COSMIC BACKGROUND RADIATION TEMPERATURE LARGE NUMBERS HYPOTESIS EXPLAINED

AND ITS CALCULATION FROM THE PLANCK ´S TEMPERATURE. CALCULATION OF THE VARIABILITY THE "FINE CONSTANT OF STRUCTURE” AND

THE GRAVITATIONAL ONE WITH THE AGE OF THE UNIVERSE. THE FIRST PHOTON CREATED BY THE UNCERTAINTY PRINCIPLE

For: Ramón Garza Wilmot garzawilmot@gmail.com Abril 10/2014 Monterrey, N.L. Mexico INTRODUCTION Arthur Eddington, Edward Milne, Paul Dirac mainly, 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 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 relations. Dirac formulated a number without units this way: Nd = qe^2 / 4Πεo G me^2 ≈ 4.2 e42 Eddington, more accurate formulated Ne = Π^2 q^4 / G^2 mp^2 me^2 ≈ 5e79 We must make notice that the number Eddington found is approximately the square of the number that Dirac obtained. Hemos de hacer notar que el número que obtuvo Eddington es aproximadamente el cuadrado del que obtuvo Dirac. The Intention behind all this was that N 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 tried this link, that so far doesn´t seem to be explained. On this paper, I present the reasons and the numbers I see for these relationships, 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 Π factor.

This is a simple analysis of the relationships existing among different physical 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 Planck´s units, especially with the mass of Planck. These Planck´s units are derived starting from what I call “parameters” of the gravitational and electric forces from which are derived the Planck´s 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. 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 Planck´s units that, after this, have a very clear meaning in our time, which at the same time are derived from these and just these physical constants: - The speed of the light in vacuum c - The Planck´s constant h - The Boltzmann’s 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 physical 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 Planck´s time that as we will see, does not represent an epoch back on time, but just the reciprocal of the Planck´s frequency. That´s why the term epoch, is referring to real time and make a difference with the Planck´s I go far before the Planck´s 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 simple equation shows the origin of the cosmic radiation. It doesn´t came from the annihilation of particles and antiparticles as the standard theories say. It comes from nothing less or more, from a quantum leap that created the first super energetic photon from which all the rest come. This also means that this is the just one time phenomenon, that can´t be repeat in a space than once it happen, it will never happen again in another jump of this 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 Planck´s 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 do not prevent the creation of real particles do to the same cause, as 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 apart of the unitary value of the gravitational parameter on the Planck time, 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 6 that defines all the parameters as function of time and from which Planck´s data can be obtained just by making β = 1 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 physical constants in the sense of their invariability in time and place 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 the invariable physical 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 13,700 millions 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. 1. - 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 the five universal physical constants of the chart to take the value of 1 when equations and calculations are expressed in this system.

Table 1: Fundamental physical constants

Constant Symbol Dimension Value in SI units with

uncertainties[6]

Speed of light in vacuum

c L T−1 2.99792458×108 m s−1 (exact by definition of meter)

Gravitational constant

G L3 M−1 T−2 6.67384(80)×10−11 m3 kg−1 s−2[7]

Reduced Planck constant

ħ = h/2π where h is Planck constant

L2 M T−1 1.054571726(47)×10−34 J s[8]

Coulomb constant

(4πε0)−1

where ε0 is the permittivity of free space

L3 M T−2 Q−2

8.9875517873681764×109 kg m3 s−2 C−2 (exact by definitions of ampere and metre)

Boltzmann constant

kB L2 M T−2 Θ−1

1.3806488(13)×10−23 J/K[9]

The use of this system of units brings several advantages. The first and more obvious is that it simplifies the structure a lot of physical 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 Planck´s 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 Planck´s units

Universal Gravitation Newton law

Becomes:

Using Planck´s units

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

Becomes

The famous mass-energy Einstein equation.

Becomes

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

Becomes

Planck´s 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:

To get the coefficients α, β 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 Planck´s 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: Chart 2:

Name

v

t

e

Dimension Expression Value[6]

(SI units)

Planck length Length (L)

1.616  199(97) × 10−35

m[10]

Planck mass Mass (M)

2.176  51(13) × 10−8

kg[11]

Planck time Time (T)

5.391  06(32) × 10−44

s[12]

Planck charge Electric charge

(Q) 1.875  545  956(41) × 10

−18

C[13][14][15]

Planck

temperature

Temperature

(Θ)

1.416  833(85) × 1032

K[16]

Notices: until here, reference to the web pages mentioned is ended. 2. - Basic calculations of the properties of the proton and the electron. Before 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 temperature of background radiation of microwaves, 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 the so called “quantum” energy, 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 equal 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.

