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EXACT VALUE OF THE HUBBLE CONSTANT THE MOST PRECISE VALUE OF THE HUBBLE CONSTANT

DEDUCED FROM OTHER CONSTANTS OF PHYSICS Por: Ramn Garza Wilmot garzawilmot@gmail.com April 10 of 2014 Monterrey, N.L. Mxico CALCULATION OF THE HUBBLE CONSTANT WITH AN ACCURACY UP TO THE TENTH DECIMAL FIGURE DEDUCED FROM KNOWN PHYSICS CONSTANTS. COSMIC BACKGROUND RADIATION TEMPERATURE AND ITS CALCULATION DEDUCED FROM KNOWN PHYSICS CONSTANTS. THE LARGE NUMBERS HYPOTESIS EXPLAINED. CALCULATION OF THE CHANGE OF THE ELECTROMAGNETIC AND GRAVITATIONAL FINE STRUCTURE CONSTANTS, WITH THE AGE OF THE UNIVERSE. THE FIRST PHOTON CREATED BY THE UNCERTAINTY PRINCIPLE.

INDEX Page

1.- Introduction and background.__________________________________________________ 2

2.- Basic calculation of proton and electron properties and the fine structure constant.________ 6

3.- Gravity force parameter and relation between the electromagnetic and gravitational forces. 8

4.- Planck units and a new calculation method._______________________________________ 9

5.- Calculation of the Hubble parameter and the age of the universe.______________________ 10

6.- The mass of the universe and the number of protons in it.____________________________ 11

7.- Cosmic background radiation temperature._______________________________________ 13

8.- The classic radius r of the mason.______________________________________________ 17

9.- The cosmological constant. ___________________________________________________ 18

10.- Quantitative relation between electromagnetic and gravitational forces and their change

with time___________________________________________________________________ 19

11.- Variation of values with time.___________________________________________________ 24

12.- Final conclusion and Large Numbers Hypothesis.____________________________________ 24

13.- Excel calculation table.________________________________________________________ 28

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1.- Introduction and background.

This is a review and complement of a previous analysis of the subject and practically the same, except for some corrections to the numbers and some comments of mine. It began years ago with what I called The Cyclic Universe This analysis intent to make a research on the physics history of the universe on the big picture, from the very first instants of its birth up to now. When I speak about the very first instants, I am speaking of the moment when the universe was born at the 10^(-100)seconds (1/ 10^100) sec. After the moment zero. The pretension of saying these results represent the actual universe is mine. So I will live open the option saying these results are very alike the real universe and I leave to the reader to decide if this is true or not, or at least he decided how much it seems like the real universe. I found as cause of its existence, either the mass of the universe as of the thermal background radiation, the uncertainty principle of Max Planck. I also explain the reasons for the numbers that some men of science of the kind of Arthur Eddigton, Edward Milne and Paul Dirac, who were the first modern scientists that tried to specified the universe as a whole, making calculations about its mass, the number of protons it has, its dimensions etc It is worth mention that all of them, but apparently more with Eddington and Dirac, got involved on the large numbers that the properties of the universe present. Even predicting it from empirical relationship Their idea was that it must be some kind of connection between the classical physics and the relativity with the new physics the quantum physics. Dirac was upset with the fact that there were 2 different physics without any contact among them, pretending with his Fundamental Theory get a connection among the quantum Physics, relativity and gravitation. These lead him to found quantitative relations between the electrical and gravitational forces for the universe as a whole. All based in a a-dimensional very big number, without exposing the physics reasons, except those that they were very similar to the one found for the universe and those he saw on its calculus. Eddington also explore these ideas and more recently Paul Davies whit his very interesting book The Accidental Universe Dirac formulated a number without units this way: Nd = qe^2 / 4o G me^2 4.2 e42 Eddington, more accurate, formulated Ne = ^2 q^4 / G^2 mp^2 me^2 5e79 Note: Ne from Eddington and Nd from Dirac. We must make notice that the number Eddington found is approximately the square of the number that Dirac obtained. The Intention behind all this was that Ne represents the number of protons of the universe. Other scientist saw this relation among the electrical and gravitational forces, had a fundamental importance to relate Cosmology and quantum physics and had being searching this link, that so far doesnt seem to be explained. On this paper, I present the reasons and the numbers I see for these relationships (that is, I try to explain) that in fact, link quantum physics and cosmology, at least in quantitative form. The results are numbers presented with high precision and they just depend of the values of the physics constants used to obtain them. In this case, the number I got is in fact the number of particles of what I call mason and from which is very simple to get the number of protons of the universe, knowing In this case, the mass of the mason as: m^2 = mp , me Yet, I consider more relevant for what I expose here, not the number of masons of the universe, but the proportion between electrical and gravitational forces in a number that I identified as S which differs from Eddington en the factor.

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This is a simple analysis of the relationships existing among different physics constants that allow us to glimpse the properties of the universe as a whole. Starting from this, and especially with the relationship with what has being called Plancks units, especially with the mass of Planck. These Plancks units are derived starting from what I call parameters of the gravitational and electric forces from which are derived the Plancks units with easiness. Some algebraic basic knowledge and some sundries of the classic and quantum physics will be enough to reach the objective of this writing. I consider myself that the fundamental element which leads me to these results, has being the determination of the Hubble constant starting from units which relates gravity and quantum physics in a very simple manner. In fact, the result is that Hubble constant identify by H is just a frequency of gravity which reciprocal is the age of the universe The analysis lead me to calculate the mass the universe, its radius, the number of nucleons that it contains, the temperature of the cosmic radiation background, when these things happened and what happened, and how do they change with time. Also which are the values of the parameters of the forces through the time, what relationship are among the parameters of those two forces and how can we calculate one as function of the other. And everything starting from the values obtained with the Plancks units that, after this, have a very clear meaning in our time, which at the same time are derived from these and just these physics constants: - The speed of the light in vacuum c - The Plancks constant h - The Boltzmanns constant K - The gravitational constant G It is also required the value of the proton and the electron mass at the present time, although I don't consider them as constant. This paper is not a theoretical analysis of Cosmology, neither a deep theoretical analysis of the physics laws. It is a simple analysis of the mathematical relationships among some of the constant of the physics tied to some elementary concepts of this and to the common sense. And that, nevertheless its simplicity, it has allowed me to obtain some remarkable results of the properties of universe in general , but fundamentally to be able to calculate with a high precision the temperature of the cosmic background radiation and to explain the meaning of the so call units of Planck. Such as the mass, the time, the temperature, etc. of Planck and its relationship with the properties of the proton and the electron. I must add that this analysis will take me more, and more back on time of what has being called Plancks time that as we will see, does not represent an epoch back on time, but just the reciprocal of the Plancks frequency. Thats why the term epoch, is referring to real time and make a difference with the Plancks I go far before the Plancks time. Until it had a value of 1.755281379E-99 sec., which I define as the moment when the photon number 1 emerge, carrying with it all the energy of the cosmic background radiation today and always, which value comes from the equation: Et = h/to = 3.774932982E+72 ergs This epoch and this primordial energy I got it because I obtain with high precision the actual volume of the universe and the cosmic background temperature from some physics and mathematical constants. Except with these constants which are: - Gravitation Newton constant - Plancks constant - Boltzmans constant - Light speed And with de help of masses and charge of proton and electron which I dont include as constants this analysis has being possible.

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This simple previous equation shows the origin of the cosmic radiation. It doesnt came from the annihilation of particles and antiparticles as the standard theories say. It comes from nothing less or more, than from a quantum leap that created the first super energetic photon from which all the rest come to be. This also means that this is a just one time phenomenon, that cant be repeat in a space, than once it happen, it will never happen again in another jump of the same kind. Because of this reason, it seems to me that it is not possible the creation of stable photons in function of the uncertainty Plancks principle. What could be happening, as it is seeing on the results, is that the initial photon cleaves in sons photons and the sons photons do that also, but with a difference in energy, lesser than the father photon. Even so, this does not impede the creation of real particles do to the same cause, because the results tells me that spontaneous matter creation or the increment on the number of particles is happening. Of course, these equations also resolve the cosmic background radiation in any time of the universe and of course the actual time. I define the Planck epoch not to what has being call Planck time but the real time when gravitational parameter had a unitary value. We will see that besides of the unitary value of the gravitational parameter on the Planck epoch, it does not represent any special characteristic, for I present a group of equations on which this moment are just a particular case on the variations of mass, energy, etc. All this data can be deduced from the equations of section that defines all the parameters as function of time and from which Plancks data can be obtained just by making = 1 I will begin exposing the today known as time of Planck and how it can be obtained without making the analysis that Planck use. For all this, I begin exposing what I think are really physics constants in the sense of their invariability in time to differentiate them from those which are not. That comes from the fact that the really constants, are not properties of matter but truly single conversion factors among those properties. Seen on this way, I enumerate again the invariable physics constants I will use: - The speed of the light c that relates mass and energy. - The gravitational constant G that relates the mass with the force of gravity. - The constant of Planck h that relates the energy with time. - The constant of Boltzmann K that relates the heat energy with temperature. You must notice that I have NOT included as constants, the mass of the proton mp, and the mass of the electron me and the fundamental electrical charge qe. Although I took these values, as characteristic of the current age. (About 13,600 million of years after the Big Bang. Lastly, I manifest that all this is based on the cgs system of units, where the units are: the centimeter, the gram and the second. The unit of electric charge is that of the electron or electrostatic unit of charge. The temperature is shown in degrees Kelvin or absolute. And to end this prologue, I also clear up that here I have taken as postulate that the universe is tri dimensionally spherical since I use for its volume 4/3 R^3

ANTECEDENTS Taken from: http://estudiarfisica.wordpress.com/2013/08/25/los-systems-of-unit-geometric-natural-and-of-planck / And from Wikipedia:

Units of Planck The Units of Planck or natural units, is a system of units first-time proposed in 1899 by Max Planck. The system measures several of the fundamental magnitudes of the universe as: time, length, mass, electric charge and temperature, by making use of five universal physics constants of the chart to take the value of 1 when equations and calculations are expressed in this system.

