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Microcosmos and macrocosmos together


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Development of a theory of origin of the Universe based on the mathematical calculation of the Hubble constant and the temperature of the cosmic background radiation. Calculation based on known physical constants of nature.

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Microcosmos and macrocosmos together

  1. 1. 1 INDEX
  2. 2. 2 FIRST PART: PREFACE------------------------------------------------------------------------------------------------------------------------2 1.- Units of Planck-------------------------------------------------------------------------------------------------------------6 2. – Some basic calculation of proton and electron properties and the fine structure constant. --–8 3.- Gravity parameter and relation between the electromagnetic and gravitational forces.---------10 4.- Planck units and a new calculation method.--------------------------------------------------------------------11 5.- Calculation of the Hubble parameter and the age of the universe ---------------------------------------13 6.- The mass of the universe and the number of protons it has.----------------------------------------------14 7. – The temperature of the universal cosmic background radiation.---------------------------------------16 8.- The "r" the classical radius of mason.-----------------------------------------------------------------------------20 9.- The cosmological constant.-------------------------------------------------------------------------------------------21 10.- Quantitative relation between electromagnetic and gravitational forces and their change with time.-------------------------------------------------------------------------------------------------------------------------23 11.- Origin of the thermal energyof the CBR -----------------------------------------------------------------------25 12.- Variation of values with time.---------------------------------------------------------------------------------------28 13.- Final conclusion and large numbers hypothesis.------------------------------------------------------------29 SECOND PART: INTRODUCTION AND PURPOUSE:-------------------------------------------------------------------------------34 1.- Description of the Forces.---------------------------------------------------------------------------------------------35 2.- General algebraic definition of the 4 forces.---------------------------------------------------------------------35 3.- Mathematical definition for each of the 4 forces from the standard information known.---------37 4.- Simple symmetry of the parameters of the forces.------------------------------------------------------------39 5.- Determination of the specific value for each force in the current era.----------------------------------40 6.- Summary of the magnitude of the coupling parameters.---------------------------------------------------43 7.- Parameters of the forces on the basis of the epoch ψ-------------------------------------------------------44 8.- Table of calculation.------------------------------------------------------------------------------------------------------47 PREFACE This work is the joining and reviewing of my two other works which titles are:
  3. 3. 3 FIRST PART: EXACT VALUE OF THE HUBBLE CONSTANT. THE MOST PRECISE VALUE OF THE HUBBLE CONSTANT DEDUCED FROM OTHER CONSTANTS OF PHYSICS. And NEWTON GRAVITATIONAL CONSTANT CALCULATED BY MEAN OF OTHER PHYSICS CONSTANTS. MUTUAL RELATIONS BETWEEN THE 4 FORCES OF NATURE AND ITS VARIATION WITH TIME. Here I decided to put both articles together and at the same time, to correct some mistakes and wrong uses of equations, to change some of the values of the physics constants I used and consequently, the results of the analysis and some new findings. As I said before, this analysis attempts to make a research on the physics history of the universe on the big picture, from the very first instants of its birth and 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. That means I recognize the Big Bang, but my results are different from the standard theories. The pretension of saying these results represents the actual universe and its birth, is mine. So I will leave my options open by saying that 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. The method is very simple. I don´t use high level math. On the contrary, the math I use is so simple that any high school student will understand it. Two simple things took me to all of these. First, I found the way of calculate the Hubble parameter by mean of some know constants of Physics, and the other was that I got the Gravitational coupling constant by mean of also some simple physics constants. This is an analysis without a theory to backup. It is a numerical analysis that is so close to reality of the numbers, that could be true. One of these results was already investigate by individuals of the size of Paul Dirac, Edward Milne, Arthur Eddington, that also without a big theoretical support for their ideas tried to explain what now is called the Large Numbers Hypotesis. They 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 presents. Even predicting it from empirical relationships. Their idea was that it must be some kind of connection between the classical physics and the relativity with, 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” to 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 dimensionlessl very big number, without exposing the physics reasons, except those that they were very similar to the ones found for the universe. 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 𝟒𝜫𝜺𝒐 𝑮 𝒎𝒆 𝟐 ≈ 𝟒. 𝟐 𝒆𝟒𝟐 Eddington, more accurate, formulated 𝑵𝒆 = 𝜫 𝟐 𝒒 𝟒 𝑮 𝟐 𝒎𝒑 𝟐 𝒎𝒆 𝟐 ≈ 𝟓𝒆𝟕𝟗
  4. 4. 4 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 doesn´t seems 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 on the Π^2 factor. 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 these, 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. As I said before, 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 these forces and how can we calculate them 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 physics 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, neutron and the electron mass at the present time, although I don't consider them as constants. 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.
  5. 5. 5 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. The whole result, will take us to know the values of the fundamental forces coupling parameters as function o the constants I mentioned and time, That is, I will be able to know their value by just knowing the elapsed time since de B.B at any epoch, the actual, the very old past, the first relevant instant which I call “ψ1” , and the future, the far away future. I also explain from where the thermal energy of the universe arose (which explanation is quite different of the standard cosmology) and the origin of matter. I will go far before the Planck´s time. When time had a value of 1.754235582839E-99 sec., which I define as the moment when the couple of 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/𝒕 𝟏 = 𝟑. 𝟕𝟕𝟕𝟏𝟖𝟑𝟒𝟐𝟔𝟔𝟖𝟓𝑬 + 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. And with the help of masses and charge of proton and electron which I don´t include as constants this analysis has being possible. This simple previous 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, 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 can´t be repeat it 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 today the creation of stable photons in function of the uncertainty Planck´s principle, unless such amount of energy density is used. What could be happening, as it is seeing from 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 and so on. 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 solve the cosmic background radiation in any time of the universe and of course on the actual time. I define the Planck epoch not to what has being call “Planck time” but the real time when gravitational parameter (or coupling parameter) had a unitary value. We will see that besides of the unitary value of the gravitational parameter on the Planck´s epoch, it seems not to 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 Planck´s data can be obtained just by making B = 1 I will begin exposing the today known as time of Planck and how it can be obtained without making the analysis that Planck used. For all these, I will 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 real constants, are not properties of matter but truly single conversion factors among those properties.
