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The Tu I obtained agrees perfectly with the accepted 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 further show how the precise CMB (cosmological microwave background) temperature of 2.725 +- 0.005 K can be derived exactly.

To do that I need to introduce the g factor, g factor is a dimensionless constant derived from the fine structure constant:

g = (2/PI)*SQRT(alpha) = 0.054383

The g factor gives the exact baryon density in the universe, which is 5.4383% of the total mass-energy of the universe.

There are three forms of mass/energy in the universe, first there is this dark energy/dark matter, almost 100%.

Then a portion g is the regular matter, i.e., baryons.

And then there is an ever smaller portion, which is the radiation energy. The radiation energy exist in the form

of CMB radiation. That portion is:

g^3/PI

Well, we know the mass-energy and radius of the universe. Take the total mass-energy of the universe, multiply by G^3/PI, then divide by the volume of the universe, that's the CMB radiation density per volume:

U = Mu * (g^3/PI) / ((4*PI/3)*Ru^3)

Since Mu = PI*N^2, Ru = PI*N, we have

U = 3*g^3/(4*PI^4) * 1/N

The radiation energy density is related to temperature by the Stephan-Boltzmann formula:

U = (PI^2/15) * (kT)^4/(HBAR*C)^3

Since we are using natural unit, HBAR=C=1. It's real easy:

(kT)^4 = 15/PI^2 * 3*g^3/(4*PI^4) * 1/N

(kT)^4 = (45/(4*PI^6)) * g^3/N

Plug in

g = (2/PI)*SQRT(alpha)

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

We get:

(kT)^4 = (90/PI^10) * alpha^(3/2) *

exp(-2/(3*alpha))

See now it contains just alpha and PI, and no fractional number!

(kT)^4 = 1.2633x10^-46

kT = 3.35256x10-12

Remember we are using natural unit, to convert it back to SI unit, keep in mind kT is energy:

kT = 3.35256x10^-12 * 1.121928x10^-11 Joules

kT = 3.76133 x 10^-23 Joules

Last step, plug in the Boltzmann constant

k = 1.3806505x10^-23 J/K

We get:

T = 2.7243180 K

The accepted observational value for T is 2.725+-0.005K.

My discrepancy is only 0.00068K, far smaller than the observational uncertainty 0.005K.

See I derived the CMB temperature based on nothing but the fine structure constant. Isn't there new physics here.

But there are more.

QUANTOKEN