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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 - the of the Planck; p

mp - the of the Planck; t - the of the Planck; p   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 of in a ;

qp - the Planck charge; e - the elementary ;  - the constant; h - the over 2pi; G - the ;

ap - the Planck ;

  a p - the Planck acceleration, which is determined based on the characteristics of the muon; F - the Planck ; p   Fp - the Planck force, which is determined based on the characteristics of the muon;

Ep - the Planck ;

  E p - the Planck energy, which is determined based on the characteristics of the muon; P - the Planck power; p   Pp - the Planck power, which is determined based on the characteristics of the muon;

Tp - the Planck ;

  Tp - the Planck temperature, which is determined based on the characteristics of the muon; k - the ;

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 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 ;

Ry - the Rydberg constant hc in J;

Rc - the Rydberg constant times c in Hz;

p DC - the Compton over 2 ; n0 DC - the neutron over 2 pi; e DC - the Compton wavelength over 2 pi;

  DC - the muon Compton wavelength over 2 pi;

a0 - the ;

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 energy;

   pl - the estimate of the value of the linear 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 , 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: l 1.616 229(38) 1035m ; m  2.176 470(51)  10  8 kg ; t 5.391 16(13) 10  44 s . (1) p pp 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 value t p is 10 . The in vacuum c , taking into account (1):

lp сs299 792 438 m11 . (2) tp The speed of light in a vacuum according to CODATA-2014 [1]: сs 299 792 458 m11 . (3)

The Planck charge qp : e qC 1.875 5459  018 ,1 (4) p  where: e the elementary electric charge according to CODATA-2014 [1]: e 1.602 176 6208(98) 1019 C , (5)  the fine structure constant according to CODATA-2014 [1]:   7.297 352 5664 1033 (0.000 000 0017 10 ). (6) It is known [2] that: 2 7 36 2 qp10 m p l p  3.517 673 932  10 C , kgm ; (7) 2 7 38 2 e10 mpp l  2.566 970 689  10 C , kgm . (8) The Planck constant over 2pi h with (1,3,5,6,8): 2 mppl h 1.054 572 0440 1034 Js , (9) t p or: 34 h mpp l c 1.054 572 1144 10Js , (10) or: ec2 h  1.054 571 8001  1034 Js . (11) 107 The Planck constant over 2pi h according to CODATA-2014 [1]: h 1.054 571 800  1034 Js.(13) (12) The gravitational constant G taking into account (1,3,5,6,12): l3 p 11 3  1  2 (13) G2 6.674 082 298  10 m kg s , mtpp or: 2 lcp G 6.674 083 188  1011 m 3 kg  1 s  2 , (14) mp or: hc 11 3  1  2 (15) G2 6.674 081 199  10 m kg s , mp or: 23 lcp G 6.674 085 179  1011 m 3 kg  1 s  2 , (16) h or: 25 tcp G 6.674 086 069  1011 m 3 kg  1 s  2 , (17) h or: 22 lcp G107  6.674 085 177  10 11 m 3 kg  1 s  2 . (18) e2 The Gravitational constant according to CODATA-2014 [1]: G6.674 08(31) 1011 m 3 kg  1 s  2 . (19)

The Planck acceleration ap :

lp 51 1 2 (20) amp 2 5.560 815 075  10 s , tp or:

c 51 1 2 amp  5.560 815 4460  10 s . (21) t p

The Planck force Fp :

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 Ep : 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: ec2 9 (28) EJp 7 1.956 112 970  10 . 10 tp

The Planck power Pp with (25):

Ep 52 PWp  3.628 372 528  10 , (29) tp or with (23): 52 Ppp F c 3.628 372 230  10 W . (30)

The Planck temperature Tp :

E p Tp  , (31) k where Ep  the Planck energy, k  the Boltzmann constant, according to CODATA-2014 [1]: k 1.380 648 52(79) 1023JK 1 , (32) then with (24):

Ep TK 1.416 807 867  1032 , (33) p k then with (25):

Ep TK 1.416 807 678  1032 , (34) p k then with (26):

Ep TK 1.416 807 772  1032 , (35) p k then with (27,28):

Ep TK 1.416 807 349  1032 . (36) p k The Planck temperature according to CODATA-2014 [1]:

