_{1}

^{*}

We try briefly the relationship between numbers and some aspects of physical reality. By means of a simple set of mathematical and physical tools what we wanted to find was dimensionless numbers that could fit with a particular symmetry. In this paper we describe a small sheaf of numerical results.

In his book “Philosophy of Physics” [

Also it’s known that P.A. Dirac, inspired by Eddington, Milne and others suggested a reconsideration of Cosmology based on the large dimensionless numbers that could be constructed from the fundamental constants of nature. Namely, all very large numbers occurring in nature are interconnected [

Besides, there is the issue of reality’s stuff: Is it continuous or discrete? We assume that spacetime is granu- lar.

We’ll analyze relationship among physical constants using a simple tool-kit of mathematical and physical concepts described as defined below.

I. Symmetry (ng + mj) where n, m are natural numbers. And the ratio

II. Series

III. As for the subject of the discreteness of space-time, we’ll apply Avogadro’s number [

IV. An item called “sit”, associated with the topic III, representing a space-time size, arbitrarily very small.

Define

(By the way you can obtain a good approximation to the number p using properly topics I and II, as we described in a paper time ago).

Without further delay we will describe some examples of the matter at hand.

Start looking back on the topics I and II. Assign specific values to each

will include two concepts more:

Euler’s number e = 2.7182818…

And Neutron-Proton mass ratio [

Obtaining the following equation of evolution

Resulting volume

This new volume

Therefore the evolution from the Torus

The Higgs field has a nonzero expectation value

The energy in electron volts of a photon after Planck equation [

Assign a specific frequency

The resulting equation relates the volume of a particular Torus

Now it’s interesting to see the following numerical equivalence

Therefore rearranging the equation for the evolution described above

Volume inside a Torus

Suppose:

Therefore the volume of this particular Torus is defined as follow

The distance light travels in one second in vacuum

Write three spatial axes light will travel

Duration of travel in each of the axes

(It’s worth to say that according to the most recent data from the cosmic microwave background (CMB), the age of the universe is around 10^{17} seconds [

Consequently

Therefore polyhedron’s volume

A simple arithmetic operation shows that

The results of paragraphs 1, 2 and 3 lead us to write the schematic sequence of evolution

Proton Compton wavelength

The Compton wavelength of the proton

Relationship between

Now, consider a sphere whose radius is equal to

And the volumen inside a Torus defined in Equation (13)

Trying to abreviate symbols

Now will write the resulting formula

(it is assumed that the volume units are canceled on both sides of the equation).

Einstein’s constant denoted K (kappa) is a coupling constant that appears in his field equations, whose value is given by

Write the volume of a particular torus

will apply the atomic mass constant

Consider a system whose mass is

and whose acceleration is equal to

Therefore the system acquires a force

It’s easy to check that Einstein’s gravitational constant units are given by

Apply an arbitrary value to the fourth method’s topic associated with the time dimension

Now, will arrange all the concepts in the following formula

The energy density of Cosmic microwave background (CMB) in the current epoch, at a temperature T_{0} = 2.726 K

Looking for a dimensionless number, write the following equation

h refers to Planck constant

The letter e refers to the Euler’s number = 2.7182818…

As for Torus volume in Equation (27) let’s rewrite Equation (13)

The quantity 10^{92} could be written differently:

As for the CMB, the spectral radiance peaks at

in the microwave range of frequencies.

We should also mention the ratio between

Starts with Bekensteing-Hawking equation [

C refers to speed of light in vacuum (already referenced in paragraph 3).

Newtonian constant of gravitation

Write the surface’s area of a torus

Define a certain dimension of length associated to Avogadro’s constant

which is equivalent to the Planck scale [

Assign to the larger radius of the torus the value

As for the smallest radius

Now write the area of this particular torus

Summarize the formula for entropy

Symbol

which in other way reads

α is the fine-structure constant [

Since the aim of this paper is only to review some numerical approaches to the physical constants and the physical amounts that defines the universe and reality, nobody should have to wait a theory nor one set of predictions.

We found interesting review the numerical equivalence described by Equation (13) because the accuracy of significant digits between the constants involved in both volumes. Still more when proton Compton wavelength fits numerically (20).

The above considerations are also valid for the material developed under paragraph 5, while recognizing greater freedom (arbitrariness) in the use of the “sit”.

We think appropriate to briefly comment the numerical connection among Equations (13), (20) and (26). It allow us to note a numerical linkage between one parameter belonging to Quantum mechanics, i.e. proton Compton wavelength

As for the items 1 and 2, considering the assumptions or theories about cosmic inflation and related matters, we have seen curious the sequence (16). Of course always from a numerical point of view.

Under the heading 6, we review two subjects. On one side is the number of photons in the Universe. Although it is still a speculative matter, estimations range around 10^{90}, hence we have seen interesting the value obtained in the Equation (27) related to the Avogadros number i.e.

Finally, the matter of black hole entropy shows high numerical accuracy. Although we have chosen arbitrarily the type of Surface and the value of the “sit”. As the values of speed of light and Planck constant are very accurate, we would have a more accurate value of G, the Newtonian constant of gravitation.

As for the numerology applied to Physics and Cosmology we have selected a little set of subjects. In our view they are numerically interesting. Maybe someone can see in it some kind of theoretical inspiration.

We want to thank Kelly Sang and Freya Zhang for helpful recommendations in the correct edition of this paper.

AlbertoCoe, (2015) Some Numerical Curiosities about the Universe. Journal of Modern Physics,06,1671-1678. doi: 10.4236/jmp.2015.611169