探讨宇宙膨胀的力学原因（英文译文）

Exploration on the Mechanical Causes of the Expansion of the
Universe

Wu Dongmin from Universe Discovery

Abstract: This paper explored the mechanical causes of the expansion of the universe from the perspective of celestial mechanics.
Discovery: The radiation repulsion between two galaxies is directly proportional to the product of the square of the number of stars in the two galaxies. F=Kx2y2S1S2E1E2/R2c2
Discovery: The magnitude of radiation pressure borne by a celestial body is equal to the amount of energy received by the celestial body per second divided by light speed. F=E/ct
Keywords: Universal Gravitation; Radiation Repulsion; Photon Momentum; Luminosity-Mass Ratio

Einstein added the term “cosmic constant” in his gravitational field equation to balance universal gravitation, thus keeping the universe stable. What is “cosmic constant” exactly? Einstein believed it was “anti-gravity”, which was intrinsic in space-time instead of originating from any particular source like other forces. Later on, theoretical physicists returned to “cosmic constant” again and considered it as a mechanical cause driving the expansion of the universe. To be specific, it was “dark energy” in space-time. What dark energy is and how dark energy interacts with galaxies specifically remain inconclusive. This paper found that the light radiation repulsion of galaxies might be the real cause of the expansion of the universe from the perspective of celestial mechanics.
Light radiation pressure is the repulsion exerted by celestial bodies with strong radiation in galaxies to surrounding space-time, which is also called light radiation repulsion. Both light radiation repulsion and universal gravitation are long-range forces. Obviously, the universal gravitation between galaxies is the force of attraction that keeps galaxies close to each other while the radiation repulsion between galaxies is the force of repulsion that pushes galaxies away from each other. This paper analysed the strength of the universal gravitation and radiation repulsion between galaxies. If radiation repulsion was greater than universal gravitation, the mechanical cause of the expansion of the universe was thus found.

1. Photon Momentum and Momentum Theorem

In 1905, Einstein proposed the “photon theory” and successfully explained the photoelectric effect. He again proposed the hypothesis that photons had momentum in 1917, which was proved by the X-ray scattering experiment conducted by Compton in 1923. The energy, momentum and impulse of photons can be calculated with the following formulas. p=E/c is obtained from E=mc2 and p=mc (photon momentum). F=Δp/t is obtained from I=F•t and F•t=Δp (momentum theorem). Wherein, E stands for photon energy (J), p for photon momentum (kgm/s), m for mass (kg), c for light speed as a constant (2.998 x 108m/s), t for time (s), Δp for change in momentum (kgm/s), I for impulse (N•s or kgm/s) and F for acting force (N).
The radiation repulsion of a celestial body can be understood as an acting force produced by the change of photon momentum after the celestial body receives photon radiation, which is also known as impact force. The acting force is in the same direction with light radiation, whose magnitude depends on that of change in momentum. After a photon is absorbed, its change in momentum is equal to the initial momentum of photon. Namely, F=E/c•t is obtained from F•t = Δp = p = E/c. The magnitude of radiation pressure borne by a celestial body is equal to the amount of energy received by the celestial body per second divided by light speed.

2. Estimation of the radiation repulse of the sun to the earth

According to the experimental data, radiation power of about 1,000W/㎡ can be obtained in the direct sunlight of earth surface. Namely, the energy of about 1,000J can be obtained. Outside the atmosphere, the radiation power measured is 1,368W/㎡. Combining the earth’s radius of 6,378km with the atmosphere’ thickness of 1,000km, the earth has an overall radius of 7,378km (7.378 x 106m). By calculation, radiation power of the sun obtained by the earth is πx (7.378 x 106)2 x 1368=2.345 x 1017W(J/s), and the radiation repulsion of the sun to the earth is Fearth=E/c•t=2.345 x 1017/2.998 x 108 x 1=7.822 x 108N. However, the universal gravitation between the sun and the earth is 3.51 x 1022N by calculation. By contrast, radiation repulsion is very small with a difference of 14 orders of magnitude from universal gravitation.
One question occurred to me when I was at a loss. Why do so many stars come together in galaxies? I started to study radiation repulsion of galaxies and drew the following sketch for consideration. Suddenly, I found that radiation area and intensity were both related to the number of stars, and the multiple increases in radiation repulsion would be the product of squares of a number of stars in two galaxies. Radiation pressure would be greater than universal gravitation as long as there were enough stars. I was thrilled by this discovery, which was the first harvest I obtained from studying A Brief History of Time by Stephen Hawking.