Ep TK 1.416 808(33)  1032 (33) . (37) p k

The total energy luminosity Sp of a hypothetical Planck particle according to the law of Stephen - Boltzmann: 4 121 1 2 Spp T 2.284 837  10 W m , (38) where  is the Stefan-Boltzmann constant to CODATA-2014 [1]:  24k    5.670 367  108W 1 m  2 K  4.(13) (39) 60 c23h Obviously on the basis of (29) can be represented in the form:

2  Pp 121 1 2 (40) Sp  2 2.284 833  10 W m . 60 lp The main of of the [2], taking into account the accuracy of the Planck constants (of the length, of the mass, of the time): The current of Planck I : p q 11 p 2522 1 Ip  3.478 929  10 A ,  kg m s . (41) t p 

The voltage of Planck Vp : E m c2 13 pp 2722 2 Vp   1.042 96  10 V , kg m s . (42) qqpp 

The impedance of Planck Z p :

Vp 11 (43) Zp  29.979 26  , m s . I p

Obviously, the true value Z p is: c Z 29.979 2458  , m11 s . (44) p 107 

The characteristic impedance of vacuum Z0 to CODATA-2014 [1]: c ZZ4 4 =376.730313461770... (45) 0 p 107

The electric capacitance of Planck C p :

qp -45 1 2 (46) Cp  1.798 30  10 F , m s . Vp

The inductance of Planck Lp : 2 22Epp m c L  3.232 459  10-42 H ,  1 s 1 , m . (47) p 22   IIpp

The module of the magnetic induction of Planck Bp : F 11 p 5222 1 Bp  2.152 498 10 Tl , [ kg m s ]. (48) qcp

The module of the magnetic field strength of Planck H p : B 11 p 59 1 122 1 Hp  1.7129  10 [ A m ], [ kg m s ], (49) 0 6 1 1 where 0 - this is the magnetic constant, from [1]: 0 1.256 637 0614... 10[Hm ]. Obviously, the gravitational constant G and the Planck constant over 2pi h , taking into account the formulas (11,13,22,33,44) can be represented in the form: c4 G 6.674 084 08  1011 m 3 kg  1 s  2 , (50) Fp or: 22 kTp G 6.674 085 338  1011 m 3 kg  1 s  2 , (51) mF2 pp 2 eZp h  1.054 571 8001  1034 Js . (52) 

Analysis of the formulas (1-52) shows that the numerical estimates of the values of the fundamental constants that can be obtained on the basis of the Planck constants: lp,,, m p t p differ significantly from their standard values, which are presented in CODATA [1]. To improve the accuracy of these fundamental constants, it is necessary to increase the accuracy of the Planck constants: lp,,. m p t p

2. The choice of standards of fundamental constants.

To select standards of fundamental constants, we use the following criteria: 1. The accuracy of the numerical value of the fundamental constant should have the maximum possible value. That is, the number of decimal places after the decimal separator should be the largest. 2. The standard of the fundamental constant should have the minimum possible value. 3. The numerical value of the fundamental constant is determined (confirmed) experimentally. The following fundamental constants correspond to such criteria [1]: 8 1 1 the speed of light in vacuum: с2.997 924 58 10 m s (exact); the impedance of Planck: Zp 29.979 2458

(exact); the characteristic impedance of vacuum: Z0 376.730 313 461 770... (exact); the magnetic constant: 6 1 1 1 0 1.256 637 0614... 10 Hm ][ (exact); the Rydberg constant: R 109 73731.568508 (0.000065)m ; p 16 the proton Compton wavelength over 2 pi: DC  2.103 089 1 01 09(97) 10m ;the Bohr radius: 11 a0  5.291 772 1067(12) 10 m ;the neutron Compton wavelength over 2 pi: n0 16 3 DC 2.100 194 1536 14 1 m;0 the fine-structure constant:  7.297 352 5664(17) 10 ; the electron e 13 Compton wavelength over 2 pi: DC  3.861 592 6764 (18) 10 m ; the : 19  15 e 1.602 176 6208(98) 10C ;the muon Compton wavelength over 2 pi: DC  1 .867 594 308(42) 10m ; the muon mass: m 1.883 531 594(48) 1028 kg ; the Boltzmann constant: 23 1 1 the  k 1.380 648 52(79) 10JK ; proton Compton wavelength over 2 pi: the neutron Compton wavelength over 2 pi: the Boltzmann constant: k 1.380 648 52(79) 1023JK 1 1 .

