The relationship between fundamental physical constants.
There are several fundamental physical quantities related to Newtonian mechanics, Einstein's theory of relativity, electromagnetism, and quantum mechanics that are seemingly unrelated. But since all the physical processes that take place are interconnected, there must be a connection between them. These physical quantities primarily include: gravitational constant G, mass m, speed of light c, fine structure constant L, charge g, Compton wavelength l, Planck constant h, gravitational radius of the electron ggr.
These physical quantities relate to the internal structure of the particles. The space of Electromagnetic Interactions is the internal space of particles in ( 3+1+1 ) dimensional space. Why is it being considered ( 3+1+1 ) dimensional space? Because the electron density is about 10 thousand tons per cubic centimeter (this is easily calculated: the classical electron radius is 2.82 x 10^-13 cm, the mass is 9.109383 x 10^-31 kg). At such a density of matter ( 3+1)_ space bends and becomes ( 3+1+1 ) space. The space of the higher n–dimensional level is less discrete compared to the space of the lower level. For example, rotation in four-dimensional space ( in space 3+1+1 ) It is determined by six angular parameters, as opposed to three angular parameters in three-dimensional space, therefore, for example, a wave having a continuous front in ( 3+1+1 ) space will have the form of an intermittent discrete structure corresponding to the quantum structure of particles in ( 3+1) space . In isotopic space ( 3+1+1 ) the photon is not quantized. It is a continuous wave created by the vibrations of its oscillatory components. Only from the point of view of our (3+1) dimensional space, when it rotates around the spin axes, it acquires the properties of single quanta and rotational motion in one direction or the other.
To begin the consideration of fundamental physical quantities and the relationship between them, let us first consider Coulomb's law. The formula of Coulomb's law has the form :
F = K x ( g1 x g2)/ r^2
The coefficient in the Coulomb formula has the following value:
K = 8,9075517873661764 x 10^9 N x m^2 / Kl^2
This numerical value can be represented as a formula:
K = c^2 x 10^-7 Gn /m = 8,9075517873661764 x 10^9 H x m^2 / Kl^2 , where
c - is the speed of light in vacuum, equal to 2.99792458 x 10^8 m/sec
10^-7 Gn / m - is a constant value.
At first glance, the discrepancy between the dimensionality of physical quantities in the formulas can be explained by the fact that, as in Coulomb's law, the coefficient K has a value of 10^-7 Gn /m contributing its dimension to this formula, so in the formulas below ten to the degree should contribute its dimension to them.
The fine structure constant: L = 1/ 137.036 = 0, 00729735 is a dimensionless quantity, and plays a fundamental role in atomic physics.
It is expressed by the formula :
L = e2 / 2 x e0 x h x C, where
e – elementary electric charge,
eo - is an electric constant,
c - is the speed of light in a vacuum.
But the fine structure constant also plays a fundamental role in the physics of elementary ( subatomic ) particles. Only for them it manifests itself as a constant ( 1 + L ) x 10^23 .
( 1+ L ) x 10^23 is a constant that characterizes the relationship between different fundamental physical quantities . It plays an essential role in particle physics, and can be expressed in terms of the speed of light in vacuum c, the number П ( 3,14159), and the Planck mass Mr. This formula has the following form :
( 1 + L ) x 10^23 = c / ( 2 x П x Mr^2 ) , where
c -is the speed of light in a vacuum,
П - is the number of pi ( 3.14159 ),
Mr - is the Planck mass.
The relationship between the gravitational constant G and the Planck constant h can be expressed by a formula in which these two fundamental quantities are related :
Equality No.1 :
h x ( 1 +L ) x 10^23 = G ;
6.62607015 x 10^-34 x ( 1 + 0.00729735 ) x 10^23 = 6.6744229 x 10^-11 ; where
G = 6.67430(15) x 10 ^ -11 m ^2 /kg x sec^2 - the magnitude of the gravitational
the permanent one is currently accepted. ( According to other data, in laboratory experiments conducted in 2018 in two different ways, it amounted to 6,674,184(78) and 6,674,484(78), respectively. In the first group, the "time of swing" (TOS) method was used, where the proportionality coefficient depends on the oscillatory frequency of the scales. The second is the "angular acceleration feedback" (AAF) method, where the angular acceleration of independently rotating rocker balls is measured by a feedback control system, while the thread is kept uncoiled. According to the results of the team, the first method demonstrated the value of the gravitational constant, G=6.674184 x 10^(-11) m^3 /kg x s^2 the second method – G = 6.674484 x 10^(-11) m^3 / kg x s^2. The relative error was 11.6 x 10-6. Thus, the gravitational constant is constantly being refined, requiring new, more accurate ways of measuring and calculating.
L = 0.0072973525 is a fine structure constant (dimensionless value);
h = 6.62607015 x 10 ^-34 ( kg x m^2 ) / sec is Planck's constant.
