© Ph.D. Nikolay Êosinov

E-mail: kosinov@unitron.com.ua

1. THE ROBLEM OF FUNDAMENTAL PHYSICAL CONSTANTS

At the end of the 20th century in physics one more problem has appeared, which till now was not designated among major fundamental physical problems. It goes about a problem of fundamental physical constants. It has grown naturally on the basis of a lot of research results in the field of elementary particles physics. Due to this direction of researches many new fundamental physical constants have appeared. They are already separated into a single class - "atomic and nuclear constants" [2]. It is necessary to note, that their quantity much more exceeds the quantity of all other constants taken together [2].

Now near hundred physical constants are used in physics. CODATA 1998 recommend their list, which includes about 300 constants [2]. The presence of a big quantity of fundamental physical constants specifies that the modern understanding of constant fundamentality has more methodological than ontological character. If we admit the ontological existence of certain primary "truly" fundamental constants, it will be possible to explain the presence of a big quantity of fundamental constants in modern physics by their origin from the base constants. That is to say that the admission of constant ontological basis existence by all means results in the admission of the secondary status of modern physical constants.

Besides all that, the search of ontological basis for fundamental constants is dictated by the requirement of the physical theories simplicity. Researches of A. L. Simanov show that the principle of simplicity is not only gnoseological, but also ontological. It is more complicated, than simple Okcham’s rule, according to which it is not necessary to increase a number of essences without any need. The admission of both gnoseological and ontological basis simplicity with reference to ontological basis of physical constants allows to assert, that a small number of constants is enough for the description of many complex phenomena. It can be considered as one of directions in creation of the united physical theory.

However, a big quantity of constants, that all are referred to fundamental constants, puts under doubt the idea of their fundamentality. The same problem of fundamentality can be seen also amidst the family of elementary particles.

In general the problem of fundamental physical constants can be formulated as follows. The quantity growth of constants, that apply for the fundamental status, rejects the idea of the physical phenomena unity and unreasonable quantity increases new essences. Hundreds of constants can not have the fundamental status. The fundamentality can be inherent only in very small quantity of physical constants. Thus, there is a large contradiction between minimally necessary quantity of fundamental constants and their real abundance.

It is possible to assume that today known constants are compound. Then there is a question: "what new unpainted constants they can consist of and how they are connected among themselves". If such primary constants really exist, only they could apply for a role of fundamental constants. All other physical constants should be removed to the secondary status.

2. UNIVERSAL SUPERCONSTANTS

In [3-6] the researches of the fundamental physical constants problem are set. The task was to reveal the criteria of fundamentality and to reduce a number of the applicants by a rank of "truly fundamental" constants. As a result, it was discovered a group of primary constants, of which the fundamental constants consist [3-6]. There are five of them. They are the following 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 quantum of 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…).

To emphasize their "true fundamentality" they were named universal superconstants [3,5]. It is shown below, that the origin of the basic fundamental physical constants represents various combinations of universal superconstants.

3. INTERRELATION OF FUNDAMENTAL PHYSICAL CONSTANTS

The found group, which consists of five primary superconstants [4,6], has allowed to reveal for the first time a global connection between fundamental physical constants. For example, Newtonian constant of gravitation has appeared functionally dependent on other fundamental constants:

G=f (h , c, e, m_e, μ_B, R_∞, α, π).

Others fundamental physical constant are interconnected too. For example, Bohr magneton can be expressed by means of the following constants:

μ_B =f (h , c, e, m_e, R_∞, G, α).

Magnetic flux quantum can be expressed by means of the following constants:

Planck mass can be expressed by means of the following constants:

Planck length can be expressed by means of the following constants:

Planck time can be expressed by means of the following constants:

The further researches have shown that constant G and other fundamental constants can be expressed by means of universal superconstants [3, 6]:

{G, m_pl, c, h, … e, m_e, R_∞, μ_B, Ô_î} = f (h_{u ,} l_u , t_u , α , π).

The generality of fundamental physical constants is based on the fact that in their basis the rather limited quantity of primary constants lies. Next it is shown as an example how some fundamental constant are connected with universal superconstants.

For the basic constants these functional dependences are following:

- Newtonian constant of gravitation G : G=f(ħ_u,l_u,t_u,α, π);

- Planck constant h: h=f(ħ_u,α, π);

-speed of light in a vacuum c: c=f(l_u,t_u,);

-elementary charge e: e=f(ħ_u,l_u,t_u);

-electron mass m_e: m_e=f(ħ_u,l_u,t_u);

-Rydberg constant R_∞ : R_∞=f(l_u,α,π);

-proton-electron mass ratio m_p/m_e : m_p/m_e=f(α, π);

-Hubble constant H : H=f(t_u,α, π);

-Planck mass m_pl : m_pl=f(ħ_u,l_u,t_u,α, π);

-Planck length l_pl : l_pl=f(l_u,α, π);

-Planck time t_pl : t_pl=f(t_u,α, π);

-Magnetic flux quantum Ô_o : Ô_o=f(ħ_u,l_u,t_u,α, π);

-Bohr magneton μ_B : μ_B=f(ħ_u,l_u,t_u,α,).