To improve the accuracy of Planck’s constants: lp,, m p t p , we use a concept whose essence is that these constants are relied on as unknown values. Then to determine them requires three independent equations (source), in which the accuracy characteristics of the operands are higher than the accuracy characteristics of the standard values of the Planck constants:

lp,,. m p t p Obviously, the first equation is:

lp c299 792 458 m11 s , (exact). (53) tp The equation is defined on the basis of patterns: an electric charge - a function of the mass moment [2]. Then: 2 7 38 2 e10 mpp l 2.566 969 924 238 10 .. .  0, C kgm.1 (54) From (54) it follows that: e2 m l 3.517 672 883 255 617 770...  1043 kgm . (55) pp 107 Given that the accuracy of the values of the fine structure constant and the elementary charge is 1010 , it can be 10 presumed that the accuracy of the estimate of the value of the Planck mass moment is also 10 , then: e2 m l 3.517 672 8833  1043 kgm . (56) pp 107 The third independent source for estimating the values of Planck's constants: l,, m t is determined on the basis of a p p p pattern [3,4]: Planck's constants: mp and l p are golden algebraic fractals of the main characteristics   of a muon: its mass m and its Compton wavelength over 2pi DС , then:   8 mp  2.176 638 834 506 326... 10kg ; (57)

  35 lp 1.616 103 153 231 184... 10m . (58)

  Based on formulas (53) and (58), we obtain the value of the Planck time constant t p :   lp t    5.390 739 860 544 403... 1044 s . (59) p c    9 Given that the accuracy of constants m and DС is 10 , it can be assumed that the accuracy of the evaluation of       constants: mp , l p and t p is also , then:

 m  2.176 638 835 108 kg ; (60) p   35 lp 1.616 103 153 10m ; (61)

  44 t p  5.390 739 861 10s . (62)

Let the value of the moment of the Planck mass mlpp, which is given in formula (56) is a standard, then we make a comparison of the Planck constants - the length and the mass according to formulas (1) and (60,61). The value of the moment of the mass of Planck by the formula (1): 43 mpp l3.517 673 931 63 kgm.10 (63) Taking into account the accuracy of the values of the constants in the formula (1): 43 mpp l3.517 674 kgm.10 (64) The value of the moment of the mass of Planck by the formulas (60,61):  43 mpp l3.517 672 883 891... 10 kgm . (65) Taking into account the accuracy of the values of the constants in the formulas (60,61):  43 mpp l3.517 672 884 10 kgm . (66) The analysis of formulas (56), (64) and (66) shows that the concept of the fractal connection of the hypothetical Planck particle and muon can be used as a third independent source to increase the accuracy of the values Planck's constants: of the mass, of the length, of the time. In [2] it was shown that the moment of the Planck mass is equal to the moment of the mass of the electron, which is defined through the Bohr radius, then the equality is true:

mp l p m e a0, (67) where: am0 ,, e  it is, respectively: the Bohr radius, the fine-structure constant, the electron mass. According to [1] the mass of electron equals: 31 me  9.109 383 56(11) 10kg . (68)

It is known that the Compton wavelength over 2pi DC of any elementary particle with a mass m is equal to: h D  . (69) С mc Whence the moment of particle mass: h D m  . (70) С c From formulas (67) and (70) it follows that: e mp l p m eD C. (71) That is: e DC  a0, (72) or: De   C . (73) a0 From formulas (69) and (71) it also follows that: 0 h m l mDDDDDe  m p  m n  m n ...  m  . (74) p p e Cpn C0 C C C c The mass moments of all elementary particles, which are determined through their Compton wavelength over 2pi, are equal to each other and equal to the Planck mass moment. From formulas (55,56) and (74) it follows that: 0 h e210 7 m l  10 7  mDDDDDe  10 7  m p  10 7  m n  10 7  m  ...  10 7  m  10 7  . (75) p p e Cpn C0 C C C c That is, formula (74) confirms the pattern [2] that the electric charge is a function of the mass moment. It also means that there is an opportunity to improve the accuracy of Planck’s constants estimates: of the mass, of the length, of the time to a value of 109 , and the composition of these constants - the mass moment - to a value of 1010 .