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The use of this system of units brings several advantages. The first and more obvious is that it simplifies the structure a lot of physics equations because it eliminates the constants of proportionality and makes that the results of the equations doesn't depend of the value of the constants. On the other hand, it can be compared more easily the magnitudes of a great deal of different units. For example, two protons are rejected because the electromagnetic repulsion is a great deal more strong that the gravitational attraction among them. This can be proven when seeing that the protons have a charge of a natural unit of charge, but their mass is much smaller that the natural unit of mass. It also allows, avoid enough problems of rounding, mainly in calculation. However, they have the inconvenience of that when using them, it is more difficult the notice of dimensional errors. They are popular in the area of investigation of general relativity and the quantum gravity. The Plancks units usually are named in a humorous form by the scientists as units of God, because they eliminate any anthropocentric system of units.

Expression of physics laws in Plancks units

Universal Gravitation Newton law

Becomes:

Using Plancks units

. The energy of a particle or photon with radial frequency on its wave function.

Becomes

The famous mass-energy Einstein equation.

Becomes

(As an example, a body has a mass of 5,000 mass Plancks units has an intrinsic energy of 5,000 energy Plancks units on its full form.

Becomes

Plancks units system:

The previous system is based on assuming some certain constants equal to the unit (1) by agreement to relate other magnitudes through it. However, one usually finishes wondering why these 5 if we really speak of important constants at fundamental level or if they are the result of other more basic ones. Then, so arise the intent to obtain a unit of longitude starting from the well-known longitude of Planck:

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To get the coefficients , we just create a vector which have as component the power to which it has to be

the exponents of meters, seconds and kilos each one and we set the system of equations.

This imply that:

Basic Plancks Units Giving the value of 1 to the five fundamental constants, the units of time, longitude, mass, it charges and temperature are defined this way:

Name

Dimension

Expression

Value (SI units)

Planck length Length (L)

1.616 252(81) 1035 mt

Planck mass Mass (M)

2.176 44(11) 108 kg

Planck time Time (T)

5.391 24(27) 1044 s

Planck charge Electric charge (Q)

1.875 545 870(47) 1018 C

Planck temperature

Temperature ()

1.416 785(71) 1032 K

Notices: until here, reference to the web pages mentioned is ended.

2. - Basic calculation of proton and electron properties and the fine structure constant. Next I proceed to analyze how to obtain the units of Planck, without appealing to reduce at 1 the 5 basic units that he used. For these, I use the cgs system of units (centimeter, gram, second) and the electrostatic unit of fundamental charge where the constant of the force between two charges is the unit. The notation A^n will mean that A (the magnitude A) is rise to the n power. We will see how the units of Planck are related with the general properties of the universe, such as the microwave background radiation temperature, the mass, the Radius of the universe and some other more. A. Einstein deduced starting from the photoelectric effect that the light exists in discontinuous form, in packages of energy of the so called quantum, on which the energy of this quantum is defined as function of the frequency of the light and the constant of Planck.

This energy can be expressed in two like forms:

E = .w being = h / 2pi , h is the constant of Planck and w is the angular frequency of the light in radians per second.

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E can be also expressed as;

E = hf in this case f is the frequency of the light in cycles per second or Hertz

Of course, w = 2(pi). f and h is expressed in ergs-seg.

The photon doesn't have rest mass, nevertheless, as it poses energy it is possible to attribute mass to it, such that: Ef = mf. c^2 = h.f so mf = h.f / c^2 Now then, the frequency and the speed of light are related by c = f. and in consequence: = h / mf. c The same equation = h / mf.c is used to define the wavelength of quantum particles as the electron and the proton, being defined as Compton wavelength of the particle. And then: = h / m. c (2-1) The equation (2-1) is a particular case because in general and according to the foundations of the quantum physics, the wavelength of a particle is defined for the speed of it. That is to say for: = h / m v Then we have that: + = h / mp. c (2-2) - = h / me. c (2-3) As the Compton wavelengths of proton and the electron respectively, being mp and me the masses of each one of the 2 particles. Now, let us multiply among them the equations (2-2) and (2-3) + = h / mp.c X - = h / me.c +. - = h^2 / (mp. me) Let us make now that ^2 = + X - and m^2 = mp X me and we obtain a wavelength that I will call wavelength of the mason being the mass of this mason the square root of the product mp x me : = h / m.c (2-4) Here I want to make notice that the mason m is not a real particle. It is an assistant particle to make the calculations and that it is necessary to manifest some important properties of the Universe. From (2-4) we obtain other very simple derived magnitudes, all corresponding to the mason: f = c / (2-5) E = m.c^2 (2-6) E = f. h (2-7) As its seeing, they are just as they were defined, except that we refer to the mason in this case. Let us enter now into other definitions, just as the so named classic radius of the electron. This is defined for: q-^2 / r - = me. c^2 or For the proton q+^2 / r+ = mp. c^2 and: r - = q-^2/me. c^2 (2-8) r+ = q+^2/mp. c^2 (2-9) As we did with the wavelength, let us multiply both radii among them and we obtain r = q^2 / m. c^2 (2-10) In this case we use q^2 instead of q+ X q - since the magnitude of the electrical charge of the proton and of the electron are of the same magnitude.

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Now : let us divide the equation (2-4) with the (2-10) and we obtain: (h /m.c) / (q^2 / m.c^2) = h.c / q^2 This magnitude, h.c /q^2 receives a special name: reciprocal of the fine structure constant . I won't stop to explain what it means, except in the fact that it is a constant that defines the magnitude of the electric force and that it is the same for the proton and for the electron, because they have the same magnitude in their charge. The fine structure constant is generally defined with and not with h. but the difference is because the system of units used. In this case, because the exposed reason, I will call it just as the parameter of the electrical force, than we will see, it is not constant in reality. Therefore: @ = h.c / q^2 (2-11) Where the value of this @ is approximately 861 (for the time being, this approach) and the reciprocal of the fine structure constant is @ 2 pi / 861 1/ 137 From this we obtain: = h/m.c = h.c / m. c^2 = h. C. r / q^2 = @. r (2-12) Being r as it was explained, the classic radius of the mason, a longitude with a fundamental importance for what is exposed next in this writing. The electrostatic energy between a proton and an electron at the distance r (classic radius of the mason) is: Ee = (q1 x q2) / r q1 correspond the proton and q2 to the electron As q1 X q2 = q^2 then, Ee = q^2 / r But q^2 / r = m.c^2 = h.f Then the electric frequency f of the mason is: f = q^2/r. h (2-13)

3.- Gravity force parameter and relation between the electromagnetic and gravitational

forces.

Now, entering the gravitational energy between a proton and an electron at the same distance r of the previous item and in order to compare the magnitudes of the electrical force against the gravitational one. I will be defined: Eg = G. m+m - / r Eg = G. m^2 / r Where m^2 = (m+) x (m-) or m^2 = mp X me (3-1) And if Eg = F h being then F the gravitational frequency: F = G m^2 / h. r (3-2) It may be noticed that on the previous equation, the product F.h is the potential gravitational energy between an electron and a proton at the r distance.