As we see, those constants, which have traditionally the status of fundamental constants, are not primary and independent constants. From the given dependences it is clear that h, c, l_pl, t_pl, R_∞, m_p/m_e are the least complicated. It specifies that constants h, c, l_pl, t_pl, R_∞, m_p/m_e are closest to primary constants, however they are not prymary.

The use of superconstant basis allows to receive all basic fundamental physical constants by calculation. That is why the primary (ħ_u,l_u,t_u,α, π)-basis is unique.

Dimensional constants h_u, l_u, t_u follow from classical notion and are constants of physical vacuum [3 - 6]. These constants determine physical properties of space-time. Constants π and α determine geometrical properties of space-time (Fig.1).

Fig.1. Universal superconstants

Thus, the A. Poinkare’s approach, according to which the supplementation of physics and geometry is affirmed, proves to be true, [7]. According to this approach in real experiments we always notice certain "sum" of physics and geometry [8]. The superconstants confirm it by their structure.

4. A NEW VALUE OF THE CONSTANT G.

The dependence of the constant G on primary superconstants specifies that this important constant can be received by mathematical calculation.

It is known that the form of the Newtonian gravitation law (proportionality of force to mass and return proportionality to a square of distance) is checked up with much more exactness, than the definition of Newtonian constant of gravitation G. Therefore basic restriction on exact definition of gravitational forces is imposed by a constant G. Besides that, from times of Newton there exist a problem of gravitation nature and gravitational constant G essence. This constant is determined experimentally. The science does not know whether there is an analytical parity for the determination of the gravitational constant. The connection between constant G and other fundamental physical constants was not also known for a science. In theoretical physics this major constant is tried to use with Planck constant and light speed constant for the gravitation quantum theory creation and for the development of single theories. Therefore, the questions on primacy and independence of a constant G and necessity of its exact value stays on the foreground.

The numerical value of G was determined for the first time by English physicist G. Cavendish in 1798 on torsion scales by measurement of attraction force between two spheres.

New value of the constant G, recommended CODATA 1998, is [2]:

Among all universal physical constants the exactness in definition of G is the lowest. The mean square error for G exceeds an error of other constants.

It has appeared completely unexpected that constant G can be expressed by means of

electromagnetic constants. It becomes important, because the calculation of electromagnetism constants is much more exact than the calculation of constant G.

Open group of universal superconstants and revealed global connection of fundamental constants have allowed to receive the mathematical formulas for calculation of gravitational constant G [3,5,6]. There are some of this formulas. 8 equivalent formulas for calculation G are given below as confirmation to this:

G = 2πc³l_u²/αhD_o, G = c⁵t_pl²α/h_u, G = l_u³/t_u² m_e D_o, G = h_uα²/4πt_u m_pl²R_∞,

G = c³l_pl²α/h_u, G = 2l_u⁵α H/t_u² h_u, G = h_u c/α m_pl², G = c⁴l_u /E_eD_o.

It can be clear from the given formulas that the constant G is expressed with the help of other fundamental constants by very compact and beautiful parities. All formulas for Newtonian constant of gravitation keep coherence. Among physical constant, with the help of which the Newtonian constant of gravitation is submitted, there are such constants as: fundamental quantum h_u, speed of light c, fine structure constant α, Planck constant h, number π, fundamental metrics of space-time (l_u,t_u), elementary mass m_e, elementary charge e, large cosmological number D_o, belonging to big number family of Dirac, energy E_e, Planck length l_pl, Planck mass m_pl, Planck time t_pl, Hubble constant H, Rydberg constant R_∞. It specifies the single essence of electromagnetism and gravitation and the presence of fundamental unity of all physical constants.

Now, when 200 years have passed after the first measurement of G, it is possible to calculate its exact value on the basis of the received formulas, using electromagnetism constants.

As the exactness in definition of electromagnetism constants is high, the exactness of gravitational constant can approach the exactness of electromagnetic constants. All above mentioned formulas give new value of G, which is more exact in almost five times than today known value. The new value of G instead of four digits contains 9 digits [3]:

G=6,67286742(94)•10^-11 m³ kg^-1s^-2.

5. NEW VALUES OF PLANCK UNITS.

With the help of universal superconstants it was possible to receive the new formulas for Planck units [3-4]:

On the basis of these formulas the new values of Planck units are received:

These new values of Planck units are more exact almost five times than today known values.

The values of other fundamental physical constants you can find on sites:

• www.photcoef.com/236.html
• www.jsup.or.jp/shiryo/PDF/0900z53.pdf
• http://www.rusnauka.narod.ru
• http://www.schemali.narod.ru
• http://www.sciteclibrary.ru/rus/catalog/pages/2017.html
• http://www.n-t.org/tp/ng/nfk.htm

6. COMPOUND ESSENCE OF THE PLANCK CONSTANT

On December 14, 1900 Ì.Planck has declared the discovery of a new fundamental constant. Quantum has appeared in the physical theory as a postulate. Though confirmed on experience, it was not strictly proved in the quantum theory. Its origin remained always by a riddle. All attempts to deduce it from primary principles did not find the decision till now. There is still a problem question: "whether is it possible to consider a continuous field to be a primary field for quantum?" Continuous fields of classical physics and the quantums of quantum physics are considered to be so far objects, and idea to examine them from single position seems inconceivable.