3. Improving the accuracy of the numerical values of the estimates of some fundamental physical constants.

The Rydberg constant is one of the most accurately measured fundamental constants. Obviously, it is convenient to use this constant to estimate the accuracy of other fundamental physical constants, for example, the fine structure constant. Let us specify the value of the fine structure constant in terms of the Rydberg constant and the Bohr radius. The Bohr radius has the same accuracy value as the fine structure constant, but its standard uncertainty value is less. Then:

4aR0  0.007 297 352 5663 119 669 893 690... (76) On the basis of formula (72), we specify the estimate the value of the fine structure constant: 4De R 0.007 297 352 5663 908 ... (77) C  Analysis of the values of the fine structure constant: of the standard according to CODATA-2014 by the formula (6), as well as by formulas (76) and (77) shows that the weight of the tenth digit of the standard value of the fine structure constant (number 4) is greater than by the formulas (76,77). The elementary electric charge, expressed in terms of the Rydberg constant:  3 em 107 . e 4 R (78)  The Planck's constant over 2pi, expressed in terms of the Rydberg constant: 2 e  hDme c C m e c . (79) 4 R

The value Ry of the Rydberg constant times hc in J: 2 22  mce  18 Rye2h cR  2 m c cR   2.179 872 325 506...  10 J . (80) 42 R The value of the Rydberg constant times hc in J according to CODATA-2014 [1]: 18 Ry  2.179 872 325(27) 10J . (81)

The value Rc of the Rydberg constant times c in Hz: m k2 e 4 m 310 14 10 14 2 (De ) 2 c 4 c 2 Re e  e C  3.289 841 960 363 475 100...  1015 Hz , (82) c 4h3 4 mc 3 ( Dee ) 3 3 4  D e C C where ke it is the electric force constant, or the Coulombs constant: kc1072 , (83) e but with (77):  2 (84) R  e , 4DC then: 15 Rc  cR 3.289 841 960 355 208 712 664  10 Hz . (85) The value of the Rydberg constant times c in Hz according to CODATA-2014 [1]: 15 Rc  3.289 841 960 355(19) 10Hz . (86)

The value of the quantum of the electrical resistance, or the von Klitzing constant RK : e 22h 2mcD c 2Z p R eC   25 812.807 455 431 940 925 6190...  ,  m11 s . (87) K 2 7e 7  em10eCD 10   The value of the quantum of the electrical resistance, or the von Klitzing constant according to CODATA-2014 [1]: 11 RK 25 812.807 4555 (0.000 0059) ,  m s . (88)

The Josephson constant KJ , as the reciprocal of the magnetic quantum: 77 13 ee10 10    9 1 122 1 (89) KJ  2 = = 483 597.852 473 798...  10 Hz V , kg m s . h e c  ec  eZ p  Since taking into account formula (42), the dimension of the Josephson constant: 1 3 1 3        1 1 12 2 2 2 2 1 HzV skgms().   kgms  (90)     The value of the Josephson constant according to CODATA-2014 [1]: 9 1 1 KJ  483 597.8525(0.0030) 10Hz V . (91)

