Improving the accuracy of the numerical values of the estimates some fundamental physical constants. Valery Timkov, Serg Timkov, Vladimir Zhukov, Konstantin Afanasiev To cite this version: Valery Timkov, Serg Timkov, Vladimir Zhukov, Konstantin Afanasiev. Improving the accuracy of the numerical values of the estimates some fundamental physical constants.. Digital Technologies, Odessa National Academy of Telecommunications, 2019, 25, pp.23 - 39. hal-02117148 HAL Id: hal-02117148 https://hal.archives-ouvertes.fr/hal-02117148 Submitted on 2 May 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Improving the accuracy of the numerical values of the estimates some fundamental physical constants. Valery F. Timkov1*, Serg V. Timkov2, Vladimir A. Zhukov2, Konstantin E. Afanasiev2 1Institute of Telecommunications and Global Geoinformation Space of the National Academy of Sciences of Ukraine, Senior Researcher, Ukraine. 2Research and Production Enterprise «TZHK», Researcher, Ukraine. *Email: [email protected] The list of designations in the text: l p - the length of the Planck; mp - the mass of the Planck; t p - the time of the Planck; mp - the mass of the Planck, which determined through the characteristics of muon; l p - the length of the Planck, which determined through the characteristics of muon; t p - the time of the Planck, which determined through the characteristics of muon; c - the speed of light in a vacuum; qp - the Planck charge; e - the elementary electric charge; - the fine structure constant; h - the Planck constant over 2pi; G - the gravitational constant; ap - the Planck acceleration; a p - the Planck acceleration, which is determined based on the characteristics of the muon; Fp - the Planck force; Fp - the Planck force, which is determined based on the characteristics of the muon; Ep - the Planck energy; E p - the Planck energy, which is determined based on the characteristics of the muon; Pp - the Planck power; Pp - the Planck power, which is determined based on the characteristics of the muon; Tp - the Planck temperature; Tp - the Planck temperature, which is determined based on the characteristics of the muon; k - the Boltzmann constant; Sp - the total of energy luminosity of a hypothetical Planck particle; S p - the total of energy luminosity of a hypothetical Planck particle, which is determined based on the characteristics of the muon; - the constant of Stephen – Boltzmann; I p - the current of Planck; I p - the current of Planck, which is determined based on the characteristics of the muon; Vp - the voltage of Planck; Vp - the voltage of Planck, which is determined based on the characteristics of the muon; Z p - the impedance of Planck; Z p - the impedance of Planck, which is determined based on the characteristics of the muon; Z0 - the characteristic impedance of vacuum; C p - the electric capacitance of Planck; C p - the electric capacitance of Planck, which is determined based on the characteristics of the muon; Lp - the inductance of Planck; L p - the inductance of Planck, which is determined based on the characteristics of the muon; Bp - the module of the magnetic induction of Planck; Bp - the module of the magnetic induction of Planck, which is determined based on the characteristics of the muon; H p - the module of the magnetic field strength of Planck; - the module of the magnetic field strength of Planck, which is determined based on the characteristics of the muon; 0 - the magnetic constant; R - the Rydberg constant; Ry - the Rydberg constant times hc in J; Rc - the Rydberg constant times c in Hz; p DC - the proton Compton wavelength over 2 pi; n0 DC - the neutron Compton wavelength over 2 pi; e DC - the electron Compton wavelength over 2 pi; DC - the muon Compton wavelength over 2 pi; a0 - the Bohr radius; me - the electron mass; m - the proton mass; p m - the neutron mas; n0 m - the muon mass; ke - the electric force constant; RK - the von Klitzing constant; KJ - the Josephson constant; Eh - the constant Hartree energy; pl - the estimate of the value of the linear density of the Planck mass, which determined through the characteristics of muon; ps - the estimate of the value