E-mail: kosinov@unitron.com.ua

It is shown that Planck units can be determined not only under the formulas: m_pl=(žc/G)^1/2, t_pl=(Gž/c⁵)^1/2, l_pl=(Gž/c³)^1/2. The new formulas to calculate Planck units are found. From the formulas follows that the constants l_pl, t_pl, m_pl can be determined not only with the help of constants G, h, c, but also with application of others fundamental physical and cosmology constants. Formulas include universal superconstants h_u, l_u, t_u, α, π [1,2,3]. Each group of the formulas gives practically identical values of the appropriate constant. The deviations are very insignificant and also are observed in the seventh - eighth digits that is connected to various accuracy of those constants by means of which Planck units are presented. The exactest values of constants which follow from the received formulas are equal to:

The new values of constants on some orders are exacter than values recommended CODATA 1998.

The majority of physical constants do not fall under direct measurement, therefore their values are determined indirectly from relations connecting them to other constants. It concerns also Planck constants.Having opened a constant h Ì.Planck has received units of dimensionality kg, meter and second on the basis of three constants G, h, c. It is Planck length, Planck time and Planck mass. The formulas for Planck units look like:

Taking into account that the value of constant h was equal to magnitude h=6.55x10^-34J•s [7] and Newtonian constant of gravitation G value was considered equal to 6.658õ10^-11Í m² kg^-2 [8] during this period (since 1892). It is possible to suppose the formulas allowed to receive such values of Planck units:

The values of Planck units were constantly specified. In 1986 CODATA has offered most record on accuracy values:

The modern values of Planck units recommended CODATA 1998 have smaller accuracy and are considered equal to:

Modern values of these constants considerably concede on accuracy to other fundamental physical constants. The restriction on accuracy of determination of Planck units was imposed by a Newtonian constant of gravitation G.

As the hope to create the new quantum theory is connected to Planck units it is important to know what objects of the real world they are related to. The insufficient accuracy of the values of these constants forces to search for new alternative methods of determination of Planck units, including revealing interrelation of these constants with other fundamental physical constants and cosmology constants.

The author undertakes attempt [2,5] to find out whether there is an interrelation of Planck units with other fundamental physical constants. As a result, it is established that the constants lpl, tpl, mpl can be determined not only with the help of constants G, c, h by the formulas l_pl=(Gž/c³)^1/2, t_pl=(Gž/c⁵)^1/2, m_pl=(žc/G)^1/2.

There are also other formulas for their calculation. Such feature of Planck units has allowed revealing group of universal superconstants h_u, l_u, t_u, α, π [1,2,3,6]. With use of universal superconstants h_u, l_u, t_u, α, π the new mathematical formulas to calculate constants l_pl, t_pl, m_pl are received.

Three groups of the new formulas to calculate Planck constants are given below. Some of these formulas were published in [2,5,6] earlier.

12 formulas to calculate Planck length look like:

l_pl=(l_u²/D_o α)^1/2

l_pl=(e²GR_K/2πc³)^1/2

12 formulas to calculate Planck time look like:

t_pl=(t_u²/D_o α)^1/2

t_pl=(e²GR_K/2πc⁵)^1/2

10 formulas to calculate Planck mass look like:

From the given formulas it is visible that the constants l_pl, t_pl, m_pl are expressed with the help of other fundamental constants by compact relations. Among constants with the help of which these constants are presented such constants are used: fundamental quantum h_u, speed of light c, fine structure constant a, Newtonian constant of gravitation G, number ði, fundamental metrics of space - time (l_u, t_u), elementary mass m_e, big cosmology number D_o [5,6], Rydberg constant R_∞, Bohr magneton μ_B, Hubble constant H₀, rest energy of the electron E_e, Met Galaxy`s mass M_U, elementary charge e, Hartree energy E_h and Kleitzing constant R_K.

Each group of above - mentioned mathematical relations gives practically identical values l_pl, t_pl and m_pl. The results of calculation of constants` values l_pl, t_pl and m_pl received on the given formulas are given below. At calculations the new values of Newtonian constant of gravitation G and Hubble constant H₀ [5,6] received with the help of universal superconstants were used.