The constant atomic unit of energy, or the constant Hartree energy Eh : h2 2 2 18 (92) Eh2  m e c 2 R y  4.359 744 651 012...  10 J . mae 0 The value of the constant Hartree energy according to CODATA-2014 [1]: 18 Eh  4.359 744 650(54) 10J . (93) We calculate the estimates of the moment of the mass: of the proton, of the neutron, of the muon, of the electron through their Compton wavelength over 2pi: the proton: p 43 m DC 3.517 672 883 928 269 668 82 10 kgm , (94) p taking into account the accuracy of the proton mass values and its Compton wavelength over 2pi:  mDp 3.517 672 884 1043 kgm , (95) p C the neutron: 0 mDn 3.517 672 882 298 233 5456 1043 kgm , (96) n0 C taking into account the accuracy of the neutron mass values and its Compton wavelength over 2pi: 0 mDn 3.517 672 882 1043 kgm , (97) n0 C the muon:  mD 3.517 672 883 892 566 952 1043 kgm , (98)  C taking into account the accuracy of the muon mass values and its Compton wavelength over 2pi:  mD 3.517 672 884 1043 kgm , (99)  C the electron: e 43 meCD 3.517 672 884 181 455 9984 10 kgm , (100) taking into account the accuracy of the electron mass values and its Compton wavelength over 2pi: e 43 meCD 3.517 672 88 10 kgm . (101) Analysis of formulas (94 - 101) shows that the accuracy of estimates of the mass moments of the proton, of the neutron, of the muon, of the electron through their Compton wavelength over 2pi does not exceed the value 1, that is: 43 mDC 3.517 672 88 10 kgm . (102) Increase the accuracy of estimating the mass values: of the proton, of the neutron, of the electron. For this we use physical law: equality of moments of particle mass through their Compton wavelength over 2pi, of the formula (75), and the fact that the accuracy of Compton wavelength over 2pi of the elementary particles and the accuracy of the moments of their mass is higher than the accuracy of the values of the mass itself: e2 m 1.672 621 897 680 1600...  1027 kg , (103) p 7 p 10 DC e2 m=.1.674 927 471 455 85 5 10.. 1027 kg, (104) n0 7 n0 10 DC e2 31 (105) me 7 e =9.109 383 557 602 4446... 10 kg . 10 DC Taking into account the accuracy of the operands in formulas (103,104,105), the mass estimates of the proton, of the neutron, of the electron are as follows: m1.672 621 897 680 1027 kg , (106) p m1.674 927 471 46 1027 kg, (107) n0 31 me 9.109 383 557 60 10 kg . (108) Obviously, the new estimates of the mass moments of the proton, of the neutron and of the electron, taking into account the estimates of the values of their mass in formulas (106,107,108), will be close to the value of the mass moment by formula (56). Let us specify the values of the estimates of the Rydberg constant time hc in J and constant Hartree energy taking into account the calculated value of the electron mass estimate: 18 Ry  2.179 872 324 932 1 25... 10J . (109) 18 Eh  4.359 744 649 864 251... 10J . (110) Based on estimates of the values of Planck's constants - of the mass, of the length and of the time, as fractals of the main characteristics of the muon, and which are represented by the formulas (57,58,59), we calculate the estimates of the constants:   the Planck acceleration a p :

  lp 51 1 2 ap    5.561 248 840 708 248 850... 10m s , (111) ()t  2 p   the Planck force Fp :

     44 1 1 2 Fmp pa p 1.210 483 019 503 885 939 ... 10kg m s , (112)

  the Planck energy E p :

2 9 E  mc1.956 265 424 752 231 7250... 10J , (113) pp or:      9 EFp pl p 1.956 265 424 753 837 78210... 10J , (114) or:     h mpp l c E   1.956 265 424 753 034 8884... 109 J , (115) p  t ppt or: 2  ec EJ  1.956 265 424 398811 589 5 ... 109 . (116) p 7   01 t p The analysis of the values of the Planck energy constant estimates using the formulas (113-116) shows that their accuracy does not exceed the value of 109 , then the average value of the Planck energy constant estimate is:  EJ 1.956 265 425 109 . (117) p Since the accuracy of the estimation of the main characteristics of the muon is , it can be assumed that the accuracy of estimates of the Planck acceleration constants and the Planck force is also the value of , that is:  a  5.561 248 841 1051ms 1 2 , (118) p   44 1 1 2 Fp 1.210 483 020 10kg m s . (119)

  The Planck power Pp :   Ep 52 1 1 Pp    3.628 936 796 446 415 0420... 10J s , (120) t  or: p  52 1 1 Ppp F c 3.628 936 797 841 829 669...  10 J s . (121) The average value of the estimate of the Planck power with accuracy is:   52 1 1 Pp 3.628 936 797 10 J s . (122)

  The estimate of the value of the linear density of the Planck mass  pl :   mp 27 1 1  pl   1.346 843 999 501 846 250... 10kg m . (123) l  p Or taking into account the accuracy of the Planck constants, which are determined on the basis of the characteristics of the muon:   mp    1.346 844 000 1027kg 1m 1 . (124) pl  lp

  The estimate of the value of the surface density of the Planck mass  ps :

  mp     8.333 898 716 851 442 584... 1061kg 1m 2 . (125) ps  2 ()lp Or taking into account the accuracy 109 of the Planck constants, which are determined on the basis of the characteristics of the muon:   mp     8.333 898 717 1061kg 1m 2 . (126) ps  2 ()lp   The estimate of the value of the density of the Planck mass  pv :   mp   5.156 786 372 321 281 887...1096kg 1 m 3. (127) pv  3 ()lp Or taking into account the accuracy of the Planck constants, which are determined on the basis of the characteristics of the muon:   mp 96 1 3  pv  5.156 786 37210 kg m . (128) ()l  3 p

