A quantum origin of the Universe

"-But he has nothing on at all-, said a little child at last."
The Emperor's New Clothes. Andersen

