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But first let me adopt a set of natural unit, the unit is derived by setting HBAR and C to be exactly one, and assuming the electron mass is alpha, the fine structure constant, when measured in the natural unit:

m0 = Me/alpha = 1.2483x10^-28 kgs

E0 = m0*C^2 = 1.121928x10^-11 Joules

r0 = (HBAR*C)/E0 = 2.81794x10^-15 meters

t0 = r0/C = 9.39964x10^-24 seconds

r0 happen to be the classical electron radius, but don't read too much into it. There is nothing classical.

Now, in the natural unit set, let the Newton gravitational constant G be defined as:

G = 1/(2*N)

N is a dimensionless number. Since G is not known very precisely, the precise value of N is given by:

N = PI* exp(2/(3*alpha))

N = 1.48982536x10^40

If you use the accepted value of G=6.674x10-11 to calculate N, it will be about 2% bigger. But I attribute it to the fact that we are measuring G within the gravitational field of the solar system so our measurement is slightly smaller than the true value. That also explains the Pioneer 10/11 abnormality perfectly. I will talk about that when I have time.

Anyway N is calculated from alpha, G is simply the inverse of 2N, so we have associated G with the fine structure constant. That's what Eingstein had tried unsuccessfully: to associate gravity with electromagnetic force in some form.

But our story does not stop there. Using N, we can get all parameters of the scale of the universe:

Radius of the universe Ru = PI * N

Age of the universe Tu = PI * N

Mass of the universe Mu = PI * N^2

Energy of the universe Eu = PI * N^2

Hawking Entropy of the universe Su = PI * S4(N)

Here S4 means the 3-D surface area of a 4-D spacetime sphere of radius N: S4(N) = 2*PI^2*N^3

Isn't it elegant? Everything of the universe is simply a PI times a power of N. Based on that formula, the age of the universe is

Tu = PI*N

Convert it to the SI unit:

Tu = PI*N*t0

Tu = 3.1416 * 1.48982536x10^40 * 9.39964x10^-24

Tu = 4.4x10^17 seconds

Tu = 4.4x10^17/31557825 sec/year (year)

Tu = 13.94 billion years

The Tu I obtained agrees perfectly with the accepted observational age of the universe of between 13.7 and 14.0 billion years! I obtained this number using only the fine structure constant! Actually I believe my result is more precise than the observational data.

But there are more. I will derive the precise CMB (cosmological microwave background) temperature.

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