  6. 6. 6 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” or the neutron mass mn, and the fundamental electrical charge “qe” or just “q” 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 preface, I also clear up that here I have taken as postulate that the universe is tri dimensionally spherical since I use for its volume 4π/3 R^3. If it happens that the volume of it has a different formula, then the proper changes should be made. But at this time, I wouldn´t do it simplifying the calculations. 1.- Units of Planck from: of-planck / And from Wikipedia: 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. 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 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
  7. 7. 7 . 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 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, B 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: Tabla 2: Unidades de Planck básicas Nombre Dimensión Expresión Equivalencia aproximada en el Sistema Internacional Longitud de Planck Longitud (L) 1.616 252(81) × 10−35 m [1 ]
  8. 8. 8 Masa de Planck Masa (M) 2.176 44(11) × 10−8 kg [2 ] Tiempo de Planck Tiempo (T) 5.391 24(27) × 10−44 s [3 ] Carga de Planck Carga eléctrica (Q) 1.875 545 870(47) × 10−18 C Temperatura de Planck Temperatura (ML2T- 2/k) 1.416 785(71) × 1032 K [4 ] Notices: Up here, reference to the web pages mentioned ends. 2. – Some 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. 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 / 𝟐𝝅 , 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.π 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. 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 of the photon 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
  9. 9. 9 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) Signs + or – just is a reference to positive or negative charges, not a sign properly. Let us make now that 𝝀^𝟐 = 𝝀 + 𝑿 𝝀 − and 𝒎 𝟐 = 𝒎𝒑 . 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 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 /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 radius among them and we obtain 𝒓 = 𝒒^𝟐 / 𝒎. 𝒄^𝟐 (2.10) In this case we use q^2 instead of +𝑞. − 𝑞 since the magnitudes of the electrical charge of the proton and of the electron are the same. 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: “fine structure constant” . I won't stop to explain what it means, except in the fact, 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: 𝜶 = 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
  10. 10. 10 From this we obtain: 𝝀 = 𝒉/𝒎. 𝒄 = 𝒉. 𝒄 / 𝒎. 𝒄^𝟐 = 𝒉. 𝒄.𝒓 / 𝒒^𝟐 = 𝜶. 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 . 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 parameter and relation between the electromagnetic and gravitational forces. Now, entering into 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 𝟏. 𝒎 𝟐 / 𝒓 𝑬𝒈 = 𝑮. 𝒎^𝟐 / 𝒓 ergs Where 𝒎^𝟐 = 𝒎𝟏. 𝒎𝟐 or 𝒎 𝟐 = 𝒎𝒑 . 𝒎𝒆 (3.1) And if 𝑬𝒈 = 𝑭𝒈. 𝒉 being then F the gravitational frequency: 𝑭𝒈 = 𝑮 𝒎^𝟐 / 𝒉. 𝒓 (3.2) It may be noticed that on the previous equation, the product 𝑭𝒈.𝒉 is the potential gravitational energy between an electron and a proton at the “r” distance. 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 B as: 𝑩+ = 𝒉. 𝒄 / 𝑮. 𝒎𝒑^𝟐 and 𝑩 − = 𝒉. 𝒄 / 𝑮𝒎𝒆^𝟐 that takes us to: 𝑩 = 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 ) = 𝑩/𝜶 (3.4) 𝑺 = 𝟐. 𝟐𝟔𝟗𝟒𝟗𝟒𝟏𝟗𝟏𝟒𝟓𝟑𝑬 + 𝟑𝟗
  11. 11. 11 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 B is bigger today than α, 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. / a) Fundamental: Fundamental electric charge: q± = 4.8032045057 e-10 eu mass of proton: mp = 1.6726217770 e-24 gm mass of the electron m e = 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 = 6.671851565679E-08 erg-cm/gm^2 In the case of G the value I am using from now on and as this paper is a review of the previous ones, the value of G that I already calculate (shown later on the second part). I do this in order of not to change the values I got for the different parameters I am studying. b) Deduced: Parameter of Electrical force α = 8.610225752679E+02 Parameter of Gravitational force B = 1.954085733281E+42 mason radius r = 6.576236112650E-15 cm mason Compton Length wave λ = 5.66228775328360E-12 cm Frequency of the mason f = 5.29454649891554E+21cps gravitation / elect. parameter S = β / α = 2.26949419145339E+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 in a remote past, two of the fundamental forces (2) B and α were unified (take this as true for the time being). Since the difference among the magnitudes of these two mentioned are today very big, (as we have seen among B and α), 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 B would have tendency to be equal to α if we go back in time. Let us take then in fact, that there was a time when B1 = 1 And by the definition of B we arrive to : 𝑮 𝒎𝟏^𝟐 = 𝒉. 𝒄 Where m1 was the mass of the mason when B1 = 1 Then: 𝒎 𝟏 = (𝒉. 𝒄 / 𝑮)^(𝟏/𝟐) = µ (the mass of Planck) (4.1)
