Paradoxes Resolved, Origins Illuminated
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 An elegant formula for an elegant universe

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T O P I C    R E V I E W
Anthony Mai Posted - 15 Sep 2004 : 00:58:29
Physicists have all been wrong all the time, searching for the ultimate unified theory at the Planck Scale. I know it too well that the discontinuity of space and time happens not at the Planck scale, but at a scale 20 orders of magnitude higher than the Planck scale, and at a mass level 20 orders of magnitude lower than the Planck Scale.

I know this because I have unlocked the secret of the fine structure constant, and used that constant, and that constant along, to reach at the precise value of the baryon density of the universe, and the precise temperature of the CMB, which is different from the best experimental result by less than 0.025%, a precision far better than the systematic error of the experimental data. The calculation is very simple, although it is amazing in reaching such a precision, after involving dimentionless numbers of 40 to 80 orders of magnitude.

Look at an electron. Does it tell you something about the discreteness of space? Surely it does, in classical theory, if you consider electron as a point particle, and integrate the energy of the eletric field approaching the center, you will soon get a value exceeding the mass-energy of the electron, and approaching infinity as you approaches the center. You know the electrin field energy can not exceed the electron mass-energy, it must equal precisely to the electron mass-energy, so the integration must stop at a certain small scale. That scale, is where space shows discreteness, and that scale equal to the classical electron radius, 2.81794x10^-15 m.

Scientists have all been wrong in assuming the Newton gravitational constant G is a microscopic physics constant, and hence arrived at Planck Scale by setting G, HBAR, C all equal to one. G is not one! You can not derive the Planck Scale based on G equal to one, any more than you can derive Planck Scale based on the radius of the earth, or the distance from the sun to the earth, on on any other macroscopic values. Indeed, I will show you that G is a value that reflects the SIZE of the universe. The inverse of G tells us how big the universe is!

Before we do that, let me give you the basic natural units:
Length r0 = classical electron radius = 2.81794x10^-15 m
Time t0 = r0/C = 9.39964x10^-24 second
Mass m0 = electron mass/alpha = 1.2483x10^-28 kg
Energy E0 = electron energy/alpha = 1.121928x10^-11 Joules
with alpha being the fine structure constant,
alpha = 1/137.03599911

In my natural unit set, HBAR = C = 1. But G is NOT one. You will
get
G = 1/(2N), with N about 1.5x10^40

With the known value of G, you can calculate N. Unfortunately G is the worst known physics constant. It's discrepancy from the real value may be many times bigger than the officially admitted one. My estimate is the known value of G only has a precision of 2%.

The correct way to come up with N, and hence give you a correct value of G, is from the fine structure constant alpha:

N = PI * exp(2/(3*alpha)) = 1.4898254x10^40

N is the universal constant because virtually every thing of the universe can be calculated from N, when expressed in my natural unit set:
R = PI*N
T = PI*N
M = PI*N^2
S = PI*S4(N) = PI*2*PI^2*N^3, with S4(N) meaning the 3-D surface area of a 4-D spacetime sphere of radius N. S4(N) = 2*PI^2*N^3

In the above formula, T,T,M and S represents the radius, age, total mass-energy and Bekenstein-Hawking entropy of the universe.
Certainly I am not a believer of the Big Bang and my universe model is a static one, so R,T,M,S are all constants. The "age" and "radius" of the universe is simply an observation limit, we can not receive any information that's older than the universe age, or further than the universe radius.

My calculation gives T = 14.0 billion years. That's precisely the best value astronomers agree on. Notice how precise my calculation is, after involving a dimentionless number N as big as 10^40?

In my model, all energy of the universe is composed by three different forms of substance, the vast majority does not exist in any fixed time or space, their existance spread out throughout the whole spacetime of the universe, and make the space time a closed one. That's the so called dark energy and dark matter.

Then a smaller portion, let's say g, is the regular substance. They exist only at specific space locations, but exist at all times. For example, the moon, you can lok find it if you look at a specific location in the sky, but if you go back billions of years, the moon was still there.

And then, a further smaller portion, precisely equal to g^3/PI, is the substance that can only exist at specific location AND specific time. Those we call photons. The vast majority of those, coming from star radiations and turning back to dark energy and regular substance over billiongs of years, through the so called cosmetic red shift, they are the CMB, cosmological microwave background. g is the so called baryon density.

