© Ph.D. Nikolay Kosinov

E-mail: kosinov@unitron.com.ua

The aim of our research is to define a tie of electrodynamics and gravitation and to define a tie of Newtonian constant of gravitation G and electromagnetic constants. Has been discovered a global tie between Newtonian constant of gravitation G and major fundamental physical constants and has been got mathematical equation for calculation of constant G. Has been found out that Newtonian constant of gravitation G includes in oneself Planck constant h. A tie between constants which has been opened by us allows to get all the fundamental physical constants by mathematical calculation on base of special group of constants. As an initial constants for getting Newtonian constant of gravitation G we used only 4 fundamental physical constants: speed of light in vacuum, Planck constant, Rydberg constant, fine-structure constant. We discovered a group of independent primary constants, which allowed to get not only the constant G, but also the other fundamental physical constants with exactness 9 –10 digits by mathematical calculation. Results, which have been got, open the new possibilities in research of problems of microgravity, indicate on single nature of electromagnetism and gravitation and on possibility of management by gravitation with help of electromagnetic technologies.

Each physical theory uses definite fundamental physical constants. Possibilities of a theory are conditioned by constants which are laid in a base of the theory. The most important modern physical theories operate by constants G, h, c in their different combinations. So, for example, Newton’s theory of gravity is G-theory. The general theory of relativity (GRT) is a classic (G, c)-theory. The relativity quantum theory of field is a quantum (h, c)- theory [1]. Each of these theories operates by one or two dimensional constants. Discovering of Planck length, Planck mass and Planck time gave hope on possibility of creation of the new quantum theory on base of three constants. However, attempts to create a unified theory of electromagnetic field, particles and gravitation on base of three dimensional constants - (G, h, c)-theory, did not give expected results. There is no such a theory yet [1]. They hope that constants G, h, c is the base for future theory.

A lot of things indicates on that three dimensional constants must be enough for creation of unified theory. In the same time several hundreds constants are using in modern physics [2]. Why do their amount so great? If to consider them as a true fundamental constants then their amount are obviously very big. Only a few constants must be fundamental, but neither tens and certainly nor hundreds of constants. Not without purpose only from three basic units - metre, kilogram and second can be got all the derivative units which have mechanical nature.

So a big contradiction between a necessary amount of fundamental physical constants and their real abundance exists. Up to now its vaguely which three constants must put together a base of future theory this task is very difficult. Causes of this difficulty consist in obscure essence of many fundamental constants and in obscure sources of their origin. Therefore its important to find out whether constants G, h, c that necessary and sufficient combination of constants which able to become a base of quantum gravitation theory. In spite of big efforts of scientists, minimum constant basis, which sufficient for description of properties of fields and particles, has not found up to now.

The reason is that that majority of famous fundamental physical constants do not independent. But they are component constants. In this work are shown constants, from which has been got majority of fundamental physical constants, and how they connect between themselves.

L.de Broglie named Planck constant – mysterious constant. Although 100-year celebration of Planck constant h and of quantum theory has passed a curtain of mystery has not taken from this major fundamental constant and her physical essence opened not fully. P.Dirac was the first who noticed that a constant h is a component constant. He began to use another constant h , which did not contain the coefficients 2π [3]. Its important to find out, whether other fundamental physical constants and Newtonian constant of gravitation G pretend to the status of primary and independent constants or not. Our researches opened perfectly unexpected universal interdependency and deep interconnection between all fundamental physical constants. We have discovered a group of independent constants. This group lies in base of all fundamental physical constants. Fundamental physical constants functionally dependent to three dimensional constants and two dimensionless constants: fundamental quantum h_u

(h_u=7.69558071(63) •10^-37 J s), fundamental length l_u

(l_u=2.817940285(31) •10^-15 m), fundamental time t_u

(t_u= 0.939963701(11) •10^-23 s), fine-structure constant α (α = 7.297352533(27) •10^-3), number π

(π =3.141592653589).

Functional dependencies for some basic constants are shown beneath. So, for example, Newtonian constant of gravitation G has following functional dependence: G=f (h_u, l_u, t_u, α, π ). Constants from group h_u, l_u, t_u, α, π determine values of other fundamental physical constants: Planck mass m_pl=f (h_u, l_u, t_u, α, π ), Planck length l_pl=f (l_u, α, π ), Planck time t_pl=f (t_u, α, π ), elementary charge e=f (h_u, l_u, t_u), elementary mass m_e=f (h_u, l_u, t_u), Planck constant h=f(h_u, α, π ), speed of light in vacuum c=f(l_u, t_u), Rydberg constant R_∞ =f (l_u, α, π ), proton-electron masses ratio m_p/m_e=f(α, π ).

We conducted researches of role of constants h_u, l_u, t_u, α, π and their place among other fundamental constants and explored possibilities of using them as the basic and universal constants.