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 a 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.λ and in consequence: λ = h / mf. c The same equation λ = 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: λ = 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: λ = h / m v Then we have that: λ+ = h / mp. c (2-2) λ - = 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) λ+ = h / mp.c X λ - = h / me.c λ+. λ - = h^2 / (mp. me) Let us make now that λ^2 = λ+ X λ- 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 : λ = h / m.c (2-4) Here I want to make notice that the mason “m” is not a real particle. It is a particle, assistant 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 /λ (2-5) E = m.c^2 (2-6) E = f. h (2-7) As it´s 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. 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 ħ 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: λ = h/m.c = h.c / m. c^2 = h. C. r / q^2 = @. r (2-12) Being “r” as it was explained, 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. - The parameter of the force of gravity. 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 And if Eg = F h being then F the gravitational frequency: F = G m^2 / h. r (3-1) It is 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 β as: β+ = h.c / G.mp^2 (3-2) and β - = h.c / Gme^2 (3-3)....... that takes us to β = h.c / Gm^2 (3-4) When multiplying one with the other: Let us divide now the equation (3-4) 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 = β/@ = 2.2688180080e+39 (3-5)

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 β it is bigger today that @, the gravitational force is S times weaker than the electric one. Now, I enumerate the basic values and the derivates from these numbers: 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/kelv Gravitational constant G = 6.67384 e-8 erg-cm/gm^2 b) Derived: Parameter of Electrical force @ = 861.022575260 Parameter of Gravitational force 1.95335035241 e+42 mason radius r = 6.5762361127 e-15 cm mason Compton Length wave λ = 5.6622877533 e-12 cm frequency of the mason f = 5.2945464989 e+21 cps mason gravitational radius rg = 2.8985295821 e-54 cm gravitation / elect. parameter S = β / @ = 2.2688180080 e+39 CALCULATION OF THE UNITS OF PLANCK STARTING FROM THE PARAMETER OF THE GRAVITATIONAL FORCE. Let us enter into matter: 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 β 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 that β would be equal to @. Let us take then in fact, that there was a time when β1 = 1 And by the definition of β we arrive to :

G m1^2 = h.c Where m1 was the mass of the mason when β1 = 1 Then: m1 = (h.c / G)^(1/2) = µ (the mass of Planck) (3-6) That is to say that the mass of Planck is that when β = 1 and it proceeds from the value of the mason. Even more, it was the mason.

Note that except for the use of h instead of ħ , µ = 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 2, 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 µ^2 = h.c/G = β. m^2 then: µ = β^(1/2). m (3-7) Therewith in mind, the data of the chart 2 are easily derived just making the substitution of

h by ħ I repeat: µ is the mass of the mason with current value of m = (mp * me)^(1/2) lp is the Compton wavelength of µ fp is the Compton frequency of µ ep is the energy of µ etc, etc. In other words, I say that the mass of the mason is NOT constant. It has diminished from µ in the time 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: lp = h/µ.c = G.µ/c^2 = (h.G /c^3)^(1/2) = 4.0512107518e-33 cm In summary: µ = (h .c / G)^(1/2) = 5.4556996322 e-5 grams λp = lp = h / µ. c = (h G / c^3) ^ (1/2) = 4.0512107518 e-33 cm fp = c / λp = (c^5 / h. G)^(1/2) = 7.4000706546 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) = 4.9033382981 e+16 erg Let us see the equation (3-1) with values: F = 2.3336144548e-18 cps (3-8) That corresponds to a wavelength L of 1.2846700421e+28 cm since L = c/F (3-9)

