9.-ARROW OF THE ELECTROMAGNETIC TIME. ORIGIN OF THE NUMERIC VALUE OF ELECTRON MASS AND THE ELECTRON-PROTON MASS RATIO

The symmetry with respect to the time of the equations that it describe to the electromagnetic field, introduces a mystery in the reality that is observed; this symmetry suggests that an accelerated charge will emit electromagnetic waves either forward or backwards in the time, the reaction to the accelerating force will be produced so much by the answer of the rest of the past universe and the future universe. The fact that only salient electromagnetic waves are observed induces to think that the past universe behaves as a not well absorbent one and the future universe as a good one absorbent. Only the Steady-State model of Universe is able to justify the correct answer in both sense of the time. (Jayant Narlikar. The structure of the Universe).

In an universe with critical energy density ρ, as it necessarily establishes the Living Universe model, the value of this one depends on the Hubble radius:

ρ= 3 c² / 8 π G R_h²      (9.1)

If we consider a radio sphere R_h (Hubble radius) with center in a point (P), we obtain a total energy M with the following value:

M = ρ(4/3) π R_h³      (9.2)

Substituting in this expression the value of the density (9.1), we obtain:

M = c² R_h / 2 G     (9.3)

Let us to consider a solid angle Ω such as the volume V of the cone that subtends from the point P until R_h is such that the energy density given by M/V, where M is the energy calculated in (9.2), is numerically equal to the electron mass m_e, that is to say, 9.1 10^-28 g/cm³. This consideration assures us that if the electric charge has some relationship with the mass, in the suitable cone there will be an electric charge at least and therefore any electromagnetic wave emitted from the point P will be absorbed in its itinerary, independently of its value, through this cone. The considered volume will be V = Ω π R_h³ / 3. Consequently we obtain:

m_e = 3 c² (1 cm³) / 2 G Ω π R_h²

Ω = 3 c² (1 cm³) / 2 G m_e π R_h²

The term (1 cm³) is replaced in each case by the length unit that is used.

If we admit a value of the Hubble radius of 1.796 10²⁸ cm, we obtain for Ω the value of 0.021892 rad. that coincides with the triple of the value of the fine structure constant: Ω = 3 α. Since α = e² / c hbar (hbar = h /2π), we can find an expression function of the fundamental constants that will give us the value of the electron mass:

m_e = c³ hbar (1 cm³) / 2 G e² π R_h²     (9.4)

The expression 1 / R_h² is the cosmological constant Λ, e²/c hbar is α, the expression (9.4) will be:

m_e = (1 cm³) c² Λ / 2 G α π     (9.5)

It is easy to see that this relationship doesn't depend on the magnitude longitude, neither of the arbitrary election of their unit neither value, using inches instead of centimetres it would continue being valid. This assures that any electromagnetic wave emitted from P will be absorbed in its itinerary toward the future.

We could apply the expression (9.5) to the other three charged elementary particles, the quarks. In this case the charges are 2/3 and 1/3 of the electron charge, we would obtain the values of 9 m_e and 9/4 m_e for the masses of the quarks down and up respectively. If we consider that a proton is composed of two up quark and a down quark, the components mass of a proton will be 13.5 m_e, the rest until the proton mass would be due to the connection energy generated by the strong interaction. The value of the proton mass is obtained from the following expression, in which only the electron mass, the fine structure constant and the number 13.5 takes part:

m_pr = 13.5 m_e/[α exp(Σ_n=1,2,3... n² αⁿ)] = 1836.1375 m_e      (9.6)

If we take the value of 9.10938188 10^-28 g. for the electron mass and the value of 7.29735254 10^-3 for α, the value obtained with the expression (9.6) for the proton mass with the first four terms of the series is 1.67260775 10^-24 g.

The measured real value of the proton mass is 1.67262158 10^-24 g.

1.67262158 10^-24 g = 1836.1527 m_e     (9.7)

Nevertheless, the expression (9.6) is valid with the quarks in rest. In the proton the quarks is in movement. In consequence the quark sea will suffer an increment in its mass that it justifies the difference among the expressions (9.6) and (9.7).

If we substitute in the expression (9.4) the value of all the well-known constants, we can find the values of the Hubble radius and the Hubble constant:

Hubble Radius: 1.79619 10²⁸ cm.

Hubble Constant: 1.6691 10^-18 sg^-1.

Cosmological Constant: 3.099536 10^-57 cm²

Naturally, just as I indicated in the epigraphs 2 and 3, this value of the Hubble radius corresponds to the temporary radio sphere, that is to say, to the radius of the black hole in the universe mother. Inside the black hole, in the universe son, the value observed in the temporary coordinates t₁ and t₂ it will be their respective projections on the axes temporary 1 and 2; since they are ortogonales and if we admit that the universe is isotropic and homogeneous also in the space of the times, you concludes that the observed Hubble radius will be sin(45°) * R_h, in this case 1.2701 10²⁸ cm. that it corresponds to an apparent age of 13,434 million years.

The expression (9.4) seems to indicate that the electron mass has been bigger in the past, this would imply a significant variation in the energy levels of the atoms that it is not observed. In consequence as much R_h as H would be constant along the history of t₂ time, that is to say, this model also describes a Static Universe. In an observable universe, where the cause-effect principle is completed, an electromagnetic arrow of the time exists. The cosmological redshift could be effect of the reduction of the electromagnetic waves in their trip toward the future.

If we keep in mind that this model had origin in a quantum postulate, the situation that describes this model it is similar to the duality wave-particle, in this case the duality is Big bang Universe/Steady-State Universe. We should not give up any of them, each one of them has a moment in that it can be applied with success. The universe would have been born in the appearance of a black hole in the nucleus of a galaxy in our Universe mother, growing about the gravitational time and reaching the appropriate size to allow the appearance of the electric charges and the time electroweak, starting from that moment the universe would be in a stationary state with apparent expansion. In section 14 are detailed this process. The real age of our universe would only make sense from the point of view of some hypothetical observers in our universe mother.

This model could also give the origin of the values of the stable elementary particles rest masses: to assure the correct electromagnetic answer of the Universe either in the future or the past.

_{© Jorge Ales, 2002. http://www.livinguniverseweb.com}