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It is also necessary to make notice that in this system of units, G the gravitational constant it is not unitary. As in the case of the electrical charge, I here named parameter of the gravitational force as: + = h.c / G.mp^2 and - = h.c / Gme^2 that takes us to: = h.c / Gm^2 (3-3) When multiplying one with the other: Let us now divide the equation (3-3) by the (2-11) and we obtain a constant that it relates the magnitude of the gravitational forces with the electric ones whose terms are:

S = q^2 /Gm^2 = /@ = 2.26881627e+39 (3-4)

I must make notice that the magnitudes of the parameters of the forces of are inversely proportional to the magnitudes of the forces itself, and this way although is bigger today than @, the gravitational force is S times weaker the electric one. Now, I list the basic constants values and the deduced from it: The values I use, are those that come from. http://physics.nist.gov/cuu/Constants / a) Fundamental: Fundamental electric charge: q = 4.8032045057 e-10 eu mass of proton: m+ = 1.6726217770 e-24 gm mass of the electron m - = 9.1093829100 e-28 gm Constant of Planck : h = 6.62606957 e-27 erg-seg speed of the light in vacuum c = 2.99792458e+10 cm/seg Boltzmann Constant K = 1.380648800 e-16 erg/kelvin Gravitational constant G = 6.67384 e-8 erg-cm/gm^2 b) Deduced: Parameter of Electrical force @ = 861.02257731 Parameter of Gravitational force = 1.95335035241 e+42 mason radius r = 6.5762366097 e-15 cm mason Compton Length wave = 5.6622877533 e-12 cm Frequency of the mason f = 5.2945464989E+21 cps mason gravitational radius rg = 2.8985295821E-54 cm gravitation / elect. parameter S = / @ = 2.2688180026 e+39

4.- Planck units and a new calculation method. Let us enter into the subject: Let us accept the basic ideas of the Big-bang and let us establish down that in a remote past, the fundamental forces (4) were unified. Since the difference among the magnitudes of these two mentioned are today very big, (as we have seen among and @), then we conclude that, in the past and by reason of this unification, the magnitudes of the parameters were smaller than they are today. That is to say for example would have tendency to be equal to @ if we go backwards in time. Let us take then in fact, that there was a time when 1 = 1 And by the definition of we arrive to : G m1^2 = h.c

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Where m1 was the mass of the mason when 1 = 1 Then: m1 = (h.c / G)^(1/2) = (the mass of Planck) (4-1) That is to say that the mass of Planck is that when = 1 and it proceeds from the value of the mason. Even more, it was the mason then. Even if or m1 are the square roots of (h c / G), it doesnt mean that it exist a negative as there are not a any negative m which come from the product mp x me, there is not the case ^2 = + X - Note that except for the use of h instead of , = m1 is equal to the value of the mass of Planck but in another system of units. The same thing happens with the other units of Planck of the chart 1, provided is use the cgs units system. We see therewith, how we can obtain the values of the units of Planck without appealing to make unitary the 5 used by him. and since ^2 = h.c/G = . m^2 then:

= ^(1/2) x m (4-2) Therewith in mind, the data of the chart 1 are easily derived just making the substitution of h by I repeat: is the mass of the mason with current value of m = (mp * me)^(1/2) lp is the Compton wavelength of fp is the Compton frequency of ep is the energy of etc, etc. In other words, I say that the mass of the mason is NOT constant. It has diminished from on the epoch of Planck to m today. And in consequence the masses neither of the electron and the proton are constant. One of the consequences of the values obtained for the longitude of Planck, is that it acquires the same value with different forms of calculation. On this way: = (h.G /c^3)^(1/2) = 4.0512107518e-33 cm In summary: lp = h/.c = G./c^2 = 4.0512107519 e-33 cm = (h .c / G)^(1/2) = 5.4556996321 e-5 grams p = lp = h / . c = (h G / c^3) ^ (1/2) = 4.0512107519 e-33 cm fp = c / p = (c^5 / h. G)^(1/2) = 7.4000706545 e+42 cps tp = 1 / fp = (h G / c^5) ^ (1/2) = 1.3513384489 e-43 seg ep = h. fp = (h.c^5 / G)^(/2) = 4.9033382980 e+16 erg

5.- Calculation of the Hubble parameter and the age of the universe Let us see the equation (3-2) with values:

F = 2.3336144604e-18 cps (5-1)

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That corresponds to a wavelength L of 1.2846700391e+28 cm since L = c/F Also an energy e = F. h = 1.5462691764e-44 ergs (5-2) And a mass of mg = e/c^2 = 1.7204564817e-65 grams (5-3) It is to make notice, that this last mass of the gravitational energy between proton and electron possibly is of a virtual particle of exchange, whose life time is the age of the universe and whose Compton wavelength is equal to the radius of the Universe. In fact, calculation of give us: g = h / (mg. c) = 1.2846700391E+28 cm Does this last mass is the graviton? (5-3) We can say that the radius of the universe is the wave length of this virtual particle. The interesting thing of the equations of this section and first of all the (5-1), is that expressed in kilometers per second by megaparsec, corresponds to the value of the Hubble constant measured at this time, that is to say: 1 mega parsec = 3.08567758E+24 cm 1 km/sec/ 1 megaparsec = 100000/3.08567758 E+24 sec^(-1) = 3.24077929E-20 seg. With easy we get : 2.3336144604E-18 sec^(-1) = 7.2007818230E+01 km/sec/mega parsec. constant de Hubble H = 2.3336144604E-18 sec^(-1)

H = 72.00781823 km/sec/megaparsec From this we can obtain the current age of the universe as: = 1 / H in years of 365.256363004 days = 1.3578736473e+10 years About 13,578 millions of years, making clear that when I speak of current age, I defined it as epoch, the time that has passed since the B.B. And the wavelength corresponds to the Radius of the universe R = 1.2846700391E+28 cm. I cannot explain why the equation (5-1) represents the Hubble constant. But I can say that its value coincides remarkable well with the most recent value of it. Maybe what the equation really represents is that the mass m^2 = (mp x me) varies with the reciprocal of time and in fact, the Hubble constant is the reciprocal of the universe age. A direct implication of the previous is that the universe is expanding at the light speed in all moment,

6.- The mass of the universe and the number of protons it has. It must be notice that you can calculate the mass of the universe, its density, the number of protons and electrons easily with these values. Just only with the values of the constant of the gravitation, the speed of the light, the constant of Planck, the masses of the proton and of the electron and the fundamental electrical charge as the following simplified way: W. G M^2 / R = M C^2 R = W GM/C^2 (6-0)

According with what I have seen, W has being use with different values depending of the theory in use. In the case of Friedmann equation:

H^2 = 8 G /3 C^2 - K/ R^2 + C^2/3

If we consider a flat universe, with the constant of curvature zero and if the cosmological constant also zero, W = 2 in such a manner than :

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R = 2 GM/ C^2

And this is supposing that the total energy of the universe is constant as consequence of an adiabatic expansion (no energy supply), but on this case I am proposing, universe energy is not constant, it has being growing up since de Big Bang.

To decide which W to use on (6-0), I departure from some simple assumptions and self-evident (At least for me):

- The universe is all there is and self contained.

- All form of energy is contained in the universe, including light and cosmic radiation.

- Nothing can escape from the universe, not even the light. If something could get away, there the universe would be. In consequence, the universe is a large black hole, the biggest one.

-On a black hole, energy from out coming photons is lost completely. Considering a photon with an energy hf and considering also that gravitational energy on the surface of a black hole is GMm/R being M the mass of the black hole, R its radius and m the mass trapped by the hole which in this case is hf/C^2 = m, then:

h f = G M m/ R

h f = G M (hf/C^2)/ R

R = G M / C^2 (6-1)

Then W = 1 and R is the radius for the universe, M is its mass which volume is:

Vol. = 4 / 3 R^3

Density = M / Vol = 3 C^2/(4 G) R^2 = 1.94802218087E-29 grams/cm^3

But C^2/R^2 = H^2 and then = 3 H^2/ 4 G Also M = C^3 / GH = 1.7300442483E+56 grams

If N (quantity of masons) = N

N = M/m = R.C^2/(G . m) = C^3/(H. G. m) = (h.C/ G.m^2) X (r. C^2/G.m) N = x q^2/ G m^2

N = S = ^2/@ (6-2) Since M = Np X mp and also M = (^2/@) x m And if m^2 = mp X me and D = mp/me, is deduced that :

Nprot = (^2/@) / D^(1/2)

Nprot = 1.0343308165E+80 actual In consequence, the number Np of masons at Plancks epoch was: Np = 1/@p (6-3) That is, the reciprocal of the parameter of the electric force in the time of Planck. We see then, that the values of the units of Planck, corresponds to the current values, just by using the parameters of the corresponding forces, that is to say:

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Remembering that in the time of Planck = 1 and = h.c / G.m^2 on any time becomes m lp becomes fp becomes f ep becomes energy of m rp = lp becomes r classic radius p = 1 is transformed in the current Sp = becomes current S Tp becomes current T Notes: In the last case of microwave background radiation temperature, I pass to calculate it in the following item. So the units of Planck have a very clear sense, they are the values of those units at the current time as they were at the age or epoch of Planck Note: Recent cosmological research speaks about an expanding accelerating universe instead of the opposite as it should being expected because gravity, and that in the future, galaxies we can see today, will be moving faster than light and we wont be able to see it any more. In my personal opinion, these ideas are wrong. I dont consider myself an expert in this subject (by far), but it seems than some of these ideas are in flagrant contradiction with what is already known. I dont see any special reason to abandon the special relativity concepts about the limits for matter to have a speed faster than light. It has been said (to avoid contradictions), that galaxies are not moving, but is the space what is growing. But to me whatever they said, if the distance among galaxies is growing, is because they are moving. If I take without accepting that a galaxy could be moving at a speed above the light speed, light emitted by the galaxy would be moving at the light speed and eventually will reach us. So this assert is absolutely false. So, never a galaxy will go out of the possibility of be seeing, because what I said and because as far as it is in the future, Hubble constant will be smaller and so the product HxR will always be C.