Also an energy e = F. h = 1.5462691727e-44 ergs (3-10) And a mass of mg = e/c^2 = 1.7204564817e-65 grams (3-11) 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 λ give us: λg = h / (mg. c) = 1.2846700421E+28 cm Does this last mass is the graviton? We can say that the radius of the universe is the wave length of this virtual particle. In the final table I expose, you can see this is true for all times, including the time for the first photon. The interesting thing of the equations of this section and first of all the (3-8), 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 megaparsec = 3.08567758 × e24 cm 1 km/seg /1 megaparsec = 100,000/3.08567758 e24 seg^(-1) 2.3336144548e-18 cps = 72.007818037 Then, the Hubble constant H = 2.3336144548e-18 cps H = 72.007818037 km/seg/megaparsec From this we can obtain the current “age” of the universe as: ψ = 1 / H ψ = 1.3588273726e+10 years = 4.2851980023e+17 seconds About 13,588 millions of years And the wavelength corresponds to the “Radius” of the universe R = 1.2846700421e+28 cm. It must be notice that you can calculated the mass easily with these values of the universe, it´s density, the number of protons and electrons. 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: M = R C^2 / G Vol. = 4 π / 3 R^3 Density = M / Vol = 3 R^4 c^2/(4π G) N (quantity of masons) = N

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

N = β S = β^2/@ (3-12)

In consequence, the number of masons µ in the time of Planck (tp) was:

Np = 1/@p since β = 1

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: Remembering that in the time of Planck β = 1 and β = h.c / G.m^2 µ becomes m lp transform in λ fp becomes f ep becomes energy of m rp = lp becomes r classic radio βp = 1 is transformed in the current β Sp = becomes current S Tp becomes current T Notes: In the last case of microwaves 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 in the age of Planck 4. – a) The universal background radiation temperature. Let us begin making notice that the temperature of Planck deduced from the energy of Planck, is equal to the mass energy of the mass of Planck µ 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 / λo 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, λo 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 λo, equal to fo = c / λo T = h.c /z.K. λo = h λo / z.K T = h.c /z.K.λo = 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: T = 2 mi.c^2 / z.K the one that applied to µ give us:

Tp = 2 µ c^2 / zk (4-1) Tp^2 = 4 µ^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 (4-2) Equal to the temperature of the chart 2 except that this chart doesn't take in count the value of 2/z This temperature has a value of 1.4305709080e+32 degrees Kelvin and it presupposes the annihilation of 2 masses µ of Planck, but with a total energy of Np masses µ. A number that I will determined ahead. b) it is evident that the heat energy of the current background radiation, doesn't come from the annihilation of two single masses µ (they are too little). But of Np masses µ. Now. Do the definition of β = h.c/Gm^2 = h.r.c/Gm^2.r = (h.r/Gm^2) .c/r = c/r. H = R/r Then β = R / r (4-3) Which means, the “Radius” of the universe R in any time, divided by the classic radius of the actual mason r. A direct consequence of the above-mentioned, is that when β = 1 in the time of Planck, the radius R of the universe was equal to r, the classic radius, of the current mason and will be constant, a very special constant. As the value of the mass of the current mason doesn't have any special characteristic since it is variable, there I am to conclude that “r” is a constant magnitude through the time and as consequence of this.

r = Rp (when β1 = 1) Rp is the radius of the universe in the time of Planck. Also, since: r.c^2 = q^2 / m = constant (4-4) it is deduced that: r.c^2 = qp^2 /µ and qp^2 = r.c^2 µ = h.c / @p notes: qp is the unitary charge in the time of Planck @p = h.c/ r. c^2. µ @p = λp / r @p = 6.160379102e-19 That it is the value of @ when β = 1 Then: Np = 1 / 6.160379102e-19 = 1.623276723E+18 That it is the quantity of masons µ in the time of Planck (not the actual age)

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. c) I will Leave in undoubtedly that: Ψp = h. r / G. µ^2 = 1/ Hp = 2.1935962487e-25 seg (4-5) Defines the “age” of the Universe when m = µ and fp = Hp tp = (h.G / c^5)^(1/2) Defines the time Planck, that is the inverse of the frequency of Planck, NOT the age of the universe when m = µ ψ = h.r / G m^2 (4-6) Defines the age of the universe in any moment when it has been defined or specified m. Then the Mass of the universe in the age of Planck was: Mp = Np.µ = 8.856110220e+13 grams I use Capital Letters in referring to the Universe properties. The “Radius” was Rp = r = G.Mp /c^2 = 6.5762361127e-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 µ. 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 = 8π^5 (K.T)^4 / (15. h^3 c^3) (4-7) With a value of Det = 3.1687534056e+114 ergs / cm^3 when T = Tp Being the volume the Universe in the age of Planck equal to (4π/ 3) Rp^3 This would be 1.1912990690 e-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 = 3.7749329818e+72 ergs Energy that certainly there would be to remain constant along the full history of the universe. Sited down, that this energy is conserved and that this for: Det(ψp) X Vp = Det current X current Vol (Tp)^4 X Rp^3 = (Tact)^4 X Ract^3 (4-8)