Estimates of values: of the linear density of the Planck mass  pl , of the surface density of the Planck mass  ps , of the density of the Planck mass  pv based on the Planck constants according to CODATA-2014 and taking into account the accuracy values 105 of the Planck mass :

mp   1.346 64 27kg 1 m 1,10 (129) pl l p mp    8.331 96 061kg 1m 2 ,1 (130) ps ()l 2 p mp    5.155 18 096kg 1m 3.1 (131) pv ()l 3 p Estimates of the main of Planck units of the electromagnetism which are determined on the basis of the characteristics of the muon:   The current of Planck I p :

11  qp  I  3.479 199 648  1025 A , kg22 m s 1 . (132) p   t p 

  The voltage of Planck Vp :

 2 13  E m c   pp 2722 2 Vp   1.043 037 815  10 V , kg m s . (133) qqpp 

  The impedance of Planck Z p :

  Vp Z  29.979 2458  , m11 s . (134) p   I p

  The electric capacitance of Planck C p :

 qp C  1.798 157 26370  10-45 F , m 1 s 2 . (135) p    Vp

  The inductance of Planck L p : 2  22Epp m c L   3.232 206 307  10-42 H ,  1 s 1 , m . (136) p 22   ()()IIpp

  The module of the magnetic induction of Planck Bp :

  11  F  p 5222 1 Bp  2.152 832 659  Tl , [ kg m s ].10 (137) qcp

  The module of the magnetic field strength of Planck H p :

  11  B  p 59 1 122 1 Hp  1.713 169 797  10 [ A m ], [ kg m s ]. (138) 0   The estimate of the Planck temperature Tp , which is determined on the basis of the characteristics of the muon:

  Ep TK  1.416 917 77  1032 . (139) p k   The estimate of the total energy luminosity S p of a hypothetical Planck particle, which is determined on the basis of the characteristics of the muon: 4 121 1 2 Spp ( T )  2.285 545  10 W m . (140) Estimates of the Planck constant over 2pi h , which are determined on the basis of the characteristics of the muon: 2 mlpp() h 1.054 571 800 1034 Js , (141)  t p or:  34 h mpp l c 1.054 571 800 10Js , (142) and too: 2 e  34 hDme c C  m e c 1.054 571 8001  10 Js . (143) 4 R Comparative analysis of formulas (9,10) on the one hand and formulas (141,142,143) on the other hand with a Standard using formula (12) shows that Planck's constants: of the length, of the mass, of the time, which are determined based on the characteristics of the muon, are more preferable in the application, than their standard values. The accuracy of the operands in formulas (11,143) is not lower than 1010 , then taking into account formulas (141,142), the estimate of the Planck constant over 2pi can be represented as: h 1.054 571 8001 1034 Js . (144)

Estimates of the Gravitational constant G , which are determined on the basis of the characteristics of the muon:  3 ()lp G 6.673 045 869  1011 m 3 kg  1 s  2 , (145) 2 mtpp() or:  2 lcp G 6.673 045 869  1011 m 3 kg  1 s  2 , (146)  mp or:

hc 11 3  1  2 G 6.673 045 867  10 m kg s , (147) ()m 2 p or:  23 ()lcp G 6.673 045 871  1011 m 3 kg  1 s  2 , (148) h or:  ()tc 25 Gp 6.673 045 871  1011 m 3 kg  1 s  2 , (149) h or:  ()lc 22 G107 p  6.673 045 870  10 11 m 3 kg  1 s  2 , (150) e2

or: c4 G=6.673 045 869 1011 m 3 kg  1 s  2 , (151)   Fp or: 22 kT()p G 6.673 045 871  1011 m 3 kg  1 s  2 . (152) 2 ()mFpp

The average value of the estimate of the Gravitational constant by the formulas (145 - 152): G6.673 045 870 1011 m 3 kg  1 s  2 . (153) Specify the estimated value of the elementary electric charge:  3 e107 m  1.602 176 620 8020  10 19 C . (154) e 4 R  Or taking into account the accuracy of the operands: eC1.602 176 620 80 1019 . (155) Estimation of the basic characteristics of the hypothetical Planck particle based on the characteristics of the muon increases the accuracy of the values of some fundamental physical constants.