Astronomers agree g is some where between 5% and 6% Well, I can tell you the exactly value of g:
g = 2/PI * SQRT(alpha) = 5.4383%
Correspondingly, the portion of CMB energy out of the total energy of the universe is
g^3/PI
Using the formulas for the universe, as given previously, and knowing that volume of a sphere is 4*PI/3 * R^3, we can calculate the precise energy density of CMB:
u = 3g^3/(4*PI^4*N)
How elegant this formula is, it involves only N, g and PI. And N and g both depends on fine structure constant only. So we have used just the fine structure constant and PI. The precise result is:
u = 8.3122x10^-47
Keep in mind we are using my natural physics units, not the international units of length, time and energy. In natural unit,
HBAR and C are all one and can be omitted. the energy density of thermo radiation is simply:
u = PI^2/15 * (kT)^4
This leads to:
(kT)^4 = 15*U/PI^2 = 15 x 8.3122x10^-47 /PI^2
(kT)^4 = 1.2633x10^-46
kT = 3.35256x10^-12
Still keep in mind we are in the natural unit. kT is energy, so to convert it back to international unit of Joules:
kT = kT * E0 = 3.35256x10^-12 * 1.121928x10^-11 Joules
kT = 3.761331x10^-23 Joules
Put in Boltzmann constant k = 1.3806505x10^-23 J/K
T = 2.724318 K

See it? You see it? The most precise experimental value is:

T = 2.725 +/- 0.005 K

My result differ by just 0.025%, and so it matched exactly within experimental error. I reach that precision using only alpha and PI, and my calculation have involved huge dimentionless numbers more than 40 orders of magnitude big. Such precision is indisputable.

There is another, less precise way to come up with this number. We can assume the SUN is an average star, we can estimate how much energy stars like the sun radiate, over the course time length equal to the universe age. We can do the calculation using the solar constant and distance between the earth and the sun, and know mass of the sun. This radiation energy will all transform into CMB so we can calculate the CMB energy density.

I will not repeat the calculation here, but the result is also very precise, it's only 0.1% different from the accepted experimental value 2.725K.

So there is this strong proof that CMB is NOT the remains of the Big Bang, but merely star radiation energy over billions of years.

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7   L A T E S T    R E P L I E S    (Newest First)
Anthony Mai Posted - 18 Sep 2004 : 11:11:35
Correction:
"But it is true that the equivalence principle has to break down at some small scale, it is just that Planck Scale is where it happens. "
Should be:
"But it is true that the equivalence principle has to break down at some small scale, it is just that Planck Scale is NOT where it happens. "
Anthony Mai Posted - 18 Sep 2004 : 11:06:46
Jeremy:

I do not know your formula for the value of Planck constant, or the theories you talked about that relates G with h/hbar or C.

But from a fundamental point of view, any attempt to derive or calculate the specific value of hbar, C, or attempt to show a physics relationship between G, hbar, C, are by definition WRONG.

My theory never attempted to associate G with hbar and C. And I reject the idea that G is related, or can be calculated from hbar and C. If yu get the wrong impression that I am trying to calculate G using hbar and C, then I am sorry. But I can understand where the misunderstanding came.

hbar and C are both fundamental physics constants. Being fundamental physics constant means they exist by themselves without reliance on any one else. So they should naturally be considered as one in a natural unit set. They take the current none zero fractional decimal value ONLY because of the particular unit set we human race have choosen as our international unit set, for example it depends on that pile of alloy metal some where in Paris which we call 1 kilogram. Silly but true. So the SI unit set is purely incidental.

So any attempt to look for reasons of specific values of hbar and C, beyond the incidental nature of why we choose SI units, are by definition wrong. Asking why hbar = 1.0546x10^-34 J*S is the same as asking why hbar shall be one in the natural unit set.

But G is NOT a fundamental physics constant as hbar and C are. I have shown that G is actual a reciprocal number of the size of the universe. But even putting that association away G is still not fundamental. Because unlike hbar and C, which are microscopic in nature, The G, as well as the equivalence principle that Einstein's General Relativity is based on, are macroscopic only, in microscopic world both G and the equivalence principle breaks down, both necessarily by logic and reasoning, and by experimental evidence.

The Planck Scale gives us a set of very tiny length and time scale but HUGE mass scale, so huge that the Planck mass is 20 orders of magnitude bigger than masses of fundamental particles. Theoretical physicists tell us that time and space breaks down at Planck Scale. Ironically they did not tell us the same thing for Planck Mass, because of fear that all things bad could happen if they dare to say so. But if you look at Planck Mass the same way you look at Planck Length and Planck Time, basicaly what it means is for anything lighter than Planck Mass, you can no longer calculate gravity using G, and General Relativity is no longer correct, nor is the equivalence principle. And that covers all fundamental particle mass scales!!!

But it is true that the equivalence principle has to break down at some small scale, it is just that Planck Scale is where it happens. Equivalence Principle says Inertial Mass and Gravitational Mass are always equivalent and the same. Certainly any form of energy is equivalent to mass (E=MC^2), which is both inertial mass and gravitational mass. Any form of energy, that is including the gravitational field energy.

And that's where the trouble comes, gravitational field energy is an energy and so it generate gravity itself. But the gravity generated from gravity is still a form of energy and it also generate grand son gravity, even very tiny. And so on to great great grandson gravity, etc, etc.

Even worse, All those energies are negative energies, so we would have gravitons that has negative energies. A fundamental particle that has negative energy? That's weird. It means its mass is also negative. You push it one way it actually accelerates the opposite way.

The equivalence principle is in deep trouble!

The way out of this, is considering G not as a fundamental attractive force between masses, but rather, a universal effect that all the masses in the universe COLLECTIVELY encloses and curves the spacetime we are in, and then all masses travel within that curved spacetime.