  12. 12. 12 That is to say that the mass of Planck is that when B = 1 and it proceeds from the value of the mason. Even more, it was the mason then. Even if μ or mp are the square roots of (𝒉 𝒄 / 𝑮), it doesn´t mean that it exist a negative μ as there are not a any negative “m” which come from the product mp x me, there is not the case μ^2 = μ+ X μ- (by the way, I am not sure this is true, maybe in fact there was a negative μ) Note that except for the use of h instead of ħ , µ = mp 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. Also note that I call m1 the mass of the mason when B = 1 We see therewith, how we can obtain the values of the units of Planck without appealing to make unitary the five units used by him. and since µ^𝟐 = 𝒉. 𝒄/𝑮 = 𝑩. 𝒎^𝟐 then: µ = 𝑩^(𝟏/𝟐)∗ 𝒎 (4.2) Therewith in mind, the data of the chart 1 are easily derived just making the substitution of h by ħ So: µ is the mass of the mason which current value is 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 on the epoch of Planck (and much bigger into the past). 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. 𝑮 /𝒄^𝟑)^(𝟏/𝟐) = 𝟒. 𝟎𝟓𝟎𝟔𝟎𝟕𝟏𝟖𝟖𝟕𝟐𝟏𝟎𝟏𝑬 − 𝟑𝟑 𝒄𝒎 𝑳𝒑 = 𝒉/µ. 𝒄 = 𝑮.µ/𝒄^𝟐 = 𝟒. 𝟎𝟓𝟎𝟔𝟎𝟕𝟏𝟖𝟖𝟕𝟐𝟏𝟎𝟏𝑬 − 𝟑𝟑 𝒄𝒎 µ = (𝒉 . 𝒄 / 𝑮)^(𝟏/𝟐) = 𝟓. 𝟒𝟓𝟔𝟓𝟏𝟐𝟓𝟔𝟏𝟖𝟒𝟖𝟔𝟒𝑬 − 𝟎𝟓 𝒈𝒓𝒂𝒎𝒔 𝝀𝒑 = 𝒍𝒑 = 𝒉 / µ. 𝒄 = (𝒉 𝑮 / 𝒄^𝟑) ^ (𝟏/𝟐) = 𝟒. 𝟎𝟓𝟎𝟔𝟎𝟕𝟏𝟖𝟖𝟕𝟐𝟏𝟎𝟏𝑬 − 𝟑𝟑 𝒄𝒎 𝒇𝒑 = 𝒄 / 𝝀𝒑 = (𝒄^𝟓 / 𝒉. 𝑮)^(𝟏/𝟐) = 𝟕. 𝟒𝟎𝟏𝟏𝟕𝟑𝟑𝟎𝟔𝟒𝟑𝟏𝟏𝟑𝑬 + 𝟒𝟐 𝒄𝒑𝒔 𝒕𝒑 = 𝟏 / 𝒇𝒑 = (𝒉 𝑮 / 𝒄^𝟓) ^ (𝟏/𝟐) = 𝟏. 𝟑𝟓𝟏𝟏𝟑𝟕𝟏𝟐𝟏𝟗𝑬 − 𝟒𝟑 𝒔𝒆𝒈 𝒆𝒑 = 𝒉. 𝒇𝒑 = (𝒉. 𝒄^𝟓 / 𝑮)^(/𝟐) = 𝟒. 𝟗𝟎𝟒𝟎𝟔𝟖𝟗𝟐𝟐𝟖𝟎𝟑𝟗𝟔𝑬 + 𝟏𝟔 𝒆𝒓𝒈 5.- Calculation of the Hubble parameter and the age of the universe Let us see the equation (3.2) with values: 𝑭 = 2.33291916712283E-18 𝒄𝒑𝒔 (5.1) That corresponds to a wavelength 𝑳 = 𝟏. 𝟐𝟖𝟓𝟎𝟓𝟐𝟗𝟏𝟔𝟔𝟒𝟏𝟒𝟖𝑬 + 𝟐𝟖 𝒄𝒎
  13. 13. 13 since 𝑳 = 𝒄/𝑭 Also an energy 𝒆 = 𝑭. 𝒉 = 𝟏. 𝟓𝟒𝟓𝟖𝟎𝟖𝟒𝟕𝟎𝟑𝑬 − 𝟒𝟒 ergs (5.2) And a mass of 𝒎𝒙 = 𝒆/𝒄^𝟐 = 𝟏. 𝟕𝟏𝟗𝟗𝟒𝟑𝟖𝟖𝟏𝟎𝟕𝟕𝑬 − 𝟔𝟓 grams (5.3) It is to make notice, that this last mass of the gravitational energy between proton and electron possibly is 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. 𝟐𝟖𝟓𝟎𝟓𝟐𝟗𝟏𝟔𝟔𝟒𝟏𝟒𝟖𝑬 + 𝟐𝟖 𝒄𝒎 Is this last mass the graviton? (5.3) I think so. We can say that the radius of the universe is the wave length of this virtual particle. But the analysis of the results shows some relationship of it with the electromagnetic force. A thing I will study latter. 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: 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 : 2.33291916712283E-18 sec^(-1) = 7.2007818230E+01 km/sec/mega parsec. constant of de Hubble H = 2.33291916712283E-18 sec^(-1) 𝑯 = 𝟕𝟏. 𝟗𝟖𝟔𝟑𝟔𝟑𝟕𝟐 𝒌𝒎/𝒔𝒆𝒄/𝒎𝒆𝒈𝒂𝒑𝒂𝒓𝒔𝒆𝒄 𝑯 = 𝑮. 𝒎^𝟐/𝒉. 𝒓 (5.4) And 𝒎 = (𝒉. 𝒓/𝑮𝝍)^(𝟏/𝟐) (5.5) From this we can obtain the current “age” of the universe as: ψ = 1 / H in years of 365.256363004 days 𝝍 = 1.3592323485𝐸 + 10 𝒚𝒆𝒂𝒓𝒔 About 13,592 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. being the BB at time=0 And the wavelength corresponds to the “Radius” of the universe 𝟏. 𝟐𝟖𝟓𝟎𝟓𝟐𝟗𝟏𝟔𝟔𝟒𝟏𝟒𝟖𝑬 + 𝟐𝟖 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 at all moment. One of the interesting things I got from taking H = 1/ψ and from (2.10) is: 𝒒^𝟐 = 𝑮. 𝒎^𝟑. 𝒄^𝟐. 𝝍/𝒉 (5.6) 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, it´s density, (the number of protons and electrons will be calculated later because other data must be obtained before) 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:
  14. 14. 14 𝑾. 𝑮 𝑴^𝟐 / 𝑹 = 𝑴 𝑪^𝟐 𝑹 = 𝑾 𝑮𝑴/𝑪^𝟐 (6-0) According with what I have seen, W has been use with different values depending of the theory in use. In the case of Friedmann equation: 𝑯^𝟐 = 𝟖𝝅 𝑮 𝝆 /𝟑 𝑪^𝟐 − 𝑲/ 𝑹^𝟐 + 𝜟 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 that: 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 start 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 𝝅 / 𝟑 𝑹^𝟑 𝑫𝒆𝒏𝒔𝒊𝒕𝒚 𝝆 = 𝑴 / 𝑽𝒐𝒍 = 𝟑 𝑪^𝟐/(𝟒𝝅 𝑮) 𝑹^𝟐 = 𝟏. 𝟗𝟒𝟕𝟒𝟒𝟏𝟑𝟗𝟔𝟗𝟓𝟖𝟗𝟑𝑬 − 𝟐𝟗 𝒈𝒓𝒂𝒎𝒔/𝒄𝒎^𝟑 But 𝑪^𝟐/𝑹^𝟐 = 𝑯^𝟐 and then 𝝆 = 𝟑 𝑯^𝟐/ 𝟒𝝅 𝑮 Also 𝑴 = 𝑪^𝟑 / 𝑮𝑯 = 𝟏. 𝟕𝟑𝟏𝟎𝟕𝟓𝟔𝟐𝟕𝟖𝟐𝟔𝟔𝟖𝑬 + 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 𝑵 = 𝑩 𝒙 𝒒^𝟐/ 𝑮 𝒎^𝟐 𝑵 = 𝑩 𝑺 = 𝑩^𝟐/𝜶 (6.2) Since M ≈ Np X mp and also 𝑴 = (𝑩^𝟐/𝜶)∗ 𝒎
  15. 15. 15 Without taking on count the electrons mass. And if 𝒎 𝟐 = 𝒎𝒑 . 𝒎𝒆 and 𝑫 = 𝒎𝒑/𝒎𝒆, is deduced that : 𝑵𝒑𝒓𝒐𝒕 ≈ (𝑩^𝟐/𝜶) / 𝑫^(𝟏/𝟐) 𝑵𝒑𝒓𝒐𝒕 ≈ 1.0349474410𝐸 + 80 actual In consequence, the number Np of masons at Planck´s epoch was: 𝑵 = 𝟏/𝜶𝒑 (6.3) That is, the reciprocal of the parameter of the electric force in the epoch of Planck. I can´t at this time calculate the number of protons and electrons until I find the ratio between them in different epochs. This will be calculated later. 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 B = 1 and B = h.c / G.m^2 at any time, so: µ becomes m lp becomes λ fp becomes f ep becomes energy of m rp = lp becomes r classic radius Bp = 1 is transformed in the current B Sp = becomes current S Tp becomes current T Notes: In the last case of microwave background radiation temperature, I will 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 won´t be able to see it any more. In my personal opinion, these ideas are wrong. I don´t 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 don´t 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 that 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 H.R will always be C. 7. – The temperature of the universal cosmic background radiation.
  16. 16. 16 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 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 𝒛 = 𝟓 − 𝟓𝒆^(−𝒛) 𝒛 = 𝟒. 𝟗𝟔𝟓𝟏𝟏𝟒𝟐𝟑𝟏𝟕𝑬+ 𝟎𝟎 K is the constant of Boltzman, λo it is the wavelength to which the 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 (7-1) The one that applied to µ give us: 𝑻𝒑 = 𝟐 µ 𝒄^𝟐 / 𝒛𝒌 (7-1) 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 (7-2) Equal to the temperature of the chart 1 except that this chart doesn't consider the value of 2/z. This temperature has a value of 𝟏. 𝟒𝟑𝟎𝟕𝟖𝟒𝟎𝟕𝟎𝟕𝟕𝟗𝟕𝟓𝑬 + 𝟑𝟐 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. It must be noticed I said “equivalent” to two masses of Planck, but I don´t mean that two masses really annihilated each other or at least I am not sure at this moment. Now, from the definition of 𝑩 = 𝒉. 𝒄/𝑮𝒎^𝟐 = 𝒉. 𝒓. 𝒄/𝑮𝒎^𝟐.𝒓 = (𝒉. 𝒓/𝑮𝒎^𝟐) . 𝒄/𝒓 = 𝒄/𝒓. 𝑯 = 𝑹/𝒓 Then 𝑩 = 𝑹 / 𝒓 (7.3) Which means, B 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, that it is universal constant. 𝑹𝒑 = 𝒓 Rp is the radius of the universe at the epoch of Planck. Also, since: 𝒒^𝟐/ 𝒎 = 𝒓. 𝒄^𝟐 = 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 (7.4) It is deduced that: 𝒓. 𝒄^𝟐 = 𝒒𝒑^𝟐 /µ and 𝒒𝒑^𝟐 = 𝒓. 𝒄^𝟐 µ = 𝒉. 𝒄 / 𝜶𝒑