7. The temperature of the universal background radiation. Let us begin making notice that the temperature of Planck can be deduced from the energy of Planck, as equal to the mass energy of the mass of Planck because its value comes from the following: We know that, when two opposed particles interact, that is to say matter and antimatter, they disappear leaving of radiation that carries the energy of both, the temperature of the process it is:

T = b / o law of Wien Where b this defined by: b = h.c/z.K z is the solution of the equation (5 - z)e^z = 5 z = 4.965114231740001 K is the constant of Boltzman, o it is the wavelength to which the electromagnetic emission of radiation is maximum in a black body at the temperature T. fo is the frequency corresponding to that wavelength o, equal to fo = c / o

T = h.c /z.K. o = h o / z.K T = h.c /z.K.o = h.fo/ z .K

Since h.fo is the maximum generated energy equal to 2mi.c^2 where mi is the mass of the particles that interact:

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T = 2 mi.c^2 / z.K (7-1) The one that applied to give us: Tp = 2 c^2 / zk (7-1) Tp^2 = 4 ^2 c^4 / z^2 K^2 = 4 h.c^5 /G z^2 K^2 Tp = 2 (h.c^5/G)^(1/2) / z.K (7-2) Equal to the temperature of the chart 1 except that this chart doesn't take in count the value of 2/z This temperature has a value of 1.4305471683e+32 degrees Kelvin and it presupposes the annihilation of 2 masses of Planck, but with a total energy of Np masses . A number that I will determined ahead. It must be noticed I said equivalent to two masses of Planck, but I dont mean that two masses really annihilated each other. Now, from the definition of = h.c/Gm^2 = h.r.c/Gm^2.r = (h.r/Gm^2) .c/r = c/r. H = R/r Then = R / r (7-3) Which means, is equal to the Radius of the universe R in any time, divided by the classic radius of the actual mason r? Which I consider, without proving it right now, is universal constant.

Rp = r Rp is the radius of the universe at the epoch of Planck. Also, since: r.c^2 = q^2 / m = constant (7-4) It is deduced that: r.c^2 = qp^2 / and qp^2 = r.c^2 = h.c / @p notes: qp is the unitary charge at the epoch of Planck @p = h.c/ r. c^2. @p = p / r @p = 6.1603791167E-19 That it is the value of @ when = 1 Then: Np = 1 / 6.1603791167E-19 = 1.6232767191E+18 That it is the quantity of masons at the epoch of Planck (not the Plank time) Note for the English translation: The time of Planck is not the age of the universe at that moment. It is just the inverse of the frequency of Planck in rad/sec. I will leave in undoubtedly that: p = h. r / G. ^2 = 1/ Hp = 2.1935962436E-25 sec Defines the age of the Universe when m = and fp = Hp tp = (h.G / C^5)^(1/2)

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Defines the time Planck, that is the inverse of the frequency of Planck, NOT the age of the universe when m =

= h.r / G m^2 (7-5) Defines the age of the universe in any moment when it has been defined or specified the value of m. Then the Mass of the universe in the age of Planck was: Mp = Np. = 8.856110199E+13 grams I use Capital Letters in referring to the Universe properties. The Radius was Rp = r = G.Mp /C^2 = 6.576236097E-15 cm. That is to say equal to the classic radius of the mason, obviously a constant characteristic of the universe and Mp is the mass of the universe in the age of Planck. The temperature of Planck it is the temperature that would be generate by the annihilation of 2 . This temperature will allow us to calculate the density of generated heat energy. This it is calculated with the formula of Planck: Density of thermal energy Det = 8^5 (K.T)^4 / (15. h^3 C^3) With a value of Det = 3.1685430751E+114 ergs / cm^3 when T = Tp Being the volume the Universe in the age of Planck equal to (4/ 3) Rp^3 This would be 1.1912990606E-42 cm^3 And the total heat energy in the age of Planck equal to the density of heat energy multiplied by the volume: Etp = 3.7746823888E+72 ergs (7-6) Energy that, certainly would remain constant along the full history of the universe. Being established down, that this energy is conserved and is given by: Det(p) X Vp = Det current X current Vol (Tp)^4 X Rp^3 = (Tact)^4 X Ract^3 (7-7) Or what is the same : T^4 X R^3 = 1.1910799613E+86 kelvin^4 X cm^3 (7-8) That is to say, when conserving the energy, the temperatures and the radii are defined for (7-8) Then we can calculate the value of the temperature of current background radiation as consequence of the conservation of the heat energy:

Tact = Tp X (Rp / Ract)^(3/4) We can also see it of this other way: As = R/r (7-3) Then do of (7-7) (Tp/Tact)^4 = ^3 (7-8)

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And because according to (7-2) Tp = 2 (h.C^5/G)^(1/2) / z.K And because = h. c/Gm^2 it is deduced that: (Tact)^2 = 4 h.C^5/(G.K^2 .z^2 .^(3/2)) (7-9) The previous equation is general and it is valid for any time in which is known Vg: in the Planck epoch when = 1 and T = Tp From this equation we can get another that had being already obtained in another analysis, but here I get it with better of support. KzT = 2 {h c / G m^2}^(1/2) X{m C^2/ ^(3/4) = 2 m C^2/ ^(1/4)

K.z.T = 2 .m .C^2 / ^(1/4) (7-10) And replacing for its value gives us: T = {(16.G.m^6.C^7)/ (h.(Kz)^4)}^(1/4) (7-11) That it can be expressed as: T = m^(3/2) (7-12) Being = {2 G^(1/4) C^(7/4) }/ {(h)^(1/4) Kz} constant (7-13) = 3.5499848873E+38 Kelvin / gm^(3/2) T act 2.7377357857E+00 degrees K (7-14) That tells us that the value of the temperature of the background radiation depends exclusively of the mass of the mason or rather, of the quadratic mean of the product of the masses of the proton and of the electron. The equation doesn't say what causes what. That is to say, if the reduction in m is cause by the reduction in T or vice versa. It just expresses a dimensional relationship. The actual measured temperature of the background radiation it is 2.72548 0.02 Kelvin That is, it can go from 2.708 to 2.748 kelvin. Or what is the same, the calculated temperature is inside the range of the actual measurement. Now then, since the temperature can be expressed as function of m, and in function of (the time), we can find an expression for the temperature as function of the age of the universe. Everything is a matter to combine the equations (7-12) with the (7-5) From where: (T/ )^(4/3) = m^2 y m^2 = (h r / G) / The result is: T = K1/ ^(3/4) (7-15) Where is the age of the universe in seconds and Constant K1 = {2^4 h^2 r^3 C^7/(Kz)^4/G^2}^(1/4) = 4.58532205571E+13 K degrees. sec^(3/4) For example: for the time of Planck and making use of (7-15) when p = 2.1935962436E-25 sec Tp = K1 / p^(3/4) = 1.4305471683E+32 degrees K

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And for the current age when act = 1 / H = 4.2851979921E+17 sec Tact = 2.7377357857E+00 degrees K Let me attach here a section of an article that I took from the Internet where a Hindu scientist measured the background radiation at such distance that the age of the universe was 2, 760 millions years. Ref: http://adsabs.harvard.edu/abs/2008A%26A...482L..39S Ref. http://astroverada.com/torres/pubs/files/la_RCF_torres.pdf For that, he used Measurements of the spectra of the coming light from gas clouds of intergalactic carbon monoxide (CO). They revealed a temperature of growing CBR with distance. Srianand and other [12] measured the temperature of the CBR when the universe had an age of 2760 millions of years ( redshift z = 2.418). The temperature could be determined analyzing the spectrum of the absorbing lines in these clouds. The result of this measurement is a temperature of 9.15 0.7 degrees kelvin, which is consistent with the value of 9.315 Kelvin that the theory predicts of the big bang for that time OK, 2,760 millions of years are 8.7039360000e+16 sec. Those that applied to the equation (7-15) result in a temperature of: 9.048782372 degrees K A temperature with a difference of 0.10 Kelvin degree, quite consistent regarding the measurements. Where I differ of the standard theory, is that it says that at the 400,000 years the temperature was of 3,000 Kelvin (I have read of 360,000, 60,000 years etc. Without consistency in this figure) or decoupling temperature between photons and electrons and I obtain at that age 6,850 kelvin. On my results, the decoupling happened until the 1,203,000 years of age, which is 3 times more , when the temperature was of 3000 Kelvin I do believe that the results differ because the standard theory supposes that the temperature of Planck was reached in the time of Planck , but I already show that this is not right, because it confuses the inverse the frequency of Planck with the age the universe when was unitary. And also for the accepted mass conservation which is not right in my case because it is variable. And I would not be able to know what would be the decoupling temperature when the charge and the mass of the protons and electrons were bigger than what they are today. It is possible that it would be higher than 3000 Kelvin when the mass of the mason was bigger.

