SPACE-TIME SYMMETRY

 Thus, the quantum of force in the gravitational range of fluctuations corresponds to the quantum of action in an electromagnetic range of fluctuations. Quantum of action works in the microworld. Quantum of force works in the megaworld. The physical sense of quantum of force can be perceived in the following reasoning chain. The universe is at least four-dimensional and closed. Hence, any "straight line" goes on a circumference. The maximal length of a circumference in the universe is X = 1,26245190072E+26 m. The resting proton in three-dimensional space moves in four-dimensional space along a time circumference of the same length. Hence, the concept of centripetal force is applicable to proton: f = ma = mv²/r. Substituting the speed of light instead of velocity, and X instead of r, we shall receive the quantum of force:

f = mc²/X = 1,190760067E-36 N.

If we shall divide not by the large circumference of the universe, but by the radius of curvature of universe, we shall receive fbar, or f*2p , which is the analogue of hbar, or h/(2p). And this will be the minimally possible force applied to any proton in the universe:

fbar =f*2p mc²/r = 7,481766157E-36 N.

In the closed world there is no straight lines; and we can conclude, that any proton is always under the action of the minimal force, determined by the quantum of force, or under the action of the force, which is multiple of quantum of force. Consequently, the force is also the quantum physical quantity.

Surprising similar results received independently.

In May 2000 I have found out about existence of the work “The Wave Equations for Oscillator with Planck's Constant and with a Quantum of Force”, Phys. Chem. Earth (A), Vol.24, No.8, pp. 721-725, 1999, performed independently by Alexander Malimon. The Internet-link to this work is: http://www.copernicus.org/EGS/pce/part_a_vol_24_no8b.html. The author of the quoted work has received a set of results very close to results received in my work. But instead of "graviton", he uses the term "inverse photon". According to his estimations, the quantum of force lays in a range ~ 10^-37 -:- 10^-36 N, and the La-mbda point (I name it boundary frequency) lays in the region about 400 Hz. It is also surprisingly that he has assumed the opportunity of existence of low-frequency vacuum fluctuations, symmetric to CMB radiation. According to his estimations, these fluctuations lay in a range from 4 to 40 days. (Compare this result with result in the third line in the table above.) Such "relict radiation" can be expressed in space granulation into cells with the characteristic sizes, which have been mentioned above. A.N. Malimon has assumed, that these cells have their own potentials of gravitational and electromagnetic fields. And these fields can influence on quantum fluctuations of systems in these cells. The author writes about experimental observations of sudden frequency steps, on the clocks based on the quantum frequency standards, which is located in the different parts of the world. In his work Alexander Malimon has written down the equation for harmonic oscillator with the quantum of force. This equation is symmetric to the Schr�dinger equation, which was written down with the quantum of action.

New results

In the summer of 1999 I have noticed one strange numerical concurrence written in Normalized Units: G' = 1/Exp(a+1/a); where G' - gravitational constant in reducible Normalized Units (units, independent from a humane); a is a fine structure constant. The further analysis has shown, what it must be exactly thus. Indeed, in the very beginning we have imposed the condition of symmetry between gravitational and electromagnetic fluctuations; and a is a constant describing the electromagnetic interactions in the language of quantum electrodynamics. Then G' is the gravitational fine structure constant. An exponent on one hand, or the logarithm on the other hand, occurs as result of the symmetry inside/outside, or the symmetry between X and 1/X. In the summer of 2000 I has received the unexpected development in the analysis of the Graity-Thermal Coil. As a result of this analysis, it was found out, that the Newton gravitation law must be symmetric to Coulomb law. It must contain the gravitational constant in empty space, which is the analogue of electric permittivity of empty space; and relative permittivity of the medium, etc. Look the page The Earth's Core Is Overheated Emptiness for more details. The crazy results, which can be hardly accepted by a scientific public in the future 100 years, are shown on page Gravitational Mirror, where with the help of transformations:

x' = x/(x²+y²), y'=y/(x²+y²);
x = x'/(x'²+y'²), y=y'/(x'²+y'²), (11)

one can find out the coordinates of our imaginary images. Those transformations are the elementary transformations inside/outside; the transformations of photon space into graviton space and visa verse. These transformations will be useful in geology, because they connect our real and imaginary images, relatively the border between the mantle and the Earth’s core; and also in biology, relatively the membrane of a cell, with a DNA-molecule on one hand of transformations, and the humane, carrier of this molecule, on the other hand of transformation equations. (The DNA-molecule is a reflection of a human, who lives or lived somewhere in the far end of our closed but boundless Universe.)