  17. 17. 17 notes: qp is the unitary charge at the epoch of Planck 𝜶𝒑 = 𝒉. 𝒄/ 𝒓. 𝒄^𝟐.µ 𝜶𝒑 = 𝝀𝒑 / 𝒓 𝜶𝒑 = 𝟔. 𝟏𝟓𝟗𝟒𝟔𝟏𝟑𝟎𝟕𝟖𝟓𝟖𝟖𝟏𝑬− 𝟏𝟗 That it is the value of α when Bp = 1 or Bp Then, as N = B^2/α (6.2) So: 𝑵𝒑 = 𝟏 / 𝟔. 𝟏𝟓𝟗𝟒𝟔𝟏𝟑𝟎𝟕𝟖𝟓𝟖𝟖𝟏𝑬 − 𝟏𝟗 = 𝟏. 𝟔𝟐𝟑𝟓𝟏𝟖𝟔𝟎𝟎𝟏𝟏𝟔𝑬 + 𝟏𝟖 That it is the quantity of masons µ 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: 𝜳𝒑 = 𝒉. 𝒓 / 𝑮.µ^𝟐 = 𝟏/ 𝑯𝒑 = 𝟐. 𝟏𝟗𝟑𝟓𝟗𝟔𝟐𝟒𝟖𝟕𝟐𝟓𝟒𝟒𝑬 − 𝟐𝟓 𝒔𝒆𝒄 Defines the “age” of the Universe when m = µ and fp = Hp and Bp = 1 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 (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.µ = 𝟖. 𝟖𝟓𝟖𝟕𝟒𝟗𝟔𝟑𝟓𝟗𝟐𝟕𝑬 + 𝟏𝟑 𝒈𝒓𝒂𝒎𝒔 I use Capital Letters in referring to the Universe properties. The “Radius” was 𝑹𝒑 = 𝒓 = 𝑮. 𝑴𝒑 /𝑪^𝟐 = 𝟔. 𝟓𝟕𝟔𝟐𝟑𝟔𝟏𝟏𝟐𝟔𝟓𝟎𝑬 − 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 seems to be the temperature that would be generate by the annihilation of 2 µ. But this is not so, as we shall see. Yet it indicates relevance of the Planck´s epoch. . This temperature will allow us to calculate the density of generated heat or thermal energy. This is calculated with the formula of Planck: Density of thermal radaiation energy 𝑫𝒆𝒕 = 𝟖𝝅^𝟓 (𝑲.𝑻)^𝟒 / (𝟏𝟓. 𝒉^𝟑 𝑪^𝟑) With a value of 𝑫𝒆𝒕 = 𝟑. 𝟏𝟕𝟎𝟔𝟒𝟐𝟒𝟕𝟑𝟓𝟓𝟓𝑬 + 𝟏𝟏𝟒 𝒆𝒓𝒈𝒔 / 𝒄𝒎^𝟑 when 𝑇 = 𝑇𝑝
  18. 18. 18 Being the volume the Universe in the age of Planck equal to (𝟒𝝅/ 𝟑) 𝑹𝒑^𝟑 This would be: 𝑉𝑝 = 𝟏. 𝟏𝟗𝟏𝟐𝟗𝟗𝟎𝟔𝟖𝟗𝟑𝟖𝟐𝟕𝑬 − 𝟒𝟐 𝒄𝒎^𝟑 And the total radiant energy in the age of Planck is equal to the density of this energy multiplied by the volume: 𝑬𝒕𝒑 = 𝟑. 𝟕𝟕𝟕𝟏𝟖𝟑𝟒𝟐𝟔𝟔𝟖𝟓𝑬 + 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( 𝝍𝒑). 𝑽𝒑 = 𝑫𝒆𝒕 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 . 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝑽𝒐𝒍 ( 𝑻𝒑) 𝟒. 𝑹𝒑 𝟑 = ( 𝑻𝒂𝒄𝒕) 𝟒. 𝑹𝒂𝒄𝒕^𝟑 (7.7) Or what is the same : 𝑻^𝟒 𝑿 𝑹^𝟑 = 𝟏. 𝟏𝟗𝟏𝟖𝟔𝟗𝟏𝟒𝟗𝟖𝑬+ 𝟖𝟔 𝒌𝒆𝒍𝒗𝒊𝒏 𝟒. 𝒄𝒎^𝟑 (7.8) That is to say, when conserving the energy, the temperatures and the radius are defined for (7.8). So, if we know the radius of the universe at any moment, we can know what was or will be the temperature of the CBR. Then we can calculate the value of the temperature of current background radiation as consequence of the conservation of the thermal energy as this:. 𝑻𝒂𝒄𝒕 = 𝑻𝒑 𝑿 (𝑹𝒑 / 𝑹𝒂𝒄𝒕)^(𝟑/𝟒) We can also see it of this other way: As 𝑩 = 𝑹/𝒓 (7.3) Then do of (7.7) (𝑻𝒑/𝑻𝒂𝒄𝒕)^𝟒 = 𝑩^𝟑 (7-8) And because according to (7.2) 𝑻𝒑 = 𝟐 (𝒉. 𝑪^𝟓/𝑮)^(𝟏/𝟐) / 𝒛. 𝑲 And because 𝑩 = 𝒉. 𝒄/𝑮𝒎^𝟐 it is deduced that: (𝑻𝒂𝒄𝒕)^𝟐 = 𝟒 𝒉. 𝑪^𝟓/(𝑮. 𝑲^𝟐 . 𝒛^𝟐 . 𝑩^(𝟑/𝟐)) (7.9) The previous equation is general and it is valid for any time in which B is known Vg: in the Planck epoch when Bp = 1 the calculated temperature is precisely the Tp From this equation we can get another that had being already obtained in another separated analysis, but here I get it with better of support. 𝑲𝒛𝑻 = 𝟐 {𝒉 𝒄 / 𝑮 𝒎^𝟐 }^(𝟏/𝟐) ∗ {𝒎 𝑪^𝟐/ 𝑩^(𝟑/𝟒) = 𝟐 𝒎 𝑪^𝟐/ 𝑩^(𝟏/𝟒) 𝑲. 𝒛. 𝑻 = 𝟐 . 𝒎 . 𝑪^𝟐 / 𝑩^(𝟏/𝟒) (7.10) Note: that that m/B of this (7.10) equation is 𝒎𝒇𝒐 = 𝟏. 𝟎𝟒𝟒𝟎𝟏𝟔𝟕𝟎𝟕𝟕𝟒𝟔𝑬 − 𝟑𝟔 As we will see latter. Meaning the relation among the mass of mason with CBR temperature
  19. 19. 19 And replacing B 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 = 𝜴 𝒎^(𝟑/𝟐) (7.12) Being 𝜴 = {𝟐 𝑮^(𝟏/𝟒) 𝑪^(𝟕/𝟒) }/ {(𝒉)^(𝟏/𝟒) 𝑲𝒛} constant (7.13) 𝑻 𝒂𝒄𝒕 = 𝟐. 𝟕𝟑𝟕𝟓𝟕𝟕𝟐𝟔𝟕𝟕𝟖𝟖𝑬 + 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. In fact I think that even if it is expressed as function of m I think that the real dependence is from the size of the universe, its radius. 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 ± 0.002 Kelvin Now then, since the temperature can be expressed as function of m, 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/ 𝜴)^(𝟒/𝟑) = 𝒎^𝟐 y 𝒎^𝟐 = (𝒉 𝒓 / 𝑮) / 𝜳 The result is: 𝑻 = 𝑲𝟏/ 𝜳^(𝟑/𝟒) (7.15) 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) 𝑲𝟏 = 𝟒. 𝟓𝟖𝟔𝟎𝟕𝟗𝟗𝟎𝟔𝟓𝟐𝟎𝟖𝟔𝑬 + 𝟏𝟑 𝑲 𝒅𝒆𝒈𝒓𝒆𝒆𝒔. 𝒔𝒆𝒄^(𝟑/𝟒) For example: for the time of Planck and making use of (7.15) when 𝝍𝒑 = 𝟐. 𝟏𝟗𝟑𝟓𝟗𝟔𝟐𝟒𝟖𝟕𝟐𝟓𝟒𝟒𝑬 − 𝟐𝟓 𝒔𝒆𝒄 𝑻𝒑 = 𝑲𝟏 / 𝝍𝒑^(𝟑/𝟒) = 𝟏. 𝟒𝟑𝟎𝟕𝟖𝟒𝟎𝟕𝟎𝟕𝟕𝟗𝟕𝟓𝑬 + 𝟑𝟐 𝒅𝒆𝒈𝒓𝒆𝒆𝒔 𝑲 And for the current age when 𝝍 𝒂𝒄𝒕 = 𝟏 / 𝑯 = 𝟒. 𝟐𝟖𝟔𝟒𝟕𝟓𝟏𝟑𝟒𝟐𝟏𝟐𝟔𝟏𝑬 + 𝟏𝟕 𝒔𝒆𝒄 𝑻𝒂𝒄𝒕 = 𝟐. 𝟕𝟑𝟕𝟓𝟕𝟕𝟐𝟔𝟕𝟕𝟖𝟕𝟓𝟓𝑬 + 𝟎𝟎 𝑲 These equations are rater complicated. But there are several simpler methods of calculus for it: T = K1/ψ^(3/4) T = mfo c^2/ ZK T = 2m c^2/(ZK B^(1/4)) According with the Wien´s law, the photons of the peak of the curve which emits at this temperature, have a wave length of : λo = b/ T with a mass-energy of mf0 = h/λo c λo = 1.058517016269E-01 cm mf0 = h/c λo = 1.044016707746E-36 grams
  20. 20. 20 For the actual temperature. 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: Ref. “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. 𝟎𝟓𝟎𝟏𝟑𝟎𝟔𝟖𝟗𝟓 𝑲𝒆𝒍𝒗𝒊𝒏𝒔 A temperature with a difference of 0.10 Kelvins. Quite consistent, regarding the measurements methods. Where I differ of the standard theory, is that it says that at the 400,000 years after the BB the temperature was of 3,000 Kelvin or decoupling temperature 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, (or 3000 Kelvins) 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 B was unitary. And also for the accepted mass conservation idea 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 have 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 Bp = 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. Rp = 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 = 𝑩. 𝒓.(𝑻𝒂/𝑻𝒑) ^(𝟒/𝟑)