3. Expression of radiation pressure

(1) The magnitude of the universal gravitation between two stars is directly proportional to the product of their masses and inversely proportional to the square of their distance, namely F=Gm1m2/r2. By analogy, the magnitude of the radiation repulsion between two stars is directly proportional to the product of the number of their photons radiating each other and inversely proportional to the square of their distance. However, the number of photons is directly proportional to the radiation area and the total momentum or energy of stars, radiation sources. Then, the following expression can be obtained: F=k•S1•S2•p1 • p2 /R2 or F=k•S1•S2•E1•E2/R2•c2. Wherein, S1 and S2 stand for the radiation areas of the two stars, p1 and p2 for the total radiation momentum of the two stars, E1 and E2 for the total radiation energy of the two stars, R for the distance between the two stars, c for light speed as a constant, k for modified constant and F for radiation repulsion.
(2) Similarly, the magnitude of the universal gravitation between two galaxies is directly proportional to the product of their masses and inversely proportional to the square of their distance. By analogy, the magnitude of the radiation repulsion between two galaxies is directly proportional to the product of the number of their photons radiating each other and inversely proportional to the square of their distance. In galaxy 1 with x stars, the total momentum of radiation changes from p1 to xp1, and radiation area changes from S1 to xS1. In galaxy 2 with y stars, the total momentum of radiation changes from p2 to yp2, and radiation area changes from S2 to yS2. The repulsion between the two galaxies is Frepulsion=K•xS1•yS2•xp1•yp2/R2=K•x2•y2•S1•S2•p1•p2/R2. Similarly, Frepulsion=K•x2•y2•S1•S2•E1•E2/R2•c2. It suggests that radiation repulsion will see a rapid increase in the galaxies with multiple stars. The increase of radiation repulsion is directly proportional to the product x2y2of the number of stars radiating each other while the increase of universal gravitation is only directly proportional to the product xy of the number of stars. With the increase in the number of stars in galaxies, their radiation pressure increases xy times faster than universal gravitation. The result shows that the radiation repulsion of galaxies will exceed universal gravitation as long as there are enough stars and the value of xy is large enough. In general, a galaxy has 5 x 109 to 1014 stars, whose radiation repulsion is 1020 more than the value of xy, the magnitude of increase in universal gravitation.
Why were the above results obtained? (1) Radiation area is directly proportional to the number of stars. (2) The number of photons per unit area is also directly proportional to the number of stars due to the superposition of radiation and the increase of intensity. Therefore, the total number of photons interacting with each other will become very large.

4. Estimation of the radiation repulsion between the Milky Way Galaxy and the Andromeda Galaxy (No. M31)

The radiation repulsion of galaxies was quantitatively calculated: In Frepulsion=K•x2•y2•S1•S2•E1•E2/R2•c2, the value of the modified constant K must be measured by an experiment like G, constant of universal gravitation. It is hoped that a figure like Cavendish will appear as soon as possible among scientists with experimental conditions.
In this paper, the calculation for the repulsion of galaxies avoided the modified constant K and adopted F=E/c•t. The sun is an ordinary star which has a mass of 1.989 x 1030kg with a radius of 6.963 x 108m and a total photon radiation power of 3.847 x 1026W(J/s). Therefore, its data is used as a mean value of stars in the galaxy to make estimation within the range of existing astronomical data which are neither comprehensive nor very accurate. The Milky Way Galaxy has a mass of 4.177 x 1041kg with a diameter of 1.3011 x 1021m (1.4 x 105 light-years, 1ly=9.2938 x 1015m) and 3 x 1011 stars. The Andromeda Galaxy has a mass of 8.354 x 1041kg with a diameter of 2.0446 x 1021m (2.2 x 105 light-years) and 4 x 1011 stars, whose distance from the Milky Way Galaxy is 2.3504 x 1022m (2.53 x 106 light-years). The radiation power of the Milky Way Galaxy to the Andromeda Galaxy = Radiation area of the Andromeda Galaxy/large sphere surface area x total radiation power of the Milky Way Galaxy=(2.0446/2 x 1021)2•π/4•π•(2.3504 x 1022)2 x 3 x 1011 x 3.8 x 1026=5.39 x 1034(W or J/s). The radiation repulsion of the Milky Way Galaxy to the Andromeda Galaxy is F1=E/c•t=5.39 x 1034/2.998 x 108•1=1.799 x 1026(N). The radiation power of the Andromeda Galaxy to the Milky Way Galaxy = Radiation area of the Milky Way Galaxy/large sphere surface area x total radiation power of the Andromeda Galaxy=(1.3011/2 x 1021)2•π/4•π•(2.3504 x 1022)2 x 4 x 1011 x 3.8 x 1026=2.911 x 1034(W or J/s). Radiation repulsion of the Andromeda Galaxy to the Milky Way Galaxy is F2=E/c•t=2.911 x 1034/2.998 x 108•1=0.971 x 1026(N). Combined repulsion is F=F1+F2=1.799 x 1026+0.971 x 1026=2.77 x 1026(N).