That is to say, when conserving the energy, the temperatures and the radii are defined for (4-8) 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 β = R/r (4-9) Then do of (4-8) (Tp/Tact)^4 = β^3 (4-10) And because according to (4-2) Tp = 2 (h.c^5/G)^(1/2) / z.K And because β = h. c/Gm^2 it is deduced that:

(Tact)^2 = 4 h.c^5/(G.K^2 .z^2 .β^(3/2)) (4-11) The previous equation is general and it is valid for any time in which β is known Vg: in the time Planck when β = 1 and T = Tp From this equation we can obtain another that had being already obtained in another analysis, but here I obtained with better of support now. KzT = 2 {h c / G m^2}^(1/2) X{m c^2/ β^(3/4) = 2 m c^2/ β^(1/4)

K.z.T = 2 .m .c^2 / β^(1/4) (4-12) And replacing β for its value gives us: T = {(16.G.m^6.c^7)/ (h.(Kz)^4)}^(1/4) (4-13) That it can be expressed as:

T = Ω m^(3/2) (4-14)

Being Ω = {2 G^(1/4) c^(7/4) }/ {(h)^(1/4) Kz} constant (4-15)

Ω = 3.5500437985E+38 Kelvin / gm^(3/2) T act = 2.7377812177 degrees K 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 degrees Kelvin

The difference among the theoretical one that I have calculated and the actual one can be due to a different series of causes. The small difference can be due to the % of the mass of the proton that is really rest mass, because apparently there is uncertainty among the scientific community about this. The error if wanted to call this way, it is of the order of 4.5 parts in 1 thousand. or 0.0123 degrees K. It could also being certain degree of error caused by the incorrect value of the fundamental constants that I have taken as good. And a third one that I consider the most probable, it is that the heat energy has been partially absorbed by the intergalactic media. A situation that could be reflected ,obviously, in a reduction of the temperature of the background radiation regarding the theoretical one. Now then, since the temperature can be expressed in function of m, and in function of ψ (the time), we can find an expression for the temperature in function of the age of the universe. Everything is a matter to combine the equations (4-14) with the (4-6) From where: (T/ Ω)^(4/3) = m^2 y m^2 = (h r / G) / Ψ

The result is: T = K1/ Ψ^(3/4) (4-16) Where Ψ 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) = 4.5853966576e+13 K degrees. seg^(3/4) For example: for the time of Planck and making use of (4-16) when ψp = 2.1935962487E-25 seg Tp = K1 / ψp^(3/4) = 1.430570908e+32 degrees K And for the current age when ψ act = 1 / H = 4.2851980023e+17 seg Tact = 2.7377812177e+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 a such distance that 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 of 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 seg. Those that applied to the equation (4-16) result in a temperature of:

9.048782372 degrees K A temperature with a difference of 0.10 degree Kelvin, quite consistent regarding the measurementS. Where the standard theory differ of it, 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 temperature of decoupling between photons and electrons and I obtain at that age 6,850 kelvins. 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 kelvins 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 β 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 kelvins when the mass of the mason was bigger. 5. - Now then, let us see that relationship that exists among the 2 parameters of the forces, electric 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: (5-1) @ = A / m being A = h/r.c = 3.3609178000 e-23 grams constant But @ it is also same hc / q^2 or that: A /m = hc / q^2 what necessarily takes us to that. q^2 / m is constant q^2 / m = r.c^2 = constant (5-2) 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 µ)^(1/2) qp = 1.7957034941e+01 ues but also as β = µ^2 / m^2 then we would have that: m^2 = A^2 / @ ^2 = (µ^2 /β) (µ/A)^2 = β/ @ ^2 = K2 = 2.6350273189e+36 constant without units β = k2 @ ^2 (5-3) Valid for any time. Especially in Planck´s epoch when β = 1 @p = (1/k2)^(1/2) = 6.1603791019E-19 For the current time it is also deduced since N = β ^2 / @ according to (3-12) that:

N = K2^2 @ ^3 (5-4) N = 4.4321439741E+81 In the current time. In the time of Planck Np = k2^2 X @p^3 = 1.6232767228E+18 And the total mass of the universe in the time of Planck it would be Np X µ = 8.8561102197E+13 Mp = 8.8561102197E+13 grams (5-5) We can also here, calculate the mass of the particle No 1 that appeared in the Universe. So from (5-4), (5-3) and β = μ^2/m^2: 1 = (µ/m1)^3 X K2^(1/2) m 1 = µ x K2^(1/6) = 64.118197599 grams (5-6) The mass of the universe was of course M1 = N1 X m1 = 64.118197599 grams @¹ = 1 / K2^(2/3) = 5.2417533959E-25 (5-7) β¹ = @1^(1/2) = 7.2399908439 E-13 (5-8) Now we can calculate the values of @ and β when they were unified, that is to say when @u = βu. in this case Nu = βu^2 / @u = @u And since N = K2^2x@^3 then: Nu = K2^2. Nu^3 Nu = 1 / K2 = 3.7950270679E-37 As N should be ≥ 1, then, unification happened before there was some particle The mass energy of unification would be: mu. c^2 = µ.c^2/βu^(1/2) = μ.c^2 /Nu^(1/2) = 7.9594749234e+34 ergs mu = 8.8561186247E+13 grams That it is exactly equal to the total mass of the universe in the age of Planck (5-5). This would mean that among the moment of the unification of the two forces and the age of Planck, the mass-energy remained constant. After the age of Planck the mass of the universe began to increase with the creation of mass. It is also possible to calculate the temperature of unification with: From (4-14) Tu = Ω mu^(3/2) = 2.9586815984e+59 kelvins We can calculate when this happened by making use of (4-16):

T = K1/ Ψ^(3/4) y Ψu = (K1/ Tu)^(4/3)

Ψu = 8.324757140e-62 seg. Here is worth to stop in some especially remarkable result:

a) The particle No 1 had a mass of 64.118197599 grams b) This mass existed when ψ1 = h. r / G.m1^2 = 1.5881626836E-37 seg c) From the moment zero and till the current age of the universe equal to 4.2851980023e+17seg; 4.2851980023e+17/1.5881626836e-37 steps have lapsed of = 2.698210987e+54 jumps of ψ1 seconds d) If we multiply this number of jumps by the mass m1 (the mass when N=1) give us a mass of 1.7300442524e+56 grams. e) This last mass is the current mass of the universe and in consequence we may conclude that on each ψ1 jump, 64.118197599 grams/1.5881626836E-37 seg = 4.0372562749e+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 2.4137293502E+62 protons per second in the whole universe or a proton each 3.679381565e+22 km3 / seg. I could also say that ψ1 is the minimum time period that the nature admits for the spontaneous creation of matter. The question to answer now is ¿From where this radiation energy arose? If we calculate the heat energy along the history of the universe as a result of the density of 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 of this 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 Π^2/9 R^3/ λo^3 (5-9) Where R is the radius of the universe when you want to know how many photons are there and λo is the wave length of those photons in the Wien´s law peak of the curve. The moment of the arose of photon 1 is deduced from: N1 = 1 = N1^3 = a^3 R1^3/ λo1^3 Because R = cΨ y λo1 = b / T y T = K1/ Ψ^3/4 It is deduced: Ψ(Nf=1) = (b / K1 a c)^4 Where: b is the constant of Wien law = zK/ hc, a = (32Π^2/9)^(1/3) and c the speed of light. The result is. Ψ(Nf= 1) = 1.7186608419E-101 seg

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 Π^2/9

In this case, temperature is : T = K1/ Ψ^(3/4) To know when this happened, reference is that mass equivalent thermal energy is exactly equal to gravity energy. This last defined by Mg = H h/ c^2 Mt = Etp/ c^2 = 4.200179394E+51 grams And must be equal to Mg = H h/ c^2 when Nf = 1 (number of photons) Mg = H h/ c^2 cuando Nf = 1 Mg = h/c^2/ ψf1 then: ψfot1 = h/c^2/Mg = h/c^2/Mt = 1.755281379E-99 seg

1/ ψfot1 = 5.697092284E+98 = H fot1 Since there were only 1 photon which energy was all thermal and full filling Planck´s formula Et = h. w = h x Hfot1 Et = 3.774932981815E+72 lo cual ya sabíamos Temperature is then: Tfot1 = K1/ Ψfot1^(3/4) = 5.347082081E+87 kelvins The correspondent radius is Rfot1 = c/ Hfot1 = 5.262201191E-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 Π^2/9 R^3/ λo^3 it is not longer suitable for this moment since Nf = 1 and R = λ. Or the factor is now just 1 Another consequence is that factor zK/hc for Wien´s law is neither useful and must be also modified because R = λ = zK/hc/T must be accomplished: zK/hc = 2.813742170E-01 instead of 2.897772122E-01 It is very probable then, than some of the involved constants are not constants after all or a least during the BB. I will now clear up some concepts about the photons a) At the temperature T corresponds a wave length given by the Wien´s law in such a way that: T = b / λo (5-10) Where b = h c/zk (5-11)

