F m -1 1 characteristic impedance of vacuum (Z 0 ) 376.730 313 461... Ω 1 Compton wavelength (λ C ) 2.426 310 2175 (33) 10-12 m 2.426 310 2175 (33) 10-10 cm electron g-factor (g) -2.002 319 304 3622(15) -2.002 319 304 3622(15) Bohr magneton (µ B ) 927.400 915(23) 10-26 JT -1 2.780 277 998(69) 10-10 esu electron magnetic moment (µe) -928.476 377(23) 10-26 JT -1-2.783 502 153(69) 10-10 esu spin magnetic moment [µs = g (e/2m e )S] 1.608 168 258(40) 10-23 JT -1 4.821 167 12(12) 10-10 esu electron charge (e) 1.602 176 487(40) 10-19 C 4.803 204 27(12) 10-10 esu double Compton wavelength (2λ C ) 4.852 620 4350(67) 10-12 m 4.852 620 4350(67) 10-10 cm fine-structure constant (α) 7.297 352 5376 (50) 10-3 7.297 352 5376 (50) 10-3 inverse fine-structure constant (α 1 ) 137.035 999 679(94) 137.035 999 679(94) Bohr radius (a 0 ) 0.529 177 208 59(36) 10-10 m 0.529 177 208 59(36) 10-8 cm Bohr speed (αc, v 0 ) 2.187 691 254 1(14) 10 6 m s -1 2.187 691 254 1(14) 10 8 cm s -1 average radius of electron cloud (1s), 0.793 765 812 88(53) 10-10 m 0.793 765 812 88(53) 10-8 cm r 1 =3a 0 /2 Planck constant (h) 6.626 068 96(33) 10-34 J s 6.626 068 96(33) 10-27 erg s Planck constant, reduced (ћ) 1.054 571 628(53) 10-34 J s 1.054 571 628(53) 10-27 erg s spin angular momentum (S = 3 h /2) 9.132 858 19(45) 10-35 J s 9.132 858 19(45) 10-28 erg s electron rest mass (me) 9.109 382 15(45) 10-31 kg 9.109 382 15(45) 10-28 g Newtonian constant of gravitation (G) 6.674 28(67) 10-11 m 3 kg -1 s -2 6.674 28(67) 10-8 cm 3 g -1 s -2 classical electron radius (re, r 0 ) 2.817 940 2894 (58) 10-15 m 2.817 940 2894 (58) 10-13 cm Thomson cross section (σe) 0.665 245 8558 (27) 10-28 m 2 0.665 245 8558 (27) 10-24 cm 2 Rydberg constant (R ) 10 973 731.568 527(73) m -1 1.097 373 156 852 7(73) 10 5 cm -1 [1] D.P.Dănescu, Systems of measure units and relativistic aspect of electromagnetic phenomena, St. Cerc. Fizică, 6, 30 (1978). [2] D.P.Dănescu, The fundamental physical constants of electron, Buletin de Fizică şi Chimie, Vol. 2, 170 (1978). [3] D.P.Dănescu, Consideration of characteristic impedance of vacuum, Buletinul Ştiinţific şi Tehnic al Institutului Politehnic"Traian Vuia",Timişoara, 26, (40), fascicola 2, (1981). [4] D.P.Dănescu, The symmetry of Compton effect and 2λ C constant, Revista de Fizică şi Chimie, Vol. 36, Nr. 1-2-3 (2001). 6