5. Comparison between universal gravitation and radiation repulsion in the Milky Way Galaxy and the Andromeda Galaxy

By calculation, the universal gravitation between the Milky Way Galaxy and the Andromeda Galaxy is 4.22 x 1028N, which is greater than their radiation repulsion 2.77 x 1026N. The two galaxies draw close to each other. This is basically consistent with the astronomical observation result: the spectrum of the Andromeda Galaxy shows a blue shift towards the Milky Way Galaxy at a speed of about 300km/s. However, a large difference still exists between the two galaxies whose radiation repulsion and universal gravitation are two orders of magnitude apart. If the following three factors are taken into consideration, radiation repulsion can basically contend with universal gravitation:
(1) With a length of fewer than 107 light-years, Local Group of Galaxies (Group of Milky Way-Andromeda Galaxies) contains more than 50 galaxies. Satellite galaxies centering on the Andromeda Galaxy contains M33, M110, M32, NGC185, NGC147 and many other dwarf galaxies in Andromeda, forming a secondary group of galaxies. Satellite galaxies centering on the Milky Way Galaxy contains more than 10 dwarf galaxies including Large & Small Magellanic Clouds, Canis Major, Sagittarius, Crater 2, Draco, Ursa Major, Ursa Minor, Carina, Fornax, Auriga, Bootes, Sextans and Leo, forming a secondary group of galaxies as well. An increase in the number of stars involved in the two secondary groups of galaxies radiating each other will increase the value of their xy and enhance radiation repulsion.
(2) As a star of the second or third generation evolved from supernova remnants, the sun has a large amount of heavy matter and a small luminosity-mass ratio which is 1.934 x 10-4 W/kg by calculation. Nova and supernova are relatively large in luminosity mass, and the luminosity-mass ratio of supergiant can be 5,000 times that of the sun. The second generation of stars in a galaxy is significantly smaller than the first generation of stars in number. The error between the total luminosity and mass of the galaxy is large if the luminosity and mass of the sun are used for measurement. Thus, due consideration should be given.
(3) The silver sphere in the center of the Milky Way Galaxy has a length of about 2 x 104 light-years with large luminosity. AGN luminosity (including X-ray and γ–ray luminosity) of the galactic nucleus is about 1011 times more than that of the sun. Its mass is about 2 x 106 times that of the sun. The luminosity-mass ratio of the galactic nucleus is about 9.67W/kg by calculation. There are two AGNs in the center of the Andromeda Galaxy whose luminosity-mass ratio is a little larger than that of the Milky Way Galaxy.

6. Conclusions
(1) By estimation, the radiation repulsion between the two celestial bodies is very small compared with the universal gravitation between them.
(2) By estimation, the radiation repulsion between the two galaxies is able to contend against the universal gravitation between them. This is because a large number of stars in the two galaxies lead to superimposed radiation and increased intensity.
(3) It can be predicted that the radiation repulsion between groups of galaxies will exceed the gravitational attraction between them. In the large universe (above 100 Mpc), radiation repulsion will become the dominant force. Thus, the radiation repulsion between galaxies may be the real cause of the expansion of the universe.