The resulting value of the gravitational constant G is the exact value of G obtained by calculation, and not by laboratory measurements having many different kinds of errors. Having thus obtained the exact value of the gravitational constant G, it is possible to clarify the value of the Planck mass Mr. Currently, it is considered equal to Mp =2.176434 x 10^ -8 kg. After recalculation, a value equal to Mp = 2.1764143 x 10 ^ -8 kg is obtained.
For elementary particles that are attractors existing in phase spaces, there must be a phase velocity in ( 3+1+1 In space, the speed of light is less than c =2.99792458 x 10^8 m/sec. Only at a speed less than the speed of light is a particle in space ( 3+1+1 ) can remain a stable vortex formation (attractor). As will be shown below, such a speed can be a speed equal to v = 2.99631043 x 10^8 m/sec.
Equality No. 2 ( for the electron ):
mel. = v^2 x (( 1+L ) x 10^23))^2 x 10^-93 ; where
mel. = 9.1093837 x 10^-31 kg is the mass of the electron;
L = 0.0072973525 is a fine structure constant (dimensionless value),
(1 + L ) x 10^23 is the coefficient of electromagnetic resistance (3+1+1 ) dimensional space.
v = 2.99631043 x 10^8 m/sec is the velocity satisfying the equality ( phase velocity in ( 3+1+1 ) space.
10^-93 is a coefficient having a dimension of c^4 x kg ^3 / m^4.
Equation No. 2 indicates the connection of the electron velocity with the mass property acquired by it, which is a consequence of the velocity resistance in curved space (3 +1 +1 ) when the speed is v = 2.99631043 x 10^8 m/sec. This resistance creates the inertial mass of the particle.
Equality No. 3 (for the electron).
There is also a physical quantity called the gravitational radius of the electron rg. the numerical value of which is determined by the formula:
rg.= 2 x G x mel./ s ^2.
For the case when the gravitational radius is determined by the rotational velocity v = 2.99631043 x10^8 m/sec in ( 3+1+1 in space , the formula of the gravitational radius takes the form :
rg. = (2 x G x mel. / c^2) x ( v^4 / c^4 ).
The reason for the appearance of an additional multiplier v^4/ c^4 is explained by the presence of an oscillator of mass m, charge g. The gravitational radius will be approximately 1.35 x 10^-57 m.
The centripetal acceleration generated at this radius will have a value equal to :
a ca = v^2 / rg. = (2.99631043 x 10^8)^2 / 1.35 x 10^-57 =
= 6.65021 x 10^73 m/sec^2
If we compare the magnitude of the numerical value of the centripetal acceleration ( without taking into account the degree of the number ) with a numerical value of the gravitational constant G= 6.6744229, and the Planck constant h = 6.62607015, it can be seen that it occupies the middle value between them in the digital value.
That is: a ca x ((1+ L ) x 10^23)^0.5 x 10^-95.5 = G = 6.67443 x 10^-11,and the
a ca / (( 1 + L ) x^ 10^23)^0.5 x 10^-95.5 = h = 6.626068 x 10^-34; where
L - is a fine structure constant equal to 0.00729735.
10^-95.5 - is a coefficient having a dimension of m x sec x kg.
That is, the magnitude of the gravitationally constant is related to the magnitude of the centripetal acceleration in space ( 3+1+1 ) the inertial mass of the particle. Centripetal acceleration of the attractor particle in ( 3+1+1 ) space is also most likely the reason for the attraction of masses to each other and is related to the value of Planck's constant h. The Planck constant h and the gravitational constant G obtained by these calculations are very close to the values obtained by laboratory, experimental methods.
Two conclusions can be drawn from this: first, that the centripetal acceleration a c.c. in space ( 3+1+1 ) is related to both the gravitational constant G in space ( 3+1 ) and the Planck constant h in the space of electromagnetic interactions . And secondly, fundamental physical constants are determined by the properties of space, not by the properties of particles.
Equality No. 4 ( for the electron ) :
( h x l ) / ( ( 1 + 0.006755) x 10^23 )^0.5 x 10^27 = g where :
h is the Planck constant equal to 6.62607015 x 10^-34 kg x m^2/sec
l = 2.4263 x 10^ -12 m is the Compton wavelength for an electron, (currently, according to CODATA for 2018, it is 2.4263 x 10^-12 m )
g - is the charge of the electron.
10^27 - is a coefficient having a dimension satisfying the above equation.
((1+0.006755) x 10^23 )^0.5 = (me / c^2 )^0.5 - is a constant value, where
me is the mass of the electron,
c - is the speed of light in a vacuum.
Equality No. 4 indicates the relationship of the Compton wavelength of an electron with the magnitude of its charge. The charge of an electron is also a quantized quantity.