of the surface density of the Planck mass, which determined through the characteristics of muon; pv - the estimate of the value of the density of the Planck mass, which determined through the characteristics of muon. Abstract. At the 26th General Conference on Measures and Weights, it was decided to switch from natural standards in the international system of SI units to standards that are based on fundamental physical constants. This solution raises the requirement for the accuracy of the numerical values of the fundamental physical constants. A technique is proposed for improving the accuracy of numerical values of the estimates: of Planck's constant over 2pi, of gravitational constant, of electric charge, of Planck temperature, of Planck acceleration, of Planck force, of Planck energy, of electron mass, of proton mass, of neutron mass, of Rydberg constant times hc in J, of Rydberg constant times c in Hz, of von Klitzing constant, of constant Hartree energy, of Josephson constant based on their representation through Planck's constants: of length, of mass, of time. Increasing of the accuracy numerical values of Planck’s length’s and the Planck’s mass is based on the fractal similarity of the golden algebraic fractals of the main characteristics of the hypothetical Planck particle and muon. Also, to improve the accuracy of the numerical values of the fundamental physical constants, the following physical laws are applied: the ratio of the Bohr radius to the Compton electron wavelength over 2pi is equal to the fine structure constant. The moment of the mass of any elementary particle, defined through its Compton wavelength over 2pi, is equal to the moment of Planck’s mass. The fine structure constant can be determined through the Bohr radius and the Rydberg constant. Keywords: Planck's constant; fundamental physical constants; fractals; the accuracy units of measure. 1. Introduction. Some fundamental physical constants can be expressed in terms of Planck's constants: of the length lp , of the mass mp , of the time tp. According to CODATA [1], their numerical values have the following values: qp 35 8 44 lp 1.616 229(38) 10m ; mpp 2.176 470(51) 10 kg ; t 5.391 16(13) 10 s . (1) 6 From (1) it follows that the accuracy of the numerical values l p and mp is 10 , and the accuracy of the numerical 5 valueh t p is 10 . The speed of light in vacuum c , taking into account (1): lp сs299 792 438 m11 . (2) tp The speed of light in a vacuum according to CODATA-2014 [1]: сs 299 792 458 m11 . (3) The Planck charge : e qC 1.875 5459 018 ,1 (4) p where: e the elementary electric charge according to CODATA-2014 [1]: e 1.602 176 6208(98) 1019 C , (5) the fine structure constant according to CODATA-2014 [1]: 7.297 352 5664 1033 (0.000 000 0017 10 ). (6) It is known [2] that: 2 7 36 2 qp10 m p l p 3.517 673 932 10 C , kgm ; (7) 2 7 38 2 e10 mpp l 2.566 970 689 10 C , kgm . (8) The Planck constant over 2pi with (1,3,5,6,8): 2 mppl h 1.054 572 0440 1034 Js , (9) t p or: 34 h mpp l c 1.054 572 1144 10Js , (10) or: ec2 h 1.054 571 8001 1034 Js . (11) 107 The Planck constant over 2pi according to CODATA-2014 [1]: h 1.054 571 800 1034 Js.(13) (12) The gravitational constant taking into account (1,3,5,6,12): 3 lp 11 3 1 2 (13) G2 6.674 082 298 10 m kg s , mtpp or: 2 lcp G 6.674 083 188 1011 m 3 kg 1 s 2 , (14) mp or: hc 11 3 1 2 (15) G2 6.674 081 199 10 m kg s , mp or: 23 lcp G 6.674 085 179 1011 m 3 kg 1 s 2 , (16) h or: 25 tcp G 6.674 086 069 1011 m 3 kg 1 s 2 , (17) h or: 22 lcp G107 6.674 085 177 10 11 m 3 kg 1 s 2 . (18) e2 Theh Gravitational constant according to CODATA-2014 [1]: 11 3 1 2 G G6.674 08(31) 10 m kg s . (19) The Planck acceleration ap : lp 51 1 2 (20) amp 2 5.560 815 075 10 s , tp Fp or: c am 5.560 815 4460 1051 1 s 2 . (21) p t Ep p The Planck force : mlpp 44 1 1 2 (22) Fp m p a p 2 1.210 294 719 10 kg m s , tp or: mcp 44 1 1 2 Fp m p a p 1.210 294 799 10 kg m s . (23) tp The Planck energy : 29 Epp m c 1.956 113 684 10 J , (24) or: 2 mlpp 9 (25) Ep F p l p 2 1.956 113 423 10 J , t p or: mpp cl 9 Ep F p l p 1.956 113 553 10 J , (26) t p or: h 9 EJp 1.956 112 970 10 , (27) tp or: 2 ec 9 (28) EJp 7 1.956 112 970 10 .