Successfully reported this slideshow.
Upcoming SlideShare
×

# Microcosmos and macrocosmos together

29 views

Published on

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.

Published in: Science
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

### 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: http://estudiarfisica.wordpress.com/2013/08/25/los-systems-of-unit-geometric-natural-and- 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. http://physics.nist.gov/cuu/Constants / 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