L.de Broglie said that Planck constant is "mysterious constant h" [9]. He said: "Planck’s genius is worth admiring. Studying the individual physical phenomenon, he was able to guess one of the most basic and most mysterious laws of a nature. More than forty years have passed from the date of this remarkable discovery, but all of us are still far from complete understanding of meaning of this law and all of its consequences" [10]. It could be added that 100 years after this remarkable discovery all of us are still far from complete understanding of this law. The veil of mystery covers this major fundamental constant.

Planck constant h was not clear for him also. M. Planck emphasised it specially in the Nobel speech. He named it the mysterious bulletin from the real world [11,12].

Hvolson expressed that very precisely [10]. "Getting into all departments of physics, it has proved the its global meaning. It has proved, that it plays a great role in the physical phenomena. It begins to get into chemistry also. What is its physical essence? Why is it so important? Why does it interfere (better to say - is put!) in every possible physical phenomena? What is h? It is not known and not clear!"

Till now it is considered that the electromagnetic theory is obviously alien to a basis of the quantum theory – Planck constant [11]. Is it so? Is this division really proved?

The question of probable primacy and unadducement of Planck constant is very urgent. The unsolved problems of Planck constant do not allow to have the answer to other question: where arises really observable behaviour of our world from and what lays in its basis?

The universal superconstants enable to present the laws and formulas of quantum physics and also fundamental constants of physics, including Planck constant h. The discovery of a new physical constant h_u has allowed to see that Planck constant h represents a combination of primary superconstants [3,6]:

h = f(h_u,π,α).

The most important result is that new quantum of action h_u has allowed to reveal a sources of occurrence h from a continuous field. It removes a veil of mystery from the Planck constant h. It has been clear that the constant h is connected directly with properties of physical vacuum. By its origin it is obliged to existence of fundamental quantum h_u and is shown at transition of a continuous field to discrete substance.

From this it concludes that discreteness of our world arises from kontinuum. To my mind, the separation of the classical and quantum theories is one of the reasons of a deadlock condition in a physical science. The way out from impasse is seen in association of the classical and quantum approaches and in creation of the new physical theory on the basis of superconstant (h_u,t_u,l_u,π,α )-basis, which has fundamental ontological status.

7. COMPARISON OF CALCULATING AND RECOMMENDED CONSTANT VALUES

Universal superconstants h_u, t_u, l_u, π, α enable to receive by calculation not only constant G, but also other fundamental constants. Confirmation of received results correctness is almost complete concurrence of calculating values of fundamental physical constants with the values of the same constants, recommended by CODATA 1998 [2]. As an example, the comparative data for most important physical constants are given below. 

Comparison of calculating values of constants with values, which are recommended by CODATA 1998:

From here you can see that some fundamental constants, received by calculating, are more exact than their experimental values. It concerns to constants G, m_pl, l_pl, t_pl, H. It was possible for constants G, m_pl, l_pl, t_pl, H to reach a level of exactness of constants h, Ô_î, e, μ_B, m_e [3-6].

8. CONCLUSION

It is shown on the example of a problem of fundamental physical constants that concept physics fundamentality has more methodological, than ontological character. Such remoteness of fundamentality concept from ontological contents does not promote the search of ontological basis of the world.

The found five universal superconstants, which are able to substitute the large list of electromagnetic constants, universal constants, atomic and nuclear constants, become the first applicants for a rank of fundamental constants. They make ontological basis of physical constants.

The presence of global connection of physical constants answers a question, why all attempts of the scientists to construct the quantum theory on a basis of Planck constant received by addition to a constant G of two constants h and c, have no results. The reason is that constant G comprises constants h and c, and the addition of them did not give to the (G, h, c)-basis any new quality.

The revealed global interrelation between physical constant enables to specify a way, which will allow to determine practically all fundamental constants with extreme high exactness. This limit already sets the received absolutely recently [2] with unprecedented exactness a new value of Rydberg constant R_∞ ( 7,6õ10^-12). There is a real opportunity to approach exactness of other constants to exactness of Rydberg constant. For this purpose it is necessary to determine with a high exactness only two constants. One of them is the fine-structure constant α. This constant is necessary for determining with exactness of 10^-12 - 10^-13. Other constant is one of a group: h, e, m_e. It is necessary to determine it with exactness close to exactness of Pydberg constant. In this case all other constants can be received by mathematical calculation with exactness not worse, than exactness of Rudberg constant R_∞.

As you see, only two constants require now the special attention of physicists. They are the thin structure constant α and one of constants from a group h, e, m_e. Further only three constants will require a great attention of the researchers - R_∞, α, h, e, m_e and one constant from a group (h, e, m_e). They will be quite enough to calculate the values of all other physical constants with a large exactness.

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