The exactest calculated values of constants l_pl, t_pl and m_pl which follow from the received formulas:

The differences from these values are very insignificant and also are observed in the seventh - eighth digits that is connected to various accuracy of those constants by means of which the constants l_pl, t_pl and m_pl are presented:

In tables 1, 2, 3 the values of Planck units received on the above - mentioned formulas are given:

 

Table 1. Calculated values of Planck mass
Who has received and date of receiving	Formula	Value
Planck, 1900,	mpl=(žc/G)1/2	~2,16•10-8 kg
CODATA, 1986		2,17671(14)•10-8 kg
CODATA, 1998		2,1767(16)•10-8 kg
Kosinov, 2000	mpl=hutu(Do/α)1/2/lu2	2,17666773(29)•10-8 kg
Kosinov, 2000	mpl =meDo(tu•2 H0)1/2	2,17666773(32)•10-8 kg
Kosinov, 2000	mpl=me (Do/α)1/2	2,17666773(22)•10-8 kg
Kosinov, 2000	mpl=(c2lu/G) (1/Doα)1/2	2,17666773(34)•10-8 kg
Kosinov, 2000	mpl=(Eelu/Gα)1/2	2,17666773(24)•10-8 kg
Kosinov, 2000	mpl=(2μB/lu) (α•10-7/G)1/2	2,17666773(25)•10-8 kg
Kosinov, 2000	mpl=(2huluDoH0/G)1/2	2,17666773(33)•10-8 kg
Kosinov, 2000	mpl=(2H0clu2 /G) (αD0)1/2	2,17666773(47)•10-8 kg
Kosinov, 2000	mpl=MU (1/Do3α)1/2	2,17666773(47)•10-8 kg
Kosinov, 2000	mpl=(Ee α2/4πR∞G)1/2	2,17666773(23)•10-8 kg

 

Table 2. Calculated values of Planck length
Who has received and date of receiving	Formula	Value
Planck, 1900,	lpl=(Gž/c3)1/2	~1,61•10-35 m
CODATA, 1986		1,61605(10)•10-35 m
CODATA, 1998		1,6160(12)•10-35 m
Kosinov, 2000	lpl=(lu2/Do α)1/2	1,616081387(51)•10-35 m
Kosinov, 2000	lpl=(2lu3H0/c)1/2	1,616081387(68)•10-35 m
Kosinov, 2000	lpl=(Gtu2me/lu α)1/2	1,61608138(21)•10-35 m
Kosinov, 2000	lpl=(Ghu/c3α)1/2	1,61608138(18)•10-35 m
Kosinov, 2000	lpl=(α5/16π2R∞2Do)1/2	1,616081387(45)•10-35 m
Kosinov, 2000	lpl=(tu3huG/lu3α)1/2	1,61608138(18)•10-35 m
Kosinov, 2000	lpl=(luEeG/c4 α)1/2	1,61608138(21)•10-35 m
Kosinov, 2000	lpl=(lume2G/Ee α)1/2	1,61608138(31)•10-35 m
Kosinov, 2000	lpl=(e2G/c2107α)1/2	1,61608138(18)•10-35 m
Kosinov, 2000	lpl=(e2GRK/2πc3)1/2	1,61608138(17)•10-35 m
Kosinov, 2000	lpl=(lu αme2G/Eh)1/2	1,61608138(31)•10-35 m
Kosinov, 2000	lpl=(Gtu2MU/D02lu α)1/2	1,61608138(32)•10-35 m

 

Table 3. Calculated values of Planck time
Who has received and date of receiving	Formula	Value
Planck, 1900,	tpl=(Gž/c5)1/2	~5,35•10-44 s
CODATA, 1986		5,39056(34)•10-44 s
CODATA, 1998		5,3906(40)•10-44 s
Kosinov, 2000	tpl=(tu2/Do α)1/2	5,39066725(18)•10-44 s
Kosinov, 2000	tpl=(2tu3H0)1/2	5,39066725(23)•10-44 s
Kosinov, 2000	tpl=(Gtume/c3α)1/2	5,39066725(68)•10-44 s
Kosinov, 2000	tpl=(Ghu/c5α)1/2	5,39066725(58)•10-44 s
Kosinov, 2000	tpl=(α5/c216π2R∞2Do)1/2	5,39066725(15)•10-44 s
Kosinov, 2000	tpl=(tu5huG/lu5α)1/2	5,39066725(58)•10-44 s
Kosinov, 2000	tpl=(luEeG/c6α)1/2	5,39066725(68)•10-44 s
Kosinov, 2000	tpl=(lume2G/c2Eeα)1/2	5,3906672(11)•10-44 s
Kosinov, 2000	tpl=(e2G/c4107α)1/2	5,39066725(58)•10-44 s
Kosinov, 2000	tpl=(e2GRK/2πc5)1/2	5,39066725(55)•10-44 s
Kosinov, 2000	tpl=(luαme2G/c2Eh)1/2	5,3906672(11)•10-44 s
Kosinov, 2000	tpl=(Gtu4 MU/D02lu3 α)1/2	5,3906672(11)•10-44 s

Thus for the centenary period of the existence the constants l_pl, t_pl and m_pl have passed some stages on which their values were considered to be exacter or to be less exact:

All calculated values of Planck units received on the new formulas are extremely close among themselves. All of them are exacter on some orders than values recommended both CODATA 1986 and CODATA 1998.