The analysis of relations obtained for calculation of physical constants shows that many constants are interconnected. The overwhelming number of constants can be expressed by means of the fundamental metric of space – time l_u, t_u. The research has shown that among universal physical constants, some of them are invariant to the metric. It points out on their special status. It is those constants, which are noneredacible in relation to metric features of space and belongs to really fundamental constants. Such constants are: Planck constant h, fundamental quantum h_u, speed of light in vacuum c, elementary charge e, fundamental length l_u, fundamental quantum of time t_u, fine-structure constant α, number π. With the help of these fundamental constants invariant to the metric, all other fundamental physical constants can be received.

Among dimensional constants, invariant to the metric of space – time, elementary charge and speed of light in vacuum are not independent and can be expressed though other constants. The elementary charge is determined through a fundamental quantum and fundamental metric. Speed of light in vacuum is a composite constant and is determined by the fundamental metric. The Planck constant is also a composite constant. It contains fundamental quantum h_u, fine-structure constant α and number 2π. Thus, among fundamental constants invariant to variations of the metric, there are absolutely independent fundamental constants. It allows defining for them a special status. Let’s name them as universal physical superconstants. There are five such superconstants: h_u, l_u, t_u, α, π.

With the help of this five unique superconstants all laws and formulas of physics can be presented, and also all other constants of physics both known and just obtained. Distinguishing of special class "Universal superconstants " can be grounded by following consideration. By us has been got a proof that these five constants are a primary and absolutely independent constants. All of other fundamental physical constants are composite . They have secondary status and can be got on base of primary superconstants h_u, l_u, t_u, α, π. Five primary constants give unique opportunity to get exact values of those fundamental physical constants, the values of which in modern physics are famous only from experiments.

On our opinion, these five universal superconstants will be able to substitute a big list of electromagnetic constants in future, universal constants, atomic and nuclear constants and to became a base of new physical theory of fields and elementary particles. Existence of only five primary constants, lying in base of universal, electromagnetic, atomic and nuclear constants, indicates on general unity of mechanical, electrical and gravitational physical laws.

Development of physics lead to conclusion that a gravitational field must submit to quantum laws. Appearance of the Planck mass, the Planck length and the Planck time [4] has generated hope for creation of such theory, which would operate with three constants: G, h, c. For creation of relativity quantum gravitational theory constants h and c were added to constant G. On scientists’ opinion such theory would be quantum theory completely, which would describe a gravitation. However a quantum gravitation theory was not created on base of (G, h, c)-basis. We must find reasons why is it so.

What hides in the Planck length and why do the Planck units and the units of quantum electrodynamics lead to natural units of dimension – kilogram, metre, second? Such intercommunication is needed in theoretical explanation.

We have found this theoretical explanation and have got a new equations for the Planck units by using universal superconstants h_u, l_u, t_u, α, π. Here are these equations:

m_pl = m_e (D_o/ α)^1/2

l_pl = l_u (1/D_o α)^1/2

t_pl = t_u (1/D_o α) ^1/2

Here D_o – dimensionless constant, which determines by constants α and π . Its value equal 4,16650385(15) •10⁴².

These formulas show, that the Planck length and Planck time directly connected with fundamental length l_u, and fundamental time t_u and that the Planck mass related with electron mass m_e.

These formulas show, that the Planck constants are tied to fundamental constants of length, time and mass by very simple equations. The accuracy of values of Planck constants calculated on the formulas is much higher than it was known before.

Its easy to get formulas for Newtonian constant of gravitation G by using the new formulas for Planck units. Here are 7 equivalent formulas for calculation of Newtonian constant of gravitation G. These formulas were got by us on base of initial superconstants h_u, l_u, t_u, α, π :

G = c³ l_u² / h α D_o,

G = l_u² b / m_eD_o,

G = G_u c² /m_e² D_o,

G = l_u³ / t_u² m_e D_o,

G = l_u⁵ / t_u³ h_u D_o,

G = h α⁴ / 4π t_u m_e² D_oR_∞,

G = 2π c³ l_u² / h α D_o,

where: G_u – constant which value equal 2,56696941(21) •10^-45 N s²; b – constant which value equal 3,189404629(36) • 10³¹m/s².

This major constant G did not have the formula for its calculation and was determined experimentally. The numerical value G was found in England by a physicist G.Cavendish in 1798 on rotating weights by a measurement of a gravitation force between two spheres. Then value G has been constantly updating. Now value G is considered to be equal 6,673(10) •10^-11 Nm²/kg². Among all universal physical constants the accuracy in definition of G is the lowest. For example, value of constant Rydberg R_∞ has been defined with unprecedented exactness and has 14 digits while value of constant G has only 4 digits [2]. Now, after 200 years passed since the first measurement of a constant G was made, appears the possibility to calculate its exact value. Using the formulas and to compare experimental outcomes to theoretical estimation. As accuracy in definition of constants of an electromagnetism is high enough, using our formulas, where the constants of an electromagnetism include, we receive calculated value of a gravitational constant. The numerical value for a gravitational constant gives magnitude of 6,67286742(94) • 10^-11 m³ kg^-1 s^-2, which is few orders more precise than experimental value.