To this wave length λo correspond a frequency fo = c/ λo And a equivalent mass mfo = hfo/c^2 In nowadays temperature is 2.7377812177 K

λo = 1.058504031E-01 cm fo = 2.832227835E+11 rps mfo = 2.088059030E-36 grams At this point, is necessary to understand the meaning of equation:

KzT = 2 m c^2 / β^(1/4) (4-12) Here we can see that energy involved is: z KT = 2 m c^2 / β^(1/4) From this we see that terms 2 m/ β^(1/4) represents a mass equivalent to something, but ¿What?. Making the operation 2 m/ β^(1/4) in the present time, it results equal to 2.088059030E-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 Wien´s 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. Still in the present time (the equations are good for all times)

2 m/ β^(1/4) = mfo (5-11) Mt/ Nf = Et/c^2/ Nf = (32 Π^6(KT)^4 R^3/ 45 h^3 c^5)/ 32 Π^2/9 R^3/ λo^3 = mf mf = 6.693531015E-38 grams by making the operation : mfo/mf = 2.088059030E-36/ 6.693531015E-38 = 31.19517973

This last number has the particularity that is equal to 2Πz such that:

mfo / mf = 2Πz And the wave length is just that of Wien, for there is only 1 single photon which energy is all thermal and fulfills the Planck’s formula: Et = h. w = h / Ψf1 = 6.626069570E-27 X 1.7552813790E-99 Et = 3.774932981807E+72 ergs This energy remains constant at any time. In fact, we can calculate when was the moment for the photon 1 to appear taking the thermal energy at any time and proceed the other way around, or :

Ψf1 = h/ Etx . Etx is thermal energy at any time. Once this time is calculated, other characteristics can be calculated of that moment using the equations already described. I Attach a chart with the results of the calculations for different important moments in the history of the universe, including this moment in which one can observe that the whole heat energy of the universe of the background radiation comes from this only super energy photon, that later on is “fractured” in less and less energy photons and every time in more quantity. One of the things that are observed in this chart it is that the reason photon / proton is NO constant. Although the calculation that I made for this present time coincides with the measurements actually made. Since the average temperature of the stars is around 6000 kelvins (although the ranges are extensive) it is to this temperature in general, when the stars would begin to absorb radiation. Others emitted it, and in consequence the temperature of the background radiation should have experience fluctuations, depending of the presence of stellar mass. I would dare to say that where the anisotropy of the radiation is positive it should to have being from hot stars and where it is negative it should have being from cold stars. The first stable particle should have existed until @ took the value of 1, or when q^2 = h c. or when according to (5-3) (µ/A)^2 = β/@^2 (µ/A)^2 = β = 2.6350273189E+36

m@1 = (h c/G β)^(1/2) = 3.3609178000E-23 gramos

Ψ@1 = h r / G(m@1)^2 = 5.7801860421E+11 seg

T@1 = 6.9170441449E+04 kelvins 6. - Variability of the values: Without presenting the easily obtained deductions, I do expose the equations of these, in relation to the age the universe of (Ψ). m = (h r/ G)^(1/2) Ψ^(-1/2) β = c Ψ/ r T = K1/ Ψ^(3/4) @ = (c/ r K2)^(1/2) Ψ^(1/2)

α = Estruct. fine const.= 2 Π (rK2)^(-1/2) Ψ^(-1/2)

N = ( K2 c^3/ r^3)^(1/2) Ψ^(3/2)

M = (K2 c^3 h/ r^2 G)^(1/2) Ψ

Evidently, if we replace ψ = 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 Ψact – L = c Ψ. Then the value of Ψ that must be used is:

Ψ = Ψact - L/c As an example: if we want to know the values of @ at a distance L from us, we have to use : Ψ = 1.3588273726E+10 – L/c And if we want to know the local values t seconds ago, we would have to use: Ψ act – t = Ψ 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. 7. - Final comments: 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 physical 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. But besides, 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: mg = Hh/c^2 = 1.720313736E-65 grams