  21. 21. 21 with: µ = 𝑩 ^(𝟏/𝟐) ∗ 𝒎 and 𝑲𝒛𝑻 = 𝟐 𝒎 𝒄 ^ 𝟐 / 𝑩 ^(𝟏/𝟒) we arrived at: (𝑻/𝑻𝒑)^(𝟒/𝟑) = 𝟏/𝑩 and 𝑹𝒑 = 𝑩. 𝒓 (𝑻𝒂/𝑻𝒑)^(𝟒/𝟑) is reduced to: 𝒓 = 𝑹𝒑 = 𝟔. 𝟓𝟕𝟔𝟐𝟑𝟔𝟏𝟏𝟐𝟔𝟓𝟎𝑬 − 𝟏𝟓 𝒄𝒎 constant 9.- The cosmological constant. Just as interesting note and without pretending otherwise, the cosmological constant Λ 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 = 1.285052916641E+28 cm is 6.0556111042E-57 cm^(-2) Can It be speculated that? 𝜦 ≈ 𝟏/𝑹^𝟐 If this previous relationship is 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^(-89), then the cosmological constant would be of the order of 10^(180). 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%). 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 they 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, or 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 being why we talk about a B.B? And if it 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 to 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
  22. 22. 22 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. 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 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 explained 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:
  23. 23. 23 𝜶 = 𝒉. 𝒄/𝒒^𝟐 = 𝒉. 𝒄 / (𝒎. 𝒓𝒄^𝟐) = 𝒉 /𝒎. 𝒓. 𝒄 And from (5.5) 𝜶 = (𝒉𝑮𝝍/(𝒓^𝟑. 𝒄^𝟐))^(𝟏/𝟐) (10.1) Since 𝒉 /𝒓. 𝒄 is a constant value in time, it is simple to see that α depends only of the mass so: 𝛼 = 𝐴 / 𝑚 being 𝑨 = 𝒉/𝒓. 𝒄 = 3.3609178001𝐸 − 23 grams constant Which is the mass of m when α = 1 But α 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 on Planck age would be : 𝒒𝒑 = (𝒓. 𝒄^𝟐 𝒙 µ)^(𝟏/𝟐) 𝒒𝒑 = 𝟏. 𝟕𝟗𝟓𝟖𝟑𝟕𝟐𝟕𝟒𝟎𝟔𝟏𝑬 + 𝟎𝟏 𝒖𝒆𝒔 But also, as 𝑩 = µ^𝟐 / 𝒎^𝟐 then we would have that: 𝒎^𝟐 = 𝑨^𝟐 / @ ^𝟐 = (µ^𝟐 /𝑩) (µ/𝑨)^𝟐 = 𝑩/ 𝜶 ^𝟐 = 𝑲𝟐 = 𝟐. 𝟔𝟑𝟓𝟎𝟐𝟕𝟑𝟎𝟔𝟒𝑬 + 𝟑𝟔 constant without units 𝑩 = 𝒌𝟐 𝜶 ^𝟐 (10.3) Valid for any time. Especially in the epoch of Planck when B = 1 𝜶𝒑 = (𝟏/𝒌𝟐)^(𝟏/𝟐) = 𝟔. 𝟏𝟓𝟗𝟒𝟔𝟏𝟑𝟎𝟕𝟖𝟔𝟎𝑬 − 𝟏𝟗 For the current time it is also deduced since 𝑵 = 𝑩 ^𝟐 / 𝜶 according to (6-2) that: 𝑵 = 𝑲𝟐^𝟐.𝜶 ^𝟑 (10.4) 𝑵 = 𝟒. 𝟒𝟑𝟒𝟕𝟖𝟔𝟐𝟐𝟏𝟐𝟖𝟑𝑬 + 𝟖𝟏 On the current epoch. In the epoch of Planck : 𝑵𝒑 = 𝒌𝟐^𝟐 𝑿 𝜶𝒑^𝟑 = 𝟏. 𝟔𝟐𝟑𝟓𝟏𝟖𝟔𝟎𝟎𝟏𝟏𝟔𝑬+ 𝟏𝟖 And the total mass of the universe at that epoch would be : 𝑵𝒑 ∗ µ = 𝟖. 𝟖𝟓𝟖𝟕𝟒𝟗𝟔𝟑𝟓𝟗𝟐𝟕𝑬 + 𝟏𝟑 𝑴𝒑 = 𝟖. 𝟖𝟓𝟖𝟕𝟒𝟗𝟔𝟑𝟓𝟗𝟐𝟕𝑬 + 𝟏𝟑 𝒈𝒓𝒂𝒎𝒔 (10.5) Some of these numbers were obtained also in chapter 7 We can also here, calculate the mass of the particle No 1 that appeared in the Universe. So from (10.4), (10,3) and B = μ^2/m^2:
  24. 24. 24 𝟏 = (µ/𝒎 𝑩𝟏)^𝟑∗ 𝑲𝟐^(𝟏/𝟐) 𝒎 𝑩𝟏 = µ ∗ 𝑲𝟐^(𝟏/𝟔) = 𝟔. 𝟒𝟏𝟑𝟎𝟗𝟑𝟔𝟓𝟒𝟎𝟖𝟗𝑬 + 𝟎𝟏 𝒈𝒓𝒂𝒎𝒔 (10.6) The mass of the universe was of course 𝑀1 = 𝑁1 ∗ 𝑚1 = 𝟔. 𝟒𝟏𝟑𝟎𝟗𝟑𝟔𝟓𝟒𝟎𝟖𝟗𝑬 + 𝟎𝟏 𝜶 𝟏 = 𝟏 / 𝑲𝟐^(𝟐/𝟑) = 𝟓. 𝟐𝟒𝟎𝟕𝟏𝟐𝟏𝟕𝟔𝟐𝟕𝟐𝑬− 𝟐𝟓 (10.7) 𝑩 𝟏 = 𝜶 𝟏^(𝟏/𝟐) = 𝟕. 𝟐𝟑𝟗𝟐𝟕𝟔𝟑𝟐𝟖𝟔𝟔𝟏𝑬 − 𝟏𝟑 (10.8) Now we can calculate the values of α and B when they were unified, that is to say when αu = Bu. in this case 𝑵𝒖 = 𝑩𝒖^𝟐 / 𝜶𝒖 = 𝜶𝒖 = 𝑩𝒖 And since N = K2^2.α^3 then: 𝑵𝒖 = 𝑲𝟐^𝟐.𝑵𝒖^𝟑 𝑩𝒖 = 𝑵𝒖 = 𝟏 / 𝑲𝟐 = 𝟑. 𝟕𝟗𝟑𝟖𝟗𝟔𝟑𝟔𝟎𝟑𝟎𝟏𝑬 − 𝟑𝟕 As N should be ≥ 1, then, unification happened before there was any particle The mass energy of unification per particle would be: As 𝒎 = µ / 𝑩^(𝟏/𝟐) then : 𝒎𝒖 = µ/𝑩𝒖^(𝟏/𝟐) α 𝐸𝒖 = 𝒎𝒖. 𝒄^𝟐 = µ. 𝒄^𝟐/𝑩𝒖^(𝟏/𝟐) = 𝟕. 𝟗𝟓𝟗𝟒𝟕𝟒𝟗𝟎𝟒𝟓𝑬 + 𝟑𝟒 𝒆𝒓𝒈𝒔 𝒎𝒖 = 𝟖. 𝟖𝟓𝟖𝟕𝟒𝟗𝟔𝟑𝟓𝟗𝟐𝟓𝑬 + 𝟏𝟑 𝒈𝒓𝒂𝒎𝒔 But, at this time (unification of α and B) there were no any particle, then, ¿what was this mass-energy? The same as the total at the Planck´s era. And mainly, the mass of the graviton at that time and the total mass of the universe. (as you can see on the table of values trough time) 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 = 𝜴 𝒎𝒖^(𝟑/𝟐) = 𝟐. 𝟗𝟓𝟗𝟕𝟖𝟑𝟖𝟕𝟏𝟐𝟒𝟎𝟗𝟑𝑬 + 𝟓𝟗 kelvins We can calculate when this happened by making use of : 𝜳𝒖 = 𝒉 𝒓 / 𝑮 𝒎𝒖^𝟐 𝜳𝒖 = 𝟖. 𝟑𝟐𝟐𝟐𝟕𝟔𝟖𝟐𝟒𝟎𝟎𝟗𝟑𝟎𝑬 − 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 Planck´s units, the scientific tradition makes wrongly to the Planck´s 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 ψ and the inverse of Planck´s frequency as 1/fp = t There was one single moment when ψu = tu, that is in the unification, no on Planck´s epoch. 𝝍𝒖 = 𝒉. 𝒓/ 𝑮. 𝒎𝒖^𝟐
  25. 25. 25 𝒇𝒖. 𝒉 = 𝒎𝒖 𝑪^𝟐 = 𝒒𝒖^𝟐/ 𝒓 = 𝑮 𝒎𝒖^𝟐/𝒓 y 𝑮 𝒎𝒖^𝟐/ 𝒉 𝒓 = 𝟏/ 𝝍𝒖 and of course: tu = ψu Here is worth to stop in some especially remarkable results: a) At the moment I identified on the table when it was the first proton (Np=1) the mass of the universe was exactly the sum of the mass of 1 proton plus 1 electrón. Proton number 1 existed before N= 1 (the mason) Or, at any time: 𝑴 = (𝒎𝒑 + 𝒎𝒆). 𝑵𝒑 b) The mason No 1 ( N= 1) had a mass of 6.413093654089E+01 grams This mass existed when 𝝍𝑵 𝟏 = 𝒉. 𝒓 / 𝑮. 𝒎𝑵 𝟏^𝟐 = 𝟏. 𝟓𝟖𝟖𝟎𝟎𝟒𝟗𝟑𝟗𝟖𝟎𝟒𝑬 − 𝟑𝟕 𝒔𝒆𝒄 From the moment zero and till the current age of the universe equal to : 𝟒. 𝟐𝟖𝟔𝟒𝟕𝟓𝟏𝟑𝟒𝟐𝟏𝟑𝑬 + 𝟏𝟕 𝑠𝑒𝑐. 4.286475134213E+17/1.588004939804E-37 steps have lapsed of ≫ 2.6992832495E+54 jumps of ψ1 seconds each one If we multiply this number of jumps by the mass m1 (the mass when N=1) it will give us a mass of 1.731075627827E+56 grams This last mass is the current mass of the universe and in consequence we may conclude that on each ψ1 jump, 6.413093654089E+01grams/1.58800493980E-37 sec = 4.0384595119E+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 2.4131344879E+62 atoms of hydrogen per second in the whole universe, or 1 hydrogen atom each 3.681E+22 cm3 /sec. I could also say that ψ1 is the minimum time period that the nature admits for the spontaneous creation of matter. Or putting it on this way: In shorter periods of time, of 1.588004939804E-37 sec mass is not created. 11.- Origin of the thermal energy of the CBR The question to answer now is ¿From where thermal 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, with my equations, 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. This amount of energy I calculated from the epoch of Planck´s which fortunately depends only of known physics constants which at the same time allow me to calculate the today CBR temperature as the section 7 explains. And as I took as good the result of that calculation, from it is that I decided that thermal energy is constant. It is possible to calculate the number of photons in any time of the universe. It is of special interest the moment when the first photon arose. For that I will use a very simple equation of the quantum physics that says: 𝑵 𝒇𝒐𝒕 = 𝟏𝟔𝝅 𝑲^𝟑∗ 𝑻^𝟑 ∗ 𝑽 ∗ 𝜻(𝟑) /(𝒉^𝟑 ∗ 𝒄^𝟑) (11.1) Also expressed as function of the total thermal energy by using thermal density Planck´s equation would be: 𝑵𝒇𝒐𝒕 = 𝟑𝟎 𝑷 𝑬𝒕/𝝅^𝟒/ 𝑲𝑻