8. The "r" the classical radius of mason. A direct consequence of this is that when = 1 in the Planck epoch, the radius R of the universe was equal to "r", the classic radius of current mason and, and it would be constant, a very special constant. As the value of the mass of the current mason does not have any special feature since it is variable, I must conclude that "r" is a constant magnitude over time. This is provable just taking as true that the total thermal energy of the background radiation is kept constant throughout the entire history of the universe. Without knowing any reason why this should not be true. You just use the equation (7-7) that I discuss a little before: (Tp) ^ 4 X Rp ^ 3 = (Tact) ^ 4 X Ract ^ 3 and use the other known: Tact values = 2.7377357857 current temperature in Kelvin Tp = 1.4305471683E+32 Planck temperature R = 1.2846700391E+ 28 cm Radius in cm universe today. R = 6.5762360970E-15 Radius of the universe in the epoch of Planck Rp = R.(Ta/Tp)^(4/3) But according to (7-3), also: Rp = .r.(Ta/Tp) ^(4/3)

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with: = ^(1/2) x m and KzT = 2 m c ^ 2 / ^(1/4) we arrived at: (T/Tp)^(4/3) = 1/ and Rp = .r (Ta/Tp)^(4/3) is reduced to: Rp = r = 6.5762360970E-15 cm constant

9.- The cosmological constant. Just as interesting note and without pretending otherwise, the cosmological constant of Einstein has units of cm^(-2) and an estimated value of 1X10E-56. On the other hand the inverse of the square of the universal Radius = 1.2846700391E+28 cm is 0.60592212191E-56 cm ^(-2) . Can It be speculated that?

1/R^2 If this previous relationship were true, it would explain the famous "inflation" but not as an introduction "ad hoc" to Cosmology, but as an inevitable consequence of the fact that the radius of the universe was initially immensely small and therefore the force exercised by the expansion in those first moments was immense. Such a force would still exist, but with very low strength due to the current size of the universe, its RADIUS. Since I have calculated that the radius of the universe when emerged the first photon was of the order of 10^(-90), then the cosmological constant would be of the order of 10^(180) and 10^30 in the time of Planck. It has being noticing by current Cosmology and the conclusions of A. Einstein which I believe are based on assuming that the amount of matter in the universe is constant and on the basis of general relativity, there is a number called the critical density of the universe, which defined to compare it with the actual, if the universe is closed or open or flat. In the sense that if the actual density is greater that the critical, the universe is closed and will collapse in the future, if the density is less that the critical, the universe will expand forever, and if it is equal to the critical is a flat universe that will expand also but will stop at an infinite future. Description which I believe is something unreasonable, therefore does not distinguish between the open and the plane. One says that it will expand forever, and the closed will stop expanding after an infinite time. This critical density is defined by the half that I have calculated. But its value depends of the square of the constant of Hubble and thus depends on a bad measurement of H (for example a 10% error, give us an error in the density critical 19%) as you want it to be. The point here is that the observed density of the universe is insufficient for more than around 5% of the critical (with the value currently measured H) the remainder (compared with the critical) is the problem named "lost mass". In truth, these classic concepts of Modern Cosmology seem to me that sometimes they are very rare and I talk more of theorists than the practical. See these obvious cases: -The radius of the universe expressed as R = K GM/C^2 How can you talk of expansion of the universe and at the same time maintain constant the mass with this equation? It is obvious that if R is growing any of these things happens: G grows, M grows, C is reducing. But you can't keep constant parts of the 2nd member of the equation and at the same time talk about expansion. - How can we speak of a critical density if at the same time we recognize the expansion? If the universe is expanding is evident that density has already undergone the closed case, the critical and will be open -How can we say that in the Big Bang matter density was infinite or very large if you want, without explaining where this matter and this energy came? Or matter has always existed or not. If there has always been why we talk about a B.B? And if he has not always existed why they rejected the ideas of Bondi on the spontaneous matter creation? - If it weren't enough, now is added to the cosmology that the universe is larger than the distance that light can travel in the time elapsed since the B.B. contradicting them self with infinite universes in size and at the same time accepting the relativity equations, twisting relativity, by saying that the speed of light as a limit does not apply to the space, using the constancy of the speed of light as it suits them. - Also now is added that the universe is accelerating due to the pressure of the cosmological constant, but leaving aside that this acceleration is observed on very far away object showing what happened before, in the past. It was accelerated in the past, and if you want to know what happens today should think backwards. If it is seeing accelerated in the past, is slowing down in the present, and if it slowing down in the past it is accelerates in the present.

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If the cosmological constant is in fact the reciprocal of the square of the radius of the universe, then it is decreasing and the universe is slowing down, but it will not do so completely unless the radius reaches a maximum and the cosmological constant to a minimum. If it does not, it will go on expanding forever in a flat universe. I can only remember the childish problems of the middle ages, where the "wise man" of then were arguing over how many angels could dance on the head of a pin. Now, see the comment of Paul Davies and John Gribbin in their book "The Matter Myth" the paragraph that I transcribe from the original translation when they talk about the origin of the matter in the universe: Chapter 5 where has all the antimatter gone? (Free translation) "At the beginning there was energy and energy created particles and anti particles." Because of the asymmetry discovered by Fitch and Cronin, however, for every billion of anti particles that were created, a billion plus one particle were also created. When the universe cooled, all anti particles annihilated with their corresponding particles, and just left too much of a part in a billion particles unscathed. These survivors were immersed in a sea of gamma radiation when the universe was young, with billions of photons of gamma rays more or less for every particle of matter. When later the universe expanded and cooled, this gamma radiation also cooled to degenerate into the normal hot radiation. In fact, the famous cosmic microwave background that still fills the universe today is a relic of that primitive gamma radiation. In this paragraph the shortcomings of the arguments are."At the beginning there was energy and energy created particles and anti particles." Using something that they do not know where it came (energy), speculating about the creation of particles and antiparticles. Because of this energy, it was created a billion (10^9)anti particulate per every billion plus 1 particles. It was annihilated a billion of anti particles with the corresponding billion particles and it was only 1 of those two billion particle and anti particles which what left to explain the existence of matter today. Again, the deficiencies. By which reason that imbalance? No reason at all, just that it was necessary to explain that there are today a billion photons by every proton. Annihilation energy supposed to be that of the microwave background. On the other hand, if it was annihilated a billion particles and antiparticles, why all the background energy of microwaves is not a billion times more than the energy of whole matter? Although today there are one billion more photons that matter. Just compare the energies of the microwave background temperature of 2.73 Kelvin in the whole universe with the total energy of the matter and the great error will be noticed. Anyway, back to the topic. If the experimental results (in which there is to be believe and taking into account the possibility of measurement errors) show evidence of the existence of matter or dark energy that can explain the structure of galaxies, the measured amount of matter or better said, observable matter density is 8.46e-30 according to Wikipedia http://es.wikipedia.org/wiki/Universo_observable Which compared with the value that I've calculated 1.9480218087E-29 grams / cm3 is only 2.3 times lower and only 1.15 times lower if Einstein's equation is used. Then I would say that this is a problem that does not exist. In any case it should be explain only 15% and not 95% mass loss. And this would be distributed between protons and electrons created by the uncertainty principle as I explained previously, scattered through space waiting to be integrated into nebulae and stars.

10.- Quantitative relation between electromagnetic and gravitational forces and their

change with time.