My formulas show that indeed G is not a force between individual particles, but rather, a collective effect of the whole universe. Because G just happens to be equal to the reciprocal of the size of the universe!

There are good reasonings behind my formulas. But regardless whether my formula reflects some real physics, or just coincidental, the Planck Scale theoretical physicists are using are fundamentaly wrong and they have been unable to face the irony and dilemma why they accept discreteness of space and time at Planck Scale, but not mass at Planck Scale Mass.

I feel that the year 2005 will be another year 1905, the Einstein year.

--Anthony Mai
Jeremy Posted - 17 Sep 2004 : 10:12:38
Anthony, your relations may be significant or they may not. I have seen several theories relating G, h and other parameters together in relations as simple as yours and all the authors claim that this can't possibly be coincidence. Obviously they can't all be right. Human beings look for order and by golly they find it. On another thread I unveiled a formula for Planck's Constant that produces a correct number, but is it significant? I have no way to know because it was not developed from a theory but might be true nevertheless. We can only raise our eyebrow and catalog it in the back of our head when future evidence comes along.
Anthony Mai Posted - 16 Sep 2004 : 10:04:56
PI is only approximately 3.14159. PI is such a fundamental mathematical constant that anything involving any geometry at all contains PI. So it's not surprising formulas describing the basic geometry or structure of the universe contains PI.

And looks like you don't really understand natural unit. Natural unit is obtained when you set C, HBAR, and one another thing to be one. That one another thing can be either the classical electron radius, which equals to bohr radius times alpha^2, or you can set electron mass divided by alpha as the unit of mass. Either gives you the same natural unit set.

And you don't get to set G = 1 or G = 10^-39, or set G to any arbitrary number. G is just what it's value happen to be, once you fix your unit.
In SI unit G happens to be 6.67x10^-11, in my natural unit G is approximately 3.29x10^-39.

G = 1/2N is the definition formula for what N is. You can calculate N using G from this formula, provided you have precise value of G. Unfortunately we don't have a very precise value of G. Because by definition G = 1/2N, you can derive part of the set of formula for the universe, from existing theories, including Einstein cosmological equations. For example:
R = 2*G*M/C^2
is what existing theories tell us. You can confirm that using my formula set.
But my formulas is more advanced than existing theories because they nailed down the relationship between G, R, M, S. Because G, R, M, S are all related to the same N, clearly, G is a parameter related to the size of the universe.

There is no reason to believe that the size of the universe is a fundamental constant. Since there is no reason why the universe couldn't be alittle bigger or smaller. It just happen to be that big that's all.

N = PI*exp(2/(3*alpha)) is the real physics. This is not how N is defined. But it nails the relationship between N and alpha and allows us to calculate the precise value of N. Since N is associated with G, it also nails G to alpha and allows us to calculate a more precise G than what we now know.

So, even the fine structure constant alpha, is not so fundamental after all.
It also some what relates to the size of the universe.

I do not have a web site yet. My theory is still in development. But it will fundamentally change the contemporary physics research by pointing out the fact that G can not be treated as a fundamental microscopic physics constant. Theoretical researchers who work at the so called Planck Scale will not go there but they don't know why their Planck Scale is so different from the scale of fundamental particles, by as much as 20 orders of magnitude. Now I can tell them why, they made a mistake by setting G=1, that's why!
EBTX Posted - 16 Sep 2004 : 05:09:44
So, where is your web page where everything is expressed neatly ... elaborated on and generally cleaned up? If you make a web page you can control your presentation and make it much more readable.

I don't follow where PI comes into your calculation. I assume PI as in 3.14159?

I understand what you mean by "natural units". If you set C=1 and G=~10^-39 and about 1 meter as the unit length (that's the distance between two baryons if all matter were evenly spread out ... many supposed constants come with exponents in multiples of "13" (^-39, ^-26, ^-13, 0,^13, ^26, ^52, ^78) ... as though they had gotten that way over time and were functions of one another.
Anthony Mai Posted - 15 Sep 2004 : 10:31:29
Sure if you "play" with numbers, like adding correction terms like
y = 1+x-0.5x^2+0.322*x^3 sort of thing, you can get any number you want.

But I am not "playing with number". My formula contains not a single addition or subtraction, not a single fractional number, and not a single adjustable parameter. I challenge you to "play" the number and come up with something more elegant and reaches an accuracy of one in a million, like what you said.

Besides you can try the second approach I meantioned, try to calculate star radiations over the course of the age of the universe, and average the energy over the volume of the universe. All numbers are given and none-adjustable in this case: solar constant, solar mass, baryon density, universe age and diameter, etc. You will get a CMB temperature to 1 in a thousand accuracy. And it is not just a theory: stars do radiate energy and we do observer CMB. So it is a fact.
EBTX Posted - 15 Sep 2004 : 04:17:09
quote:
My result differ by just 0.025%,

If you "play" with numbers (physical constants, their dimensions, mathematical constants, etc.) you can get just about any number you want in a few hours to an accuracy of about one in a million.

Numbers are as worthless without a theory ... as a theory is without numbers which match the observed ones. Sorry, I see nothing here which answers the question ... why?

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