  26. 26. 26 And, as we know how T changes with time, we found how thermal energy was determined by the time like this: (𝝅^𝟒. 𝑲.𝑲𝟏)/(𝟑𝟎. 𝑷. 𝑬𝒕)^(𝟒/𝟑) = 𝝍 (11.2) By changing the Volume for V = Et/𝛒t. P is the factor ζ(3) = P Where V is the volume of the universe when you want to know how many photons are there and ζ(3) = P = 1+1/2^3+1/3^3+1/4^3……… = 1.202056903159594……is a constant named constant of Apéry. Actually, the average number of photos in the universe is: 3.699688334306E+87 as (11.2) said. But this result has a failure for a special case; the equation for the number of photons is good for a big amount of it, (in fact calculates the average number) but NO if there is only one or very few. Because of this, the factor for the number of photons when they are a few, can`t be expressed with (11.2). So if the number of photons is 1, the factor should be another that must be calculated. Besides, another factor has to be taking in account: The equation is for wave lengths much time shorter of the vessel where they are contained, and I will add that the wave length of photons shouldn´t being larger than twice the radius of the vessel. But in general, is good enough to count on the average, the amount of photons in the universe. Besides, there are chances of a good approach if we can calculate the mass-energy of the photons of the maximum emission at a given temperature and suppose they (or it, if there is only one) belongs to that category. I mean, if at the beginning there were only one photon, it will probably fit well with the Wien´s law. But maybe not exactly. In any case, temperature is : 𝑻 = 𝑲𝟏/ 𝜳^(𝟑/𝟒) To know when this happened, it is just a matter of using the next equation: 𝜳𝟏 = 𝒉/𝑬𝒕 = 𝟏. 𝟕𝟓𝟒𝟐𝟑𝟓𝟓𝟖𝟐𝟖𝟑𝟗𝑬− 𝟗𝟗 𝒔𝒆𝒄. (11.3) Where Et = 𝟑. 𝟕𝟕𝟕𝟏𝟖𝟑𝟒𝟐𝟔𝟔𝟖𝟓𝑬 + 𝟕𝟐 ergs as we see on (7.6) 𝟏/𝝍𝒇𝒐𝒕𝟏 = 𝟓. 𝟕𝟎𝟎𝟒𝟖𝟖𝟔𝟑𝑬 + 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 (11.4) Temperature is then: 𝑻𝒇𝒐𝒕𝟏 = 𝑲𝟏/ 𝜳𝒇𝒐𝒕𝟏^(𝟑/𝟒) = 𝟓. 𝟑𝟓𝟎𝟐𝟔𝟗𝟕𝟕𝟎𝟒𝟓𝟗𝑬 + 𝟖𝟕 𝑲𝒆𝒍𝒗𝒊𝒏 𝑻𝒉𝒆 𝒄𝒐𝒓𝒓𝒆𝒔𝒑𝒐𝒏𝒅𝒆𝒏𝒕 𝒓𝒂𝒅𝒊𝒖𝒔 𝒊𝒔 𝑹𝒇𝒐𝒕𝟏 = 𝒄/ 𝑯𝒇𝒐𝒕𝟏 = 𝟓. 𝟐𝟓𝟗𝟎𝟔𝟓𝟗𝟕𝟐𝟗𝟎𝟑𝑬 − 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 (10.9) it is not longer suitable for this moment since Nf = 1 and R = λ. So the Another consequence is that constant of Wien´s law can’t be kept and must be also modified because R = λ = zK/hc/T must be accomplished:
  27. 27. 27 b = 2.813742169568E-01 instead of b = 2.897772121304E-01 At the same time, provides the constant energy of the thermal radiation with value with value 3.7746823888E+72 ergs for all times. Otherwise if I don´t change it, the amount of first photons would be 1.893 instead of 1 which is imposible, since it can´t be fractions of a photon. Also, the factor P should be change from 1.202056903159594 to 6.349931800055E-01 At this point, is necessary to understand the meaning of equation: 𝑲𝒛𝑻 = 𝟐 𝒎 𝒄^𝟐 / 𝑩^(𝟏/𝟒) (11.5) From this we see that terms 2 m/B^(1/4) represents a mass equivalent to something, but ¿What?. Making the operation 2 m/ B^(1/4) in the present time, it results equal to 2.088033415493E-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. Clarifying again: mfo is the mass corresponding to the photon whose wavelength λo is at the peak of the curve of radiation. mf is the average mass of all the photons of the total radiation curve. So mfo = 2.088033415493E-36 mf = Et/c^2/Nf = 1.135956051340E-36 Which proportion is constant equal to 30Pz/π^4= 1.838128696115E+00 except when mfo = mf at the first moment or on 30Pz/π^4 = 1 on which case P = 6.349931800055E-01 It is really difficult to know what was happening when time was about 10 e-99 sec. old. But that won´t stop me to guess how it was. 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 came from this single super energetic photon that was subsequently "fractured" in photons each time less energetic and growing on number. 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 ψ, the time value and Excel calculates the rest. past, present and future. The use of this table has many advantages. As an example: If you want to know when was the time when electrons had a mass half of the protons, you just start to give values at the time and see what happen with the mass of the electron. So you keep on changing the time until you see in the me cell the value you want. It is not hard once you get closer. So at first make big changes, and then move the time decimal by decimal and you will easily see what´s going on. In 5 minutes or so, you will reach the value of time that gives the preselected electron mass. In general I made the calculation up to de 12th decimal. On resume: The CBR comes from the Planck´s uncertainty principle by mean of the equation (11.4). Some how it seems only work on this case in a “place” with no space (at least as we know it) at the very beginning, and once it was created the first photon, no other new one can be born. Maybe that only happens where there are no photons or any kind of particle whatsoever in the space. If this wouldn´t happen, the principle would be creating more and more energy up to who knows how much. Maybe the nothingness is necessary for the creation of something 12.- Variation of values with time