β/@ 2.26891214E+39

f/H 2.26891214E+39

R/λ 2.26891214E+39

(N/@)^1/2 2.26891214E+39

ψ/w 2.26891214E+39

(M/mg/a)^1/3 2.26891214E+39

m/mg 2.26891214E+39 Another big different number results from Ng = M/mg = 1.005739691E+121 is also related with S this way: Ng = @S^3

The result of this analysis of the units of Planck, show us that these units doesn't represent the properties of the whole universe at that time. That is to say; - That the mass of Planck it is not the mass the universe, but the mass of the mason when β was equal to 1. - That the energy of Planck is the energy of the mason - That the time of Planck was not the age of the universe but just the reciprocal of the frequency of Planck as deduced from the mass of Planck. - That the length of Planck it is not the radius of the universe when the mass was the mass of Planck but just the Compton wavelength of the mason. - That the temperature of Planck is the temperature that would emerge as a consequence of the transformation in heat energy of the equivalent of 2 masses of Planck. So when I speak of “Planck´s time” I refer to the moment when β = 1 and no to the age of the universe from the origin zero of it. In fact, it is always possible to define as real age of the universe the derived from: Ψ = 1/H = h r / G m^2 It should be remembered that these ideas does not maintain as constant 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 to not being able to explain of where this energy arose. 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. Don´t get wrong with my words, we can see the past of the universe, but altered by the current properties of this. 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 with 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, very simple way, it has being enough to look for the possible combinations of 4 constants of nature and two pieces of information (the masses of the proton and the electron) to deduce all this. I didn´t 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. 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 essay 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 estranged is that it remains 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 space, since in each instant that the radius of the universe grows, the wavelength is always smaller to the radius of the universe. I suppose myself that as the space expands, 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 equation, 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 (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 to 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 mass of the particles is inversely proportional to the size of the universe just as it 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 Cashmere. 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 antiquity. 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 as 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 haulage 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 haulage 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 ψ. 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 “Planck´s 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 reduce 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 that some constants cannot be sustain as they are today. j=32pi^2/9 can´t 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 can be sustain any more and must be modified to 1.421880671E-16 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. Blue numbers are the data, black numbers the results. END

ACTUAL alfa = 1 PLANCK N = 1 UNIFICACION Nf = 1

B = 1

pi 3.1415926536E+00 3.1415926536E+00 3.1415926536E+00 3.1415926536E+00 3.1415926536E+00 3.1415926536E+00

4pi/3 4.1887902048E+00 4.1887902048E+00 4.1887902048E+00 4.1887902048E+00 4.1887902048E+00 4.1887902048E+00

G 6.673840000E-08 6.673840000E-08 6.673840000E-08 6.673840000E-08 6.673840000E-08 6.673840000E-08

K 1.380648800E-16 1.380648800E-16 1.380648800E-16 1.380648800E-16 1.380648800E-16 1.421880671E-16

z 4.965114231E+00 4.965114231E+00 4.965114231E+00 4.965114231E+00 4.965114231E+00 4.965114231E+00

h 6.626069570E-27 6.626069570E-27 6.626069570E-27 6.626069570E-27 6.626069570E-27 6.626069570E-27

c 2.997924580E+10 2.997924580E+10 2.997924580E+10 2.997924580E+10 2.997924580E+10 2.997924580E+10

b=hc/zK 2.897772122E-01 2.897772122E-01 2.897772122E-01 2.897772122E-01 2.897772122E-01 2.813742169E-01

j=32pi^2/9 3.509192676E+01 3.509192676E+01 3.509192676E+01 3.509192676E+01 3.509192676E+01 1.000000000E+00

