Calculation formula of two-photon rest mass
Based on the mass-energy relationship of general relativity of space-time
e = MC(C2+γ2) 1/2( 1)
As can be seen, when the absolute velocity nu υ= c, there are:
E = m0c2 (2)
According to the formula of photon energy E = ω, we can get the expression of photon "relative rest mass" as follows:
m0 = ω/( c2) (3)
Where is Planck's constant (= 6.6253x 10-27 EGR seconds) and ω is the frequency of light wave. Here, let's say: η = /( c2), then the above formula can be rewritten as:
m0 =ξω(4)
Where η is a fixed constant, and the calculation method is: η = 5.2123x10-48g s; And ω is the circular frequency of photons in hertz (s- 1).
Application of Three Static Mass Calculation Formulas
Shall we use an example to verify whether this formula is correct? For example, it is known that the frequency range of visible light is1014-1015 hertz (Hz). Therefore, the "relative rest mass" of "visible light" photons can be obtained from Formula (4): 10-34-65438. Taking yellow light (frequency is 5.0812x10/4hz) as an example, the relative rest mass of this photon can be calculated to be about 2.6485 x 10-33g by using this formula. As we know, the electron's rest mass is about 9. 1085 x 10-28g, from which it is concluded that the rest mass of photons is about "one third of the electron's mass".
Experimental proof of four-photon static mass formula
Whether a new theory is correct or not lies not only in the correctness of logical contradiction and mathematical deduction, but also in whether it can explain known phenomena and predict new things. Here, it is necessary to prove the correctness of the formula for calculating the relative rest mass of photons through known facts, thus indirectly proving the correctness of the general theory of space-time relativity. The accounting procedure of the theoretical result of "photon has a relative rest mass not equal to zero" is as follows: firstly, the theoretical value is obtained by using the generalized theory of space-time relativity, and then it is verified by calculating the "deflection angle" of light near the sun and substituting it into the relevant formula. Let's assume that a Newton particle, with a mass of m, moves at a low speed in the plane of polar coordinates r and φ. According to Newtonian mechanics, the integral of its energy is:
( 1/2)r ' 2+( 1/2)R2φ' 2-GM/r = E/m(5)
(See Introduction to General Relativity, translated by F·R· Tan Gurui, translated by Zhu, Shanghai Science and Technology Publishing House,1February, 1st edition, pp. 25-27). Where φ' is the angular velocity of Newton particles, m is the mass of the star (that is, the sun) that causes Newton particles to deflect, e is the energy of Newton particles, m is the static mass of Newton particles, and g is the gravitational constant. According to Kepler's law, the integral of angular momentum a is:
A = mr2φ' (6)
As we all know, with the increase of Newton particle velocity, its relative static mass will gradually decrease. According to the "formula for calculating the relative rest mass of photons" proposed by the general theory of space-time relativity, if the speed of a particle is equal to the speed of light (C), then its "relative rest mass" becomes:
m0 = m / (7)
Then there is angular momentum:
Ac = m0r2φc ' (8)
There should be rφc '= c at perihelion, so the angular momentum of photon at this point is Ac = m0Rc. In order to satisfy Equation (5), there should be Ac≡A (i.e. "Law of Conservation of Angular Momentum"), so there is:
m0r2φc' ≡ mr2φ'
or
m0Rc≡mr2φ' (9)
Then from the formula (7):
r2φ' = Rc/
or
r4φ'2 = R2c2/2 ( 10)
R in the above formula is the distance from the center of mass of the sun to the perihelion. The time derivatives of the above categories can be eliminated by using the following formula
d /dt =φ'(d /dφ)= (Rc/ r2)(d /dφ).( 1 1)
Therefore, Equation (5) can be rewritten as:
( 1/2)(dr/dφ)2(r2c 2/2r 4)+( 1/2)(r2c 2/2r 2)-GM/r = E/m .( 12)
Introducing u = 1/r and substituting it into the above formula, we can get:
( 1/2)(du/dφ)2(r2c 2/2)+( 1/2)(r2c 2/2)U2-GMu = E/m .( 13)
Differentiate the above formula and move the term:
d2u/dφ2 + u = 2GM/c2 R2 ( 14)
Referring to the above calculation steps of Introduction to General Relativity, we can finally draw the following conclusions:
δ≈2GM/c2 R ( 15)
Thus, the deflection angle can be obtained:
α= 2δ≈4GM/c2 R ( 16)
This result is completely equal to that calculated by Einstein's general theory of relativity (1.75 "). It is also quite consistent with the actual astronomical observation results of 1952 (1.70 ") (see Theory of Space, Time and Gravity, [ibid.], p. 282). It is proved that photons do have a relative rest mass (m0) that is not equal to zero.
Five-knot theory
Above, we not only proved theoretically that the photon has a relative rest mass that is not equal to zero, but also calculated the value of the relative rest mass of the yellow photon through practical examples. This result is beyond Einstein's special theory of relativity. The actual calculation results show that the relative rest mass of various photons is about one millionth of that of electrons, so it is no wonder that people have not measured the relative rest mass of photons so far. In addition, the calculation results of the deflection angle of light near the sun prove that photons do have a relative rest mass that is not equal to zero. At the same time, it also shows that Newton's mechanics and Kepler's law are completely suitable for calculating the deflection angle of light in gravitational field. In the past, people used this theory to calculate the deflection angle of photons in the gravitational field, so the calculated results are quite different from the experimental results. The main reason is that there is a problem in estimating the relative static mass of photons. So Einstein's general theory of relativity is not the only correct space-time theory to study the motion law of objects in gravitational field.