Saturday, February 05, 2005

Predictions of the GUITAR theory

The GUITAR theory, Generalized Universal Information Theory And Relativity, is based on a well established quantum mechanical principle, expanded to the whole universe. In quantum mechanics, you can not go from a pure state to mixed states, nor can you go from mixed states to a pure state. What it says is the conservation of quantum information.

One of the fundamental principle of GUITAR is that the total quantum information of the universe, is a discrete, finite, and conserved quantity. Quantum information can not be created nor be destroyed.

The discreteness of quantum information leads to the uncertainty principle and other quantum mechanics principle. The finiteness of universal quantum information leads to a finite and enclosed spacetime of this universe, and results in the gravity we observe, which can be described as the curvature of spacetime. So GUITAR theory not only explains QM, it explains GR as well.

I am going to show some very specific and very accurate calculation results derived from GUITAR. All of them achieved amazing accuracy when compared against best known experimental results. Especially the calculation of neutron to electron mass ratio, accurate to 10 (TEN) decimal places.

I will show how these parameters are calculated: the effective "age" of the universe, the CMB temperature, the baryon density in the universe, the expectant value of the solar constant, the Pioneer Anormality Acceleration, and the proton and neutron mass.

All calculations will be based solely on the fine structure constant, alpha, and known parameters of an electron, and nothing else. Actually only alpha is truely needed, the electron is only needed because I needed to define the unit set to be able to make contact with the usual form of physics unit systems, i.e., I need a ruler to measure the quantity of time, length, mass, and energy.

The natural unit system is constituted by:
M0 The natural mass unit
E0 The matural energy unit
R0 The natural length unit
T0 The natural time unit

GUITAR predicts that in a given universe, the electron mass, which is the mass equivalent of the energy of the electron's field, extending to the whole universe, is inverse proportional to the logarism of the radius of the universe. That quantity is also known as the coupling constant of the electromagnetic force:
Me = alpha * M0

Since we know electron mass Me and the alpha, we can easily figure out M0. Once we have M0, the unit of energy E0 is simply mass times light speed squared: M0*C^2.

The Planck constant tells us how to fix the time unit T0:
E0 * T0 = Hbar
So, given Hbar and already knowing E0, we can figure out T0.

Once T0 is known, the natural length unit R0 is calculated by R0 = T0*C.

We list the numerical values of those units here, for later calculations:
M0 = 1.24831335(21)x10^-28 Kg
E0 = 1.12192809(19) x10^-11 Joules
R0 = 2.819740325(28)x10^-15 Meter
T0 = 9.399737148(94)x10^-24 Second

Please note, using the natural unit set: Hbar = C = 1. That makes the calculation real easier.

Previously I meantioned that the coupling constant alpha is inversely proportional to the logarithm of the radius of the universe. We can define a dimentionless constant N to describe the size of the universe:
N = PI * exp ((D-1)/D * (1/alpha)),
with D the dimention of space.
We know that the electric field is inverse proportional to the square of distance (d-1 ==2), and the space is 3-D, so D = 3:
N = PI * exp ((D-1)/D * (1/alpha))
= PI * exp (2/3 * 137.03599911)
N = 1.48982536x10^40

N is the large number Paul Dirac was searching for!!! N, which tells how big the universe is, is directly responsible for how weak the coupling of electromagnetic force is!!! Later I will also show it also tells us how weak the gravity force is!!!

With N known, parameters of the universe can be calculated (all results are in natural units)
Age Tu = PI * N
Radius = PI * N
Mass = PI * N^2
Energy = PI * N^2
Entropy = PI * S4(N) = 2*PI^3*N^3

Note here S4(N) is the 3-D surface area of a 4-D spacetime sphere, of radius equals N. Note how it is different from the Hawking blackhole entropy which says 1/4 of the 2-D space surface area of the 3-D space sphere of the blackhole, measured in Planck length unit.

From above, the density of the universe is:
P = 3*M/(4*PI*R^3) =( 3/4*PI^3) *(1/N)

Using the Einstein 's famous universe equation and:
P(critical density) = 3H^2/(8*PI*G) = 3/(8*PI*G*R^2)
P = 3/(8*PI^3)*(1/N)*(1/G)

Compare the two density expression, we get:

G = 1/(2*N)
(in natural units, certainly)

Numerical calculation verifies that indeed G=1/(2N) gives the correct value of G.

This is the first success of GUITAR, in explaining both alpha and G as related to the size of the universe, N.

What about baryon density? My derivation, which I do not intend to show here, pending a chance to properly publish my theory, would lead to the conclusion that:

1.Vast majority of the energy of the universe is known whose definite space location and time could not be detected. Only the space curvature effects can be detected. This we call dark energy or dark matter.

2.A small portion, g^Dt, constitute the baryon matter, who has a definite space location but whose existence expands the whole axis of time. Dt is the time dimention. Dt = 1, of course.

3.An even smaller portion, equal to g^Ds/PI, constitute the matter that do have a definite time (time is freezed for them) but whose existence expands the whole space). We know the dimention of space Ds = 3. This we call photons. The factor PI is a factor contributed by the geometric factor.

Therefore, the radiation energy density equals g^Ds/PI = g^3/PI, times the critical density, which we already know to be
P(critical) = (3/(4*PI^3)) * (1/N)

P(radiation) = P(critical) * g^3/PI = 3*g^3/(4*PI^4) * 1/N

My derivation of the g factor is:
g = 2/PI*sqrt(alpha) = 0.054383 = 5.4383%

g is also the baryon density as discussed above. g = 5.4383% matches the current accepted baryon density estimate of about 5% to 6%!!! Another success of GUITAR in explaining the baryon density of the universe.

Now, with g known, any one can calculate the density of radiation, which is also the density of CMB radiation. Once you obtain the density, using the Stephan-Boltzmann formula, you can calculate the CMB temperature. I leave it as a math homework for the readers to do the calculations, and to convert it from natural units to the standard units.

This web page may help relating radiation energy density to temperature:

My calculation gives
T(cmb) = 2.7243 K

Which is amazingly accurate, consider the best measured value is 2.725+-0.005K. My result is well within the margin of experimental error.

With the CMB energy density known and the baryon density known. We can attempt to calculate how much energy the Sun radiates, assuming the Sun is typical in the universe, and radiations from all stars contributes to CMB. The total baryon mass divided by the mass of the Sun is the number of stars in the universe. That number times the radiation power of the Sun is the total radiation power of the universe. That quantity times the age of the universe, equals to the total CMB energy of the universe, divide by volume and you get CMB energy density. Reverse the calculation process, and you get the radiation power of the Sun instead.

Again I leave that calculation as math exercise, though I may discuss it in detail later. These numbers may help: The earth-sun distance is 1.496x10^11 meter. The mass of the sun is 1.98x10^30 kg. Solar constant equals the total radiation power of the sun divided by the surface area of the sphere centered at the sun and reaching the earth orbit.

My calculation of the Solar constant leads to 1359.6Watts/(m^2*sec), which is amazingly accurate, considering the accepted value of solar constant is 1360W/(m^2*sec)!!!!

Enough for now for you guys to punch calculators to verify my numbers. I will talk about Pioneer anormality and the Proton and Neutron mass later. For that you will need a better calculator. At least an accuracy of 12 or more decimal places is required. Don't use a cheap crap calculator of just 8 decimal places accuracy!!!