r 6.576236113E-15 6.576236113E-15 6.576236113E-15 6.576236113E-15 6.576236113E-15 6.576236113E-15

K2 2.635027319E+36 2.635027319E+36 2.635027319E+36 2.635027319E+36 2.635027319E+36 2.635027319E+36

K1 4.585396658E+13 4.585396658E+13 4.585396658E+13 4.585396658E+13 4.585396658E+13 4.585396658E+13

ψ 4.285553574E+17 5.780186042E+11 2.193596249E-25 1.588162684E-37 8.324757140E-62 1.755281379E-99

m 3.903240712E-26 3.360917800E-23 5.455699632E-05 6.411819760E+01 8.856110220E+13 6.098954964E+32

q^2 2.307077352E-19 1.986445683E-16 3.224551039E+02 3.789658790E+08 5.234338643E+20 5.234338643E+20

l 5.662522667E-12 6.576236113E-15 4.051210752E-33 3.447100798E-39 2.495699405E-51 3.623930516E-70

f 5.294326851E+21 4.558724061E+24 7.400070655E+42 8.696944929E+48 1.201236244E+61 8.272577432E+79

w 1.888814250E-22 2.193596249E-25 1.351338449E-43 1.149829059E-49 8.324757140E-62 1.208813104E-80

α 8.610582969E+02 1.000000000E+00 6.160379102E-19 5.241753396E-25 3.795027068E-37 5.510645381E-56

β 1.953665619E+42 2.635027319E+36 1.000000000E+00 7.239995439E-13 3.795027068E-37 8.001843457E-75

S 2.268912136E+39 2.635027319E+36 1.623276723E+18 1.381216340E+12 1.000000000E+00 1.452070112E-19

H 2.333420835E-18 1.730048121E-12 4.558724061E+24 6.296584162E+36 1.201236244E+61 5.697092284E+98

R 1.284776640E+28 1.732856181E+22 6.576236113E-15 4.761191946E-27 2.495699405E-51 5.262201191E-89

V 8.883242212E+84 2.179596836E+67 1.191299069E-42 4.521012213E-79 6.511265974E-152 6.103668733E-265

M 1.73018781E+56 2.33360924E+50 8.85611022E+13 6.41181976E+01 3.36091780E-23 7.086520762E-61

N 4.432695632E+81 6.943368971E+72 1.623276723E+18 1.000000000E+00 3.795027068E-37 1.161923773E-93

Dm 1.947698559E-29 1.070660958E-17 7.433994075E+55 1.418226596E+80 5.161696379E+128 1.161026437E+204

T 2.737610851E+00 6.917044145E+04 1.430570908E+32 1.822660029E+41 2.958681598E+59 5.347082081E+87

λofot 1.058504031E-01 4.189321423E-06 2.025605376E-33 1.589858820E-42 9.794133047E-61 5.262201191E-89

ffot 2.832227835E+11 7.156110209E+15 1.480014131E+43 1.885654590E+52 3.060939203E+70 5.697092284E+98

1/ffot 3.530789394E-12 1.397407210E-16 6.756692244E-44 5.303198186E-53 3.266971128E-71 1.755281379E-99

R/λofot 1.213766412E+29 4.136364834E+27 3.246553446E+18 2.994726254E+15 2.548157548E+09 1.000000000E+00

Dt 4.249499104E-13 1.731940935E+05 3.168753406E+114 8.349751791E+150 5.797540750E+223 6.184695052E+336

Et 3.774932982E+72 3.774932982E+72 3.774932982E+72 3.774932982E+72 3.774932982E+72 3.774932982E+72

Mt 4.200179394E+51 4.200179394E+51 4.200179394E+51 4.200179394E+51 4.200179394E+51 4.200179394E+51

Nf = j(R/λofot)^3 6.274983091E+88 2.483497494E+84 1.200811627E+57 9.424940213E+47 5.806120473E+29 1.000000000E+00

Nf = Mt*( z/mfo)*2*z 6.275295492E+88 2.483621135E+84 1.200871410E+57 9.425409436E+47 5.806409531E+29 1.000000000E+00

mf= Mt/Nf 6.693197793E-38 1.691235608E-33 3.497783747E-06 4.456452029E+03 7.234054845E+21 4.200179393E+51 mf =

h/2/pi/z*ffot/c^2 6.693197793E-38 1.691151413E-33 3.497609618E-06 4.456230175E+03 7.233694715E+21 1.346352332E+50

mf= KT/2pi/c^2 6.693197793E-38 1.691151413E-33 3.497609618E-06 4.456230175E+03 7.233694715E+21 1.346352332E+50

mfo = mf*2*pi*z 2.088059030E-36 5.275839874E-32 1.091139926E-04 1.390198220E+05 2.256676411E+23 4.200179394E+51

mfo=hffot/c^2 2.088059030E-36 5.275839874E-32 1.091139926E-04 1.390198220E+05 2.256676411E+23 4.200179394E+51

mg 1.720313736E-65 1.275477402E-59 3.360917800E-23 4.642154582E-11 8.856110220E+13 4.200179394E+51

influence distance 1.284776640E+28 1.732856181E+22 6.576236113E-15 4.761191946E-27 2.495699405E-51 5.262201191E-89