Now then, let us see the relationship that exists among the 2 parameters of the forces, electromagnetic and gravitational. Follow these simple reasoning: @ = h.c/q^2 = h.c / (m.rc^2) = h /m.r.c Since h /r.c is a constant value in time, it is simple to see that @ depends only of the mass so: (10-1) @ = A / m being A = h/r.c = 3.3609178080E-23 grams constant

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But @ it is also hc / q^2 or A /m = hc / q^2 this necessarily takes us to that. q^2 / m is constant q^2 / m = r.c^2 = constant (10-2) This way, we can deduce the value of q in any time, the one that of Planck age would be : qp = (r.c^2 x )^(1/2) qp = 1.7957034942E+01 ues But also, as = ^2 / m^2 then we would have that: m^2 = A^2 / @ ^2 = (^2 /) (/A)^2 = / @ ^2 = K2 = 2.6350273064E+36 constant without units

= k2 @ ^2 (10-3) Valid for any time. Especially in Plancks epoch when = 1 @p = (1/k2)^(1/2) = 6.1603791167E-19 For the current time it is also deduced since N = ^2 / @ according to (6-2) that: N = K2^2 @ ^3 (10-4) N = 4.4321439636E+81 On the current epoch. In the epoch of Planck : Np = k2^2 X @p^3 = 1.6232767191E+18 And the total mass of the universe at that epoch would be : Np X = 8.856110199E+13 Mp = 8.856110199E+13 grams (10-5) We can also here, calculate the mass of the particle No 1 that appeared in the Universe. So from (10-4), (10-3) and = ^2/m^2: 1 = (/m1)^3 X K2^(1/2) m 1 = x K2^(1/6) = 64.118197548grams (10-6) The mass of the universe was of course M1 = N1 X m1 = 64.118197548grams @ = 1 / K2^(2/3) = 5.2417534126E-25 (10-7) = @1^(1/2) = 7.2399954508E-13 (10-8) Now we can calculate the values of @ and when they were unified, that is to say when @u = u. in this case Nu = u^2 / @u = @u = u And since N = K2^2x@^3 then:

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Nu = K2^2. Nu^3 Nu = 1 / K2 = 3.79502700861E-37 As N should be 1, then, unification happened before there was some particle The mass energy of unification would be: As m = / ^(1/2) then : mu = /u^(1/2) Eu = mu. c^2 = .c^2/u^(1/2) = .c^2 /Nu^(1/2) = 7.9594749045E+34 ergs mu = 8.8561101986E+13 grams That it is exactly equal to the total mass of the universe in the age of Planck (10-5). It is also possible to calculate the temperature of unification with: From (7-12) Tu = mu^(3/2) = 2.9586632349E+59 kelvins We can calculate when this happened by making use of :

u = h r / G mu^2

u = 8.32475716E-62 sec. It is necessary to insist on the difference between the inverse of the frequency of the energy of a mass and the age of the universe. On the case of the Plancks units, the scientific tradition makes wrongly to the Plancks time as age of the universe. This is not correct, that is why I want to clear it up. Time of Planck is not the age of the universe then. This is why I represent the age with and the inverse of Plancks frequency as 1/fp = t

There was one single moment when u = tu, and this happened when u = tu, that is in the unification, no on Plancks epoch.

u = h.r/ G.mu^2

fu.h = mu C^2 = qu^2/ r = G mu^2/r y fu = G mu^2/ h r = 1/ u

and of course: tu = u Here is worth to stop in some especially remarkable result: The particle No 1 had a mass of 64.118197548grams This mass existed when 1 = h. r / G.m1^2 = 1.5881626824E-37 sec From the moment zero and till the current age of the universe equal to 4.2851979921E+17seg; .2851979921E+17/1.5881626824E-37 steps have lapsed of = 2.698210928E+54 jumps of 1 seconds If we multiply this number of jumps by the mass m1 (the mass when N=1) give us a mass of 1.7300442483E+56 grams. This last mass is the current mass of the universe and in consequence we may conclude that on each 1 jump, 64.118197548grams/1.5881626824E-37 sec = 4.0372562747E+38 grams/second of mass is generated in the whole universe. The universe continues repeating the initial prescription, the rhythm of creation of matter. Actually, about 2.4137293501E+62 protons per second in the whole universe, or a proton each 3.6793815652E+22 km3 / sec. I could also say that 1 is the minimum time period that the nature admits for the spontaneous creation of matter.

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The question to answer now is From where this radiation energy arose? If we calculate the thermal energy along the history of the universe as a result of the density of this energy multiply by the volume of the universe, we find that this it is constant. That once it was generated it didn't increase neither diminish. Just the density and the temperature diminished by reason of the expansion. It is possible to calculate the number of photons in any time in the universe. It is of special interest the moment when arose the first photon. For that I will use a very simple equation of the quantum physics that says: N fot = 32 ^2/9 R^3/ o^3 (10-9) Where R is the radius of the universe when you want to know how many photons are there and o is the wave length of those photons in peak of the curve of the Wiens law. But this result has a failure; the equation for the number of photon is good for a big amount of it, but NO if there is only one or very few. Because of this, neither temperature, neither the factor for the number of photons is 32 ^2/9. So if the number of photons is 1 the factor should be also 1. In this case, temperature is : T = K1/ ^(3/4) To know when this happened, it is just a matter of using the next equation: = h / Et = 1.7553979084E-99 sec. (10-10) Where Et = 3.7746823888E+72 ergs as we see on (7-6)

1/fot1 = 5.69671400811E+98 = Hfot1 Because there is only 1 photon which energy is ALL the thermal energy in such a way that the formula of Planck is completely fulfilled.

Et = h.W = h.Hfot1 Temperature is then:

Tfot1 = K1/ fot1^(3/4) = 5.5063110829E+87 Kelvin The correspondent radius is Rfot1 = c/ Hfot1 = 5.2625505372E-89 cm Since the wave length of this first photon should be equal and no bigger than the radius Rfot1 A consequence of this is that equation N fot = 32 ^2/9 R^3/ o^3 it is not longer suitable for this moment since Nf = 1 and R = . Or the factor is now just 1 Another consequence is that Boltzman constant K cant be kept and must be also modified because R = = zK/hc/T must be accomplished: K = 1.3406348235E-16 instead of 1.38064880E-16 At the same time provides the constant energy of the thermal radiation with value 3.7746823888E+72 ergs only for this single moment. Why to change or reduce to the Boltzmann Constant at this time? Note: If you kept the value of the Boltzmann Constant value as the current value, it would appear that in the time of the creation of the photon 1 there would be an extra energy which is not thermal and instead of 3.7746823888E+72 ergs . Would be 3.9256421946E 72 ergs or 1.5095980579E 71 additional ergs. (To

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calculate this, I only use the current value of the Boltzmann Constant and modified it until Nfot = 1 and this would happen to the 1.6878944238E-99 sec. I have no explanation for this additional power in the B. B. that is not heat, but that if I translated this into temperature, it would give me a temperature of 1.224 Kelvin of "something" that could perhaps be neutrinos as they do not have rest mass. It is very probable, then, that one or some of the constants involved after all are constant after all (at least during the BB). At this point, is necessary to understand the meaning of equation: KzT = 2 m c^2 / ^(1/4) (7-10) z KT = 2 m c^2 / ^(1/4) From this we see that terms 2 m/ ^(1/4) represents a mass equivalent to something, but What?. Making the operation 2 m/ ^(1/4) in the present time, it results equal to 2.0881889740E-36 grams. Which is equal to what I call mfo that is the equivalent mass of that photon at T today with a frequency fo of the Wiens law. Let us talk about the mean equivalent mass of all the photons at T temperature. This is simple to calculate just by dividing total thermal mass Mt by the total amount of photons. Mt/ Nf = Et/c^2/ Nf = (32 ^6(KT)^4 R^3/ 45 h^3 c^5)/ 32 ^2/9 R^3/ o^3 = mf

mf = 6.6935032463E-38 grams By making the operation : mfo/mf = 2.088059030E-36/ 6.693531015E-38 = 31.197250486 This last number has the particularity that is equal to 2z such that:

mfo / mf = 2z

Clarifying again: mfo is the mass corresponding to the photon whose wavelength o is at the peak of the curve of radiation. mf Is the average mass of all the photons of the total radiation curve. Attached is a table with the results of the calculations for different important moments in the history of the universe, including the moment in which it can be seen that all the thermal energy of the universe of the background radiation comes from this single super energy photon that was subsequently "fractured" in photons each time less energetic and growing on numbers. One of the things that are seen in this table is that the reason photon/proton is not constant. Although the calculation that I have for this present age matches the measurements made. The table and the figures obtained were calculated by using of Microsoft Excel with the equations that I have outlined. In such a way that I just insert in the row of the , the time value and Excel calculates the rest. The first stable particle must have existed until @ took the value 1 this is when q^2 = h c . This is when according to (5-3) (/A)^2 = /@^2 and @ = 1 (/A)^2 = = 2.6350273065E+36

m@1 = (h c/G )^(1/2) = 3.3609178080E-23 gramos

@1 = h r / G(m@1)^2 = 5.780186001E+11 sec

T@1 = 6.9169293846E+04 kelvin

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11.- Variation of values with time Without presenting the easily obtained deductions, I do expose the equations of these, in relation to the age the universe of ().

m = (h r/ G)^(1/2) ^(-1/2) = c / r T = K1/ ^(3/4) @ = (c/ r K2)^(1/2) ^(1/2)

= fine estruct. const.= 2 (rK2)^(-1/2) ^(-1/2)

N = ( K2 c^3/ r^3)^(1/2) ^(3/2)

M = (K2 c^3 h/ r^2 G)^(1/2)

Evidently, if we replace = R/c we will have the values when the Universe had the Radius R. and if we calculate the value that would be if we observe them at the distance L from us, then; Ract- L = R = c act L = c . Then the value of that must be used is:

= act - L/c As an example: if we want to know the values of @ at a distance L from us, we have to use : = 1.3588273726E+10 L/c And if we want to know the local values t seconds ago, we would have to use: act t = It is also feasible that variations in the energy of the particles alter the value of these constants For example, if energy is given to an electron that increases its mass, it is possible than the electrical charge will also increases to maintain the reason q^2/m constant. An increase of q would mean a decrease of @ and the consequent increase of the value of the fine structure constant.