  28. 28. 28 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) (12.1) 𝑩 = 𝒄 𝜳/ 𝒓 (12.2) 𝑻 = 𝑲𝟏/ 𝜳^(𝟑/𝟒) (12.3) 𝜶 = (𝒄/ 𝒓 𝑲𝟐)^(𝟏/𝟐) 𝜳^(𝟏/𝟐) (12.4) 𝜶 = 𝒇𝒊𝒏𝒆 𝒆𝒔𝒕𝒓𝒖𝒄𝒕. 𝒄𝒐𝒏𝒔𝒕.= 𝟐 𝜫 (𝒓𝑲𝟐)^(−𝟏/𝟐) 𝜳^(−𝟏/𝟐) (12.5) 𝑵 = ( 𝑲𝟐 𝒄^𝟑/ 𝒓^𝟑)^(𝟏/𝟐) 𝜳^(𝟑/𝟐) (12.6) 𝑴 = (𝑲𝟐 𝒄^𝟑 𝒉/ 𝒓^𝟐 𝑮)^(𝟏/𝟐) 𝜳 (12.7) Of course, these are only a few, but the rest would be easily calculated with the rest of the equations 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 α at a distance L from us, we have to use : 𝜳 = 𝟒. 𝟐𝟖𝟔𝟒𝟕𝟓𝟏𝟑𝟒𝟐𝟏𝟑𝑬+ 𝟏𝟕– 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 α and the consequent increase of the value of the fine structure constant. 13.- 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 he 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: 2.269494191453E+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 it 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:
  29. 29. 29 𝑩/𝜶 = 𝟐. 𝟐𝟔𝟗𝟒𝟗𝟒𝟏𝟗𝟏𝟒𝟓𝟑𝑬 + 𝟑𝟗 𝒇/𝑯 = 𝟐. 𝟐𝟔𝟗𝟒𝟗𝟒𝟏𝟗𝟏𝟒𝟓𝟑𝑬 + 𝟑𝟗 𝑹/𝝀 = 𝟐. 𝟐𝟔𝟗𝟒𝟗𝟒𝟏𝟗𝟏𝟒𝟓𝟑𝑬 + 𝟑𝟗 (𝑵/𝜶)^𝟏/𝟐 = 𝟐. 𝟐𝟔𝟗𝟒𝟗𝟒𝟏𝟗𝟏𝟒𝟓𝟑𝑬 + 𝟑𝟗 𝝍/𝒘 = 𝟐. 𝟐𝟔𝟗𝟒𝟗𝟒𝟏𝟗𝟏𝟒𝟓𝟑𝑬 + 𝟑𝟗 (𝑴/𝒎𝒈/𝒂)^𝟏/𝟑 = 𝟐. 𝟐𝟔𝟗𝟒𝟗𝟒𝟏𝟗𝟏𝟒𝟓𝟑𝑬 + 𝟑𝟗 𝒎/𝒎𝒈 = 𝟐. 𝟐𝟔𝟗𝟒𝟗𝟒𝟏𝟗𝟏𝟒𝟓𝟑𝑬 + 𝟑𝟗 To get the number P. Dirac found as: 2.π.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: 𝒎𝒙 = 𝑯. 𝒉/𝑪^𝟐 (13.1) 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. 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 = 𝑩^𝟐 𝒙 𝒓 /𝝀 𝑵 = 𝑩^𝟐 / 𝜶 𝑵 = 𝑺 𝑩 = 𝟒. 𝟒𝟑𝟒𝟕𝟖𝟔𝟐𝟐𝟏𝟐𝟖𝟑𝑬 + 𝟖𝟏 Where B is the gravitational parameter 𝛽 = ℎ 𝐶/𝐺 𝑚^2 Let us make the number 𝑵𝒙 = 𝑴 /𝒎𝒙 (13.2) 𝑵𝒙 = (𝑹𝑪^𝟐/ 𝑮) / (𝑯/𝑪^𝟐) (13.3) where 𝒎𝒙 = 𝑯𝒉/𝒄^𝟐 (13.4) 𝑩 = 𝒉 𝑪/𝑮 𝒎^𝟐 , 𝝀 = 𝜶 . 𝒓 and 𝑯 = 𝑮 𝒎^ 𝟐/ 𝒉 𝒓 We arrived at 𝑵𝒙 = 𝑩^𝟑/ 𝜶^𝟐 = 𝑵. 𝑺 = 𝟏. 𝟎𝟎𝟔𝟒𝟕𝟐𝟏𝟓𝟔𝟗𝟓𝟒𝑬 + 𝟏𝟐𝟏 But simpler, let us just divide 𝑀/𝑚𝑥 = 𝟏. 𝟎𝟎𝟔𝟒𝟕𝟐𝟏𝟓𝟔𝟗𝟓𝟒𝑬 + 𝟏𝟐𝟏
  30. 30. 30 So to get a number as large as you want just with physical constants has nothing special, except if this number actually means something. For example, this number Nx, has at first sight no meaning other than the proportion between 2 masses, one of it (mx) doesn´t seems to have any meaning. 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). However, going deeper on these mx and Nx, I found something interesting. 1.- 𝒎/𝒎𝒙 = 𝑺 2.- therefore: 𝒎. = 𝒎𝒙. 𝑩 3.- therefore: 𝒒^𝟐 = 𝑮. 𝒎^𝟑/𝒎𝒙 4.- mx = mp (mass of Plank) when Nx =1 5.- 𝑵𝒙. 𝒎𝒙 = 𝑴 total mass of the universe at any time. 6.- And most important, mx at the first instant (ψ = 1.754235582839E-99 sec) was equal to thermal mass or 𝒎𝒙. 𝒄^𝟐 at that time was the total thermal energy. 7.- 𝑵𝒙 . 𝜶 = 𝑵. 𝑩 which shows some relation between the number of gravitons with the fine electric structure constant. From the previous equations, it can be found the next: 𝒎/𝑺 = ((𝒉𝒓^𝟐/𝑮𝒄(𝑲𝟐))^(𝟏/𝟐)/𝝍 = 𝒎𝒙 But for the moment of the BB which I will call time 1 = 1.754235582839E-99 the same equation for the time 1 is: 𝒎𝟏/𝑺𝟏 = ((𝒉𝒓^𝟐/𝑮𝒄(𝑲𝟐))^(𝟏/𝟐)/𝝍𝟏 = 𝒎𝒙𝟏 = 𝑴𝒕 = 𝟒. 𝟐𝟎𝟐𝟔𝟖𝟑𝟑𝟓𝟏𝟒𝟐𝟔𝑬 + 𝟓𝟏 grams 𝑴𝒕. 𝒄^𝟐 = 𝟑. 𝟕𝟕𝟕𝟏𝟖𝟑𝟒𝟐𝟔𝟔𝟖𝟓𝑬 + 𝟕𝟐 𝒆𝒓𝒈𝒔 𝑀𝑡. 𝑐^2 = total thermal energy from the cosmic background radiation, which is constant and can be calculated at any time by using the Planck´s equation for radiation energy of the CBR if we know the temperature and the volume of the universe. From this we arrive at: 𝑴𝒕 . 𝝍𝟏 = 𝒎𝒙. 𝝍 = 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 As mx = M/Nx, we finally arrive at. 𝑴𝒕 = (𝑴.𝝍/𝑵𝒙)/𝝍𝟏 As Mt is constant, it is deduced that 𝑴. 𝝍/𝑵𝒙 is constant also. Or: 𝑴𝒕 = (𝑴. 𝑩𝟏)/(𝑩. 𝑵𝒙𝟏) 𝑴𝒕. 𝝍𝟏 = 𝒎𝒙.𝝍 Remembering that subindex 1 means the first time, the moment 1, the first moment. Do not confuse with the epoch when B = 1 So, this is the relationship among the actual mass of the universe and the total mass-energy of the CBR. My inference on this is that mx is or could be what it has being call the graviton, the cause of the existence of m. and it is also seeing, that characteristics of the universe were defined at the moment 1 and from then and above, the rest was determined by time. There is another comment that should be made, at time 1 in order to maintain the thermal energy and at the same moment the photons to be a enter number (1 in this case) some small changes I did on the
  31. 31. 31 Wien´s law constant. from 2.897772121304E-01 to 2.813742169568E-01 and also on the factor P for the average of the number of photons from 1.202056570000E+00 to 6.349931800055E-01 . This last thing is not so important as the change on “b” the Wien´s constant. The reason is that P is for a large number of photos with wave lengths much more shorter than the radius of the universe. Note that by dividing 𝑀/𝜓 we will arrive at : 𝑀/𝜓 = 𝑀1/𝜓1 = 𝑁𝑥1. 𝑚𝑥1/𝜓1 = (𝑁𝑥1/𝜓1). 𝐻1.ℎ/𝑐^2 = 𝑁𝑥1.ℎ/ (𝜓1^2. 𝑐^2) M/ψ=(h. Nx1)/(c.ψ1)^2 = c^3/G = 4.0384595119E+38 grams/sec. (13.5) This is the matter creation rhythm depending only of the initial conditions of the universe, or what is the same; of two of the constants. So the important question is this: What is the cause of the matter creation? By seeing the (13.5) equation there is only one simple reason: The existence of these two constants. And if we want to go deeper on this matter, the final answer should be on the reasons for the value of the constants. And here is where the Big Question arrives. From where or how the values of the constants arrives regarding of their values?. How can exist the light speed if there were no light before time 1? And from where G came to be? This is a wide open field to speculate. From hidden system of universes or from God. Or from the absolute vacuum properties which will also require an explanation. The kingdom of the ineffable. 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. 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 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 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. 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