It is completely obvious that each group of the formulas should give identical values of constants l_pl, t_pl and m_pl. The approach of the calculated value received on the given formulas will occur in process of specification of fundamental physical constants values.

Relations of a kind: l_pl=(l_u²/D_oα)^1/2=(2l_u³H₀/c)^1/2=Gt_u²m_e/l_uα)^1/2=(Gh_u/c³α)^1/2=(α⁵/16π²R_∞²D_o)^1/2=(t_u³h_uG/l_u³α)^1/2= (l_uE_eG/c⁴α)^1/2= (l_um_e²G/E_eα)^1/2=(e²G/c²10⁷α)^1/2=l_um_e/m_plα=(l_uαm_e²G/E_h)^1/2=(Gt_u² M_U/D₀²l_uα)^1/2,

t_pl=(t_u²/D_o α)^1/2=(2t_u³H₀)^1/2=(Gt_um_e/c³α)^1/2=(Gh_u/c⁵α)^1/2=(α⁵/c²16π²R_∞²D_o)^1/2=(t_u⁵h_uG/l_u⁵α)^1/2=(l_uE_eG/c⁶α)^1/2= (l_um_e²G/c²E_eα)^1/2=(e²G/c⁴10⁷α)^1/2=(l_uαm_e²G/c²E_h)^1/2=(Gt_u⁴ M_U/D₀²l_u³ α)^1/2=(e²GR_K/2πc⁵)^1/2,

m_pl=h_ut_u(D_o/α)^1/2/l_u² =m_eD_o(t_u•2 H₀)^1/2=m_e(D_o/α)^1/2= =(c²l_u/G) (1/D_oα)^1/2=(E_el_u/Gα)^1/2=(2μ_B/l_u) (α•10^-7/G)^1/2= (2h_ul_uD_oH₀/G)^1/2=(2H₀cl_u² /G) (αD₀)^1/2=M_U (1/D_o³α)^1/2= (E_e α²/4πR_∞G)^1/2 it is possible to use for the coordination of a plenty of physical and astrophysical constants` values.

1. The new formulas to calculate Planck units with the help of fundamental physical constants and cosmology constants are found.

2. 12 equivalent formulas to calculate constants l_pl, 12 equivalent formulas to calculate a constant t_pl, 10 equivalent formulas to calculate a constant m_pl are received.

3. The formulas have allowed receiving calculated values of constants l_pl, t_pl and m_pl which are exacter on some orders than recommended values.

4. Each group of the formulas gives practically identical values of Planck units. The distinctions are very insignificant and also are observed in the seventh - eighth digits that is connected to various accuracy of those constants by means of which Planck constants l_pl, t_pl and m_pl are presented.

5. Exactest calculated values of Planck units:

REFERENCES

1. N. Kosinov. “Five Fundamental Constants of Vacuum, Lying in the Base of all Physical Laws, Constants and Formulas”. Physical Vacuum and Nature, N4, (2000).
2. N.Kosinov. Five universal superconstants underlying all fundamental constants, laws and formulas of physics and cosmology. Urgent problems of natural sciences of a beginning of century. Materials of the International Conference August 21-25th, 2000, St.-Petersburg, Russia. Publishing house: "Anatoliya", 2001, p.p. 176 - 179.
3. N.Kosinov Universal physical superconstants. http://piramyd.express.ru
4. N. Kosinov The big numbers in physics and cosmology. http://piramyd.express.ru/disput/kosinov/grate/text.htm
5. N. Kosinov. “Physical vacuum and gravitation”. Physical vacuum and nature, N4, (2000).
6. N. Kosinov. New about Newtonian constant of gravitation G. Fifteen equivalent formulas to calculate Newtonian constant of gravitation G. http://rusnauka.narod.ru
7. V.Larin, V.Yezhela. By century of opening of quantum of action. http://www.pereplet.ru/pops/larin/larin.html
8. http://faculty.millikin.edu/~jaskill.nsm.faculty.mu/G.html

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