4. Results.

Table 1 presents the final results of research to improve the accuracy of some fundamental physical constants.

Tabl 1 Constant value Estimations of the value The unit of The name of the fundamental according to CODATA- of the fundamental 2014 (without the physical constants of the constant standard uncertainty) proposed in the research the gravitational constant 6.674 08·10-11 6.673 045 870·10-11 m-3 kg-1 s-2 the Planck constant over 2pi 1.054 571 800 ·10-34 1.054 571 8001 ·10-34 m2 kg1 s-2 the elementary charge 1.602 176 620 8·10-19 1.602 176 620 80·10-19 C the 1.616 229·10-35 1.616 103 153·10-35 m the Planck mass 2.176 470·10-8 2.176 638 835·10-8 kg the Planck time 5.391 16·10-44 5.390 739 861·10-44 s the Planck temperature 1.416 808·1032 1.416 917 77·1032 K the electron mass 9.109 383 56·10-31 9.109 383 557 60·10-31 kg the proton mass 1.672 621 898·10-27 1.672 621 897 680·10-27 kg the neutron mass 1.674 927 471·10-27 1.674 927 471 46·10-27 kg the Rydberg constant times hc in J 2.179 872 325·10-18 2.179 872 324 93·10-18 J the Rydberg constant times c in Hz 3.289 841 960 355·1015 3.289 841 960 355 2·1015 Hz the von Klitzing constant 25 812.807 4555 25 812.807 4554 31940 Ω the constant Hartree energy 4.359 744 650·10-18 4.359 744 649 86·10-18 J the Josephson constant 483 597.8525·109 483 597.852 474·109 Hz1 V-1 Table 1. The final research results are aimed at increasing the accuracy of some fundamental physical constants.

5. Conclusions.

Since units of measurement of most constants and variables of gravitational and electromagnetic interactions can be expressed in units of measurement: of the length, of the mass and of the time, that is, through: meter, kilogram and second, it is convenient to choose Planck constants: of the length, of the mass, of the time as the basis of fundamental physical constants. However, in the practical use of these constants problems arise: 1) their low accuracy; 2) indirect, not direct connection with the characteristics of real elementary particles. To eliminate these problems, it is proposed to establish a direct relationship between the characteristics of the hypothetical Planck particle and the characteristics of the muon. Since the characteristics of the muon and the hypothetical Planck particle are golden algebraic fractals, this relationship can be established on the basis of the similarity coefficients of golden algebraic fractals. This approach improves the accuracy of the Planck length and of the Planck mass by three orders of magnitude, and of the Planck time by four orders of magnitude. Improving the accuracy of of the characteristics of the muon will automatically increase the accuracy of all fundamental constants, which are determined on the basis of the Planck constants: of the length, of the mass, of the time.

Acknowledgments

Regarding this manuscript, the authors do not have a conflict of interest in any of human activity: neither legal, nor financial, nor ethical ... and any other, both in relations with each other and in relations with other citizens and organizations. The work is done exclusively on the personal funds of the co-authors.

References

[1] Fundamental Physical Constants. https://physics.nist.gov/cuu/Constants/

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[3] Timkov, V. F., Timkov, S. V., Zhukov, V. A., Afanasiev, K.E.: “Fractal structure of the fundamental constants. Numerical evaluation of the values of some of the fundamental constants with the use of the major characteristics of the muon.”, International scientific-technical magazine: Measuring and computing devices in technological processes, ISSN 2219-9365, 3 (59), p.p. 188 – 194, 2017. http://fetronics.ho.com.ua/pdf/pdf_full/2017/vottp-2017-3.pdf https://hal.archives-ouvertes.fr/hal-01581300v1

[4] Timkov, V. F., Timkov, S. V., Zhukov, V. A., Afanasiev, K.E.: “Fractal genesis of the angles of the mixing matrix.”, Herald of Khmelnitsky National University, Khmelnitsky National University, 263(4), p.p. 263-272, 2018. http://journals.khnu.km.ua/vestnik/pdf/tech/pdfbase/2018/2018_4/(263)%202018-4-t.pdf https://hal.archives-ouvertes.fr/hal-01782443v1