  32. 32. 32 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 this writing is not a theory of our universe, because I don't dare to say this, but it is a theory of a universe. And yet, as theoretical analysis it is allows myself to speculate a bit about its results. ¿Do this universe fits our universe? Or ¿How much it seems to be like our universe? 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 first photon. 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 photon, the same photon are their anti particle, then it wouldn`t be strange their creation. This wouldn`t never happen to the created photons since they never reaches a distance (R) 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 for a large amount of photons, but not for just one or two (in which case, the wave length of the new photons is equal to the diameter of the wave length of it 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 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 or exclusion principle, 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
  33. 33. 33 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. SECOND PART: NEWTON GRAVITATIONAL CONSTANT CALCULATED BY MEAN OF OTHER PHYSICS CONSTANTS. MUTUAL RELATIONS BETWEEN THE 4 FORCES OF NATURE AND ITS VARIATION WITH TIME INTRODUCTION AND PURPOUSE: As before, what I expose here, does not intent in any way to be a theory of the 4 forces of nature. It is only an analysis of the relationships between the size of the coupling parameters of the four fundamental forces and its change with time. The study is not based on any physical theoretical analysis. It is rather a study of the numerical relationships between these parameters, the coupling parameters. It is highly speculative, but with hints of truth on the basis of the results. In this analysis we can get from the ratio of the mass of the proton to that of the electron and that of the neutron to proton, the knowledge of the magnitude of the coupling parameters of the forces, or vice versa. As an example, we can calculate the value of the gravitational constant from the constant of the weak force. We will also see how to calculate the gravitational coupling constant by knowing the mass of
  34. 34. 34 the proton, electron and neutron. It is seen how the fundamental forces could be interrelated with the fourth power of the previous less "intense". This propriety of variation with the fourth power, gives a glimpse of the possibility that there are forces of a higher and lower order than the strong force and gravitational force respectively. For example; gravitation, the weakest of the known forces could lead to the existence of another force even weaker with an intensity of down to 1e-256 weaker than the strong force. And even still more, these relationships are determined by the temperature of the cosmic microwave background radiation. The equations obtained with the values of "J" and "D" are so precise, that believe it as a coincidence I considered highly unlikely. The results do not match the traditional cosmology. For example: the standard cosmology said that during or at the time of the Big Bang, the 4 fundamental forces were one and that these were separated later. I deduced that this step was only between some of them. And that the unification of the others has not yet happened, and that it will be until the temperature is closer to the absolute zero when this unification will happen. And I am speaking of a time so remote in the future that the universe will be 10e32 times older than what it is today. Some of the magnitudes which I used are not the conventional or traditional ones, but even so, it is always possible to transform them to those conventional; for example: "m" is not a particle, but the square root of the product of the mass of the proton by the mass of the electron, or α is not the fine- structure constant but 2 π times the inverse of this constant and as well as I will be explaining. However, the end result of the following equations and the ones from the first part, are manifested in an Excel spreadsheet that will be able to locate on the web page of Scribd. Write the web address directly in the browser you are using, if the link does not operate. In the Excel executable file named Universal within this page, (which in fact includes everything or almost everything that I have written) you can download it and do the calculations for yourselves. With this worksheet, and with only the time as a variable, it may be calculate the following things in the past, present, and in the future. This sheet shows a single column. It is in the green in it part where it says “epoca” where it should be written the time to calculate all the others. The Mass, the radius, the density, the number of nucleons, the thermal energy, etc., of the universe. Microwave Cosmic Background Temperature. Charges of each one of the forces Values of the coupling parameters of the forces. Mass of the proton, electron and neutron. Wavelength of the mason. The data from the Planck Epoch The ratio photon/proton The initial conditions of the universe, when it was light for the first time. I am speaking of a time as small as 1.686888763695E-99 seconds, demonstrating that there was never being a moment of infinite density of matter or energy. But very high indeed . Of the order of 10e 204 grams/cm^3 mass density. This table is worth to study, because many answers are in its details for different epochs. Finally, remember that this chapter is supported and by necessity with the previous in: 1.- Description of the Forces. a) The strong force: is the most intense of the four, is responsible among other things to keep together the nucleus of the atom in spite of the electrostatic repulsion generated by the electromagnetic force caused by the rejection that between them suffer the protons. It explains the large amount of energy generated by the processes of nuclear fission. Its coupling constant is represented with the symbol " σ "