So, tie of Newtonian constant of gravitation G with Planck constant h ,speed of light in vacuum c, elementary mass m_e, fundamental metrics of space-time l_u, t_u. It is not necessary to add to the constant G constants h and c. Constant G contains these constants.

VALUE OF FUNDAMENTAL PHYSICAL CONSTANTS, GOT BY COMPUTATION.

Using of (h_u, l_u, t_u, α, π )- basis permitted to get all the fundamental physical constants by calculation. Some of fundamental constants, which got by calculation, more exact then their experimental values. For example:

1. Calculation value of the Newtonian constant of gravitation G has 9 digits:

G = 6,67286742(94) • 10^-11 m³ kg^-1 s^-2.

CODATA recommended value of the Newtonian constant of gravitation G (1998) has only 4 digits:

G = 6,673(10) •10^-11 m³ kg^-1 s^-2.

2. Calculation value of the electron mass m_e equal:

m_e = 9,10938186(85) •10^-31 kg.

CODATA recommended value of the electron mass (1998) equal:

m_e = 9,10938188(72) •10^-31 kg.

3. Calculation value of the Planck length l_pl equal:

l_pl = 1,616081388(51) •10^-35 m.

CODATA recommended value of the Planck length (1998) equal:

l_pl = 1,6160(12) •10^-35 m.

4. Calculation value of the Planck mass m_pl equal:

m_pl = 2,17666772(25) •10^-8 kg.

CODATA recommended value of the Planck mass (1998) equal:

m_pl = 2,1767(16) •10^-8 kg.

5. Calculation value of the Planck time t_pl equal:

t_pl = 5,39066726(17) •10^-44 s.

6. Calculation value of the deuteron-electron mass ratio m_d/m_e equal:

m_d/m_e = 3670.47802(55).

7. Calculation value of the Hartree energy : E_h= 4,35974381(44) •10^-18 J.

CODATA recommended value of the Hartree energy (1998) equal: E_h= 4,35974381(34) •10^-18 J.

8. Calculation value of the Bohr magneton: μ_B = 9,27400899(45) •10^-24 JT^-1.

CODATA recommended value of the Bohr magneton (1998): μ_B = 9,27400899(37) •10^-24 JT^-1.

9. Calculation value of the magnetic flux quantum: Φ_o= 2,067833636(91) •10^-15 Wb.

CODATA recommended value of the magnetic flux quantum: Φ_o = 2,067833636(81) •10^-15 Wb.

10. Calculation value of the Hubble parameter: H= 1,749531663(89) •10^-18 s^-1.

11. Calculation value of the temperature in atomic nucleus: T_u= 5,929889(21) •10⁹ K.

Values of constants G, m_pl, l_pl, t_pl , got by computation, instead of 4 -5 digits have 9 - 10 digits.

Additional information obout constants you can find on web-sites:

• http://www.sciteclibrary.ru
• www.photcoef.com/236.html
• www.jsup.or.jp/shiryo/PDF/0900z53.pdf
• http://www.rusnauka.narod.ru
• http://www.n-t.org/tp/ng/nfk.htm

1.Analytical expressions for calculation of gravitational constant of Newton using fundamental constants of an electromagnetism and Planck constant are obtained for the first time. The obtained numerical value of a gravitational constant by accuracy exceeds on few orders accuracy of known experimental value.

2.The correlation of fundamental physical constants is revealed and the analytical expressions for calculation of those physical constants are found, whose values were known only from experiment and did not have the formulas for their calculation.

3.The theoretical substantiation of correlation of Planck constants of length, mass and time with natural units of dimensionality (kg, metre, second) and fundamental constants is given.

4.The existence of five absolute independent fundamental constants is revealed with the special status of fundamental superconstants. These five fundamental superconstants are enough to describe all laws of physics and to express with their help all other fundamental physical constants.

5. Have been got the new formulas for Planck masses, Planck length and Planck time.

1. Manin Y. Mathematics and physics. M. , "Knowledge", 1979.
2. Peter J. Mohr and Barry N.Taylor. CODATA Recommended Values of the Fundamental Physical Constants: 1998. WWW.Physics.nist.gov/constants; Reviews of Modern Physics, Vol. 72, No. 2, 2000.
3. Dirac P. Ways of physics. M., 1983.
4. Planck M. Selected works. Ì., Science, 1975.

Back