12.- Final conclusion and large numbers hypothesis As final conclusion, the result of this analysis which practically all becomes from the fact of the finding of the Hubble constant, from which other universe properties are derived using some physics constants and other from mathematics. I especially explain the origin of what Dirac named the large numbers hypothesis that was trying to know if there is some relation between the famous 10^40 and the universe. I have found here, this number identified by me with the letter S and which calculated value up to the ten decimal figure is: 2.2688180080E+39. This number comes mainly from the actual proportion among the electrical and the gravitational forces between a proton and the electron. In addition, this number also gives a relation among other properties, between the quanta properties of the proton and the electron and those of the universe as a whole. I must make notice, this number has not any fundamental importance because is not constant in time which actual value is just an indication of this epoch on which we are living in the universe history. I enlist some other related properties which include it:

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mg = Hh/c^2 = 1.7204564858E-65 grams /@ = 2.2688180026E+39 f/H = 2.2688180026E+39 R/ = 2.2688180026E+39 (N/@)^1/2 = 2.2688180026E+39 /w = 2.2688180026E+39 (M/mg/a)^1/3 = 2.2688180026E+39 m/mg = 2.2688180026E+39 To get the number P. Dirac found as: 2..c^ 5/ (G. h.H ^ 2) = 6.31818087E 121 by means of physical constants is extremely simple. This comes from seeing the existence of a mass whose frequency in the equation of Planck is the Hubble constant. This is: mi = H. h/C^2 And the mass of the universe is M = N m where N is the number of masons of the universe and m is the mass of the mason. In addition: m^2 = me x mp M C^2 = G M^2 / R M = R. C^ 2/ G = C^ 3/G H M = N m = C^3/G H N = C^3/ (G H m) and as H = G m^ 2/ h r, then: N = (h r C^3) / (G^2 m^3) = (h^2 r C^3) / (G^2 m^4). m/h N = h^2. C^ 2/ G^2 m^4 X r C m/ h N = ^2 x r / N = ^2 / @ N = S = 4.4321439636E+81 Where is the gravitational parameter = h C/G m^2 Let us make the number Ni = M /mi Ni = (RC^2/ G) / (H/C^2) Knowing That: = h C/G m^2 , = @ . r and H = G m^ 2/ h r We arrived at Ni = ^3/ @^2 = N.S = 1.0055728015E 121 So to get a number as large as you want just with physical constants has nothing special, except if this number actually represents something. For example, this number Ni, has no meaning other than the proportion between 2 masses. It is not the same case of N, which represents the number of masons and that in turn indicates to the definition of m the number of protons in the universe (almost all of them). It should be remembered that these ideas does not maintain as constants the masses of the fundamental particles, neither that of the universe through the time, and this make a difference with the standard theories that does not want to violate the sacrosanct law of the energy conservation which takes them hopelessly to the problems of the singularity of the initial universe and not to be able to explain of where this energy came.

26

It is also necessary to make notice that the Hubble constant is not constant through the time (in fact, it defines the age of the universe) and that the observations of the current astronomical calculations reflects what today we can see and deduced of the universe, no what it was in the past. Dont get wrong with my words, we can see the past of the universe, but altered by the current properties of it. For example; to suppose that the mass of the proton is constant takes us to different results than if it is variable. The same reasons applied for the electron charge and other constants. That is to say, to evaluate the universe for what today we see could be an error. It has been said that a small variation of the constants, for example of the fine structure, would make impossible the existence of the universe for x and y reasons. And this is surely certain today, at this age of the universe. But these objections should not be applied to the past, since the nature, wisely alters other properties of the matter to maintain the existence of the universe. It is then unacceptable to lucubrate about what would pass today with values of the constants in the past. Each moment has its own characteristics that make possible the continuity of the existence. What it is this analysis? Well, in a very simple way, it has being enough to look for the possible combinations of 4 constants of nature and 3 pieces of information (the masses of the proton and the electron and the fundamental charge) to deduce all this. I didnt introduced any unknown assumption, except the one of knowing that the parameters of the electric and gravitational forces, should be smaller in the past, so, going back in time, they reach the unitary value. The result can be proven with the predictions from these calculations that can be made. The two better examples of this are the theoretical calculations of the temperature of background radiation today and 2,760 millions of years ago according to the references that I gave. It would also be possible to check this if we can check the increase of the fine-structure constant with distance or what is the same, back in time. Also I would like to add that these calculations can accommodate the famous theory of inflation, because from these the inflation will be deduced ,not just of the dimensions of the universe, but of the mass, for example, in the second 1, mass was reduced by about 10E+18 orders. On the other hand it was reduced more or less the same order in 10E+17 seconds until the present age. And the same with the temperature, which in 1 second was reduced in 10E+28 orders and took 10E+17 seconds longer to be reduced to the magnitude at the present age. On the other hand, I will say that undoubtedly this written is not a theory of the universe, because I don't dare to say this. And yet, as theoretical analysis it is allows myself to speculate a bit about its results. One of the most estrange is the last one, where I propose the spontaneous creation of light based on the principle of uncertainty. This is observed in the creation of the photon No 1. It has being said that the spontaneous creation of matter or energy is allowed provided that the distance of influence of the created particle it is not larger than its wavelength and that also, this creation always goes accompanied of its corresponding anti particle. In the case of photons, the same photons are their anti particle, then it wouldn`t be estrange their creation. What would be estrange is that they remain existing. This wouldn`t never happen to the created photons since they never reaches a distance equal to its wavelength by reason of the expansion of the universe, since in each instant that the radius of the universe grows, the wavelength is always smaller than the radius of the universe. I suppose myself that as the universe grows, the wavelength of each new coming photon from the previous one fractured is quantified and its wavelength is always a complete semi period of the radius of the universe in that instant. Calculation is simple with the previous equations, except for the correction of 32pi^2/ 9 for a large amount of photons, but not for just one (in which case, the number of photons is equal to the ratio R to the wave length of it (equal to 1) and the result is that just after the first photon, the wave length is always smaller than the universe diameter and therefore it doesn't violate the principle of uncertainty. Regarding the creation of matter shown with the increase of number of particles in time, this is more difficult to attempt an explanation. Why doesn't the created particles disappear in the vacuum if the laws demand the simultaneous creation anti mater? The answer could be in the fact that the principle of uncertainty also requires the creation of matter with energy contrary to the recently created one, and this just leaves me the alternative of that is the same gravitation the way the nature chose for matter to persist. And, the reduction in the mass of the mason? For that, I would have to think in what originates the mass and that is a road very, very difficult to travel. No wonder, I speculate that it could be due to some couple of causes. One of them is that the amount of

27

mass of the particles is inversely proportional to the size of the universe just as is shown in the equation of the time. The other, but arduous, is that as the universe grows, the resistance to the movement falls, that is to say that the inertia falls. This is too speculative, nevertheless I mention it. The theory says that the creation of matter starts from the quantum vacuum; it comes from an infinite sea of energy that is manifested with the creation and disappearance of particles in the same space. These particles in principle are no detectable but by means of very special experiments just as the one that demonstrates the experiment of Casmir. But I am convinced that if this happens and it happens frequently, the immense group of these appearances and disappearances will, on a net result, shown as if it really existed something that breaks the free movement of the things, the not well gifted ether of the middle ages. I remember a documental of television about a beach in California where at night the sea shines with an extraordinary phosphorescent light. The explanation of this phenomenon resides in some small animals that emit light, but they don't emit it in continuous form, but rather it lights on and off in each one of this animals. But as there are millions of these small animals the phenomenon is observed as a continuous light shining in the ocean. It is this way I understand this appearance and disappearance of these quanta particles. One of it last almost nothing, but many and many millions will appear as something real and continuous. Now then, this creation and disappearance of particles should be diminishing in rhythm as the universe expands, probably for some phenomenon as the exclusion principle of Pauli and in consequence the mass, the inertia would diminish with the time. This drag of the group of created and annihilated particles would be noticed as resistance to the movement, as inertia that is at the end what the mass is. But has the inconvenience of the same principle of the inertia which maintains the uniform speed unless a force is opposed to that movement. The existence of some type of drag of the vacuum would violate the inertia principle that maintains the speed constant and so the idea is obviously false. So although tempting this idea is, it has this serious inconvenient. On the attached table with Excel calculations, is shown the results with the previous equations where the reference parameter is the real time . On the first column are shown the results for the actual time. On the second one are shown the results when the electrical parameter was unitary. On the third one are shown the results when the parameter of the gravitational force was unitary, on the not properly named Plancks time. On the fourth one, are shown the time when the first mason came to be. Obviously on early times, even if appears value for the mason, in principle should be reduced to zero since it can be fractions of particles. On the fifth column can be seeing the moment of unification of the two mentioned forces. On the last one, it is seeing how the energy of only one photon, the first one, is the one is conserved trough the next universe history, the initial cause of the cosmic background radiation. Here it must be make notice again that some constants cannot be sustained as they are today. j =32pi^2/9 cant be used anymore, because this value is for a large group of photons, not for just one, then I make j = 1. It is also seeing that Boltzman constant cant be sustain any more and must be modified to get congruent results. Also, note that on the last column, total thermal mass, gravitational mass, and the mass of the first photon had all the same value. THE END

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ACTUAL alfa = 1 PLANCK Np = 1 N = 1 UNIFICACION Nfo = 1

B = 1

pi 3.141593E+00 3.141593E+00 3.141593E+00 3.141593E+00 3.141593E+00 3.141593E+00 3.141593E+00

4pi/3 4.188790E+00 4.188790E+00 4.188790E+00 4.188790E+00 4.188790E+00 4.188790E+00 4.188790E+00

G 6.673840E-08 6.673840E-08 6.673840E-08 6.673840E-08 6.673840E-08 6.673840E-08 6.673840E-08

K 1.380649E-16 1.380649E-16 1.380649E-16 1.380649E-16 1.380649E-16 1.380649E-16 1.340635E-16

z 4.965197E+00 4.965197E+00 4.965197E+00 4.965197E+00 4.965197E+00 4.965197E+00 4.965197E+00

h 6.626070E-27 6.626070E-27 6.626070E-27 6.626070E-27 6.626070E-27 6.626070E-27 6.626070E-27

c 2.997925E+10 2.997925E+10 2.997925E+10 2.997925E+10 2.997925E+10 2.997925E+10 2.997925E+10

hc/ZK 2.897724E-01 2.897724E-01 2.897724E-01 2.897724E-01 2.897724E-01 2.897724E-01 2.897724E-01

j= 32pi^2/9 3.509193E+01 3.509193E+01 3.509193E+01 3.509193E+01 3.509193E+01 3.509193E+01 1.000000E+00

D 4.285035E+01 4.285035E+01 4.285035E+01 4.285035E+01 4.285035E+01 4.285035E+01 4.285035E+01

r 6.576236E-15 6.576236E-15 6.576236E-15 6.576236E-15 6.576236E-15 6.576236E-15 6.576236E-15

4.285198E+17 5.780186E+11 2.193596E-25 1.944754E-36 1.588163E-37 8.324757E-62 1.755398E-99

mp 1.672622E-24 1.440165E-21 2.337786E-03 7.851469E+02 2.747487E+03 3.794874E+15 2.613337E+34

me 9.109383E-28 7.843384E-25 1.273198E-06 4.276043E-01 1.496328E+00 2.066753E+12 1.423268E+31

m 3.903403E-26 3.360918E-23 5.455700E-05 1.832300E+01 6.411820E+01 8.856110E+13 6.098753E+32

q 4.803205E-10 1.409413E-08 1.795703E+01 1.040657E+04 1.946705E+04 2.287868E+10 6.003851E+19

q^2 2.307077E-19 1.986446E-16 3.224551E+02 1.082967E+08 3.789659E+08 5.234339E+20 3.604623E+39

l 5.662288E-12 6.576236E-15 4.051211E-33 1.206254E-38 3.447101E-39 2.495699E-51 3.624051E-70

f 5.294546E+21 4.558724E+24 7.400071E+42 2.485318E+48 8.696945E+48 1.201236E+61 8.272303E+79

8.610226E+02 1.000000E+00 6.160379E-19 1.834262E-24 5.241753E-25 3.795027E-37 5.510828E-56

1.953504E+42 2.635027E+36 1.000000E+00 8.865595E-12 7.239995E-13 3.795027E-37 8.002375E-75

S 2.268818E+39 2.635027E+36 1.623277E+18 4.833331E+12 1.381216E+12 1.000000E+00 1.452118E-19

H 2.333614E-18 1.730048E-12 4.558724E+24 5.142040E+35 6.296584E+36 1.201236E+61 5.696714E+98

hH/C^2 1.720456E-65 1.275477E-59 3.360918E-23 3.790967E-12 4.642155E-11 8.856110E+13 4.199901E+51

R 1.284670E+28 1.732856E+22 6.576236E-15 5.830225E-26 4.761192E-27 2.495699E-51 5.262551E-89

V 8.881031E+84 2.179597E+67 1.191299E-42 8.301269E-76 4.521012E-79 6.511266E-152 6.104884E-265

=1/R^2 6.059221E-57 3.330236E-45 2.312305E+28 2.941910E+50 4.411321E+52 1.605519E+101 3.610833E+176

M 1.730044E+56 2.333609E+50 8.856110E+13 7.851469E+02 6.411820E+01 3.360918E-23 7.086991E-61

E= M C^2 1.554886E+77 2.097343E+71 7.959475E+34 7.056548E+23 5.762656E+22 3.020642E-02 6.369470E-40

N 4.432144E+81 6.943369E+72 1.623277E+18 4.285035E+01 1.000000E+00 3.795027E-37 1.162039E-93

Np 1.034331E+80 1.620376E+71 3.788246E+16 1.000000E+00 2.333703E-02 8.856467E-39 2.711855E-95

Dm 1.948022E-29 1.070661E-17 7.433994E+55 9.458155E+77 1.418227E+80 5.161696E+128 1.160872E+204

T 2.737736E+00 6.916929E+04 1.430547E+32 2.784334E+40 1.822630E+41 2.958632E+59 5.506311E+87

fot 1.058438E-01 4.189321E-06 2.025605E-33 1.040724E-41 1.589859E-42 9.794133E-61 5.262551E-89

ffot 2.832404E+11 7.156110E+15 1.480014E+43 2.880613E+51 1.885655E+52 3.060939E+70 5.696714E+98

mfo=hfo/c^2 2.088189E-36 5.275840E-32 1.091140E-04 2.123731E+04 1.390198E+05 2.256676E+23 4.199901E+51

Det 4.250275E-13 1.731826E+05 3.168543E+114 4.547115E+147 8.349198E+150 5.797156E+223 6.18305E+336

Et 3.774682E+72 3.774682E+72 3.774682E+72 3.774682E+72 3.774682E+72 3.774682E+72 3.774682E+72

Mt 4.199901E+51 4.199901E+51 4.199901E+51 4.199901E+51 4.199901E+51 4.199901E+51 4.199901E+51

Nf 6.274593E+88 2.483497E+84 1.200812E+57 6.169583E+48 9.424940E+47 5.806120E+29 1.000000E+00

mf 6.693503E-38 1.691123E-33 3.497552E-06 6.807430E+02 4.456156E+03 7.233575E+21 4.199901E+51

mfo/mf=2piz 3.119725E+01 3.119725E+01 3.119725E+01 3.119725E+01 3.119725E+01 3.119725E+01 1.000000E+00

Nfo 2.011265E+87 7.960629E+82 3.849094E+55 1.977605E+47 3.021080E+46 1.861100E+28 1.000000E+00

Nf/Np 6.066330E+08 1.532667E+13 3.169835E+40 6.169583E+48 4.038620E+49 6.555798E+67 3.687513E+94

rg 2.898530E-54 2.495699E-51 4.051211E-33 1.360601E-27 4.761192E-27 6.576236E-15 4.528719E+04

lg 1.284670E+28 1.732856E+22 6.576236E-15 5.830225E-26 4.761192E-27 2.495699E-51 5.262551E-89

A 3.360918E-23 3.360918E-23 3.360918E-23 3.360918E-23 3.360918E-23 3.360918E-23 3.360918E-23

K2 2.635027E+36 2.635027E+36 2.635027E+36 2.635027E+36 2.635027E+36 2.635027E+36 2.635027E+36

K1 4.585321E+13 4.585321E+13 4.585321E+13 4.585321E+13 4.585321E+13 4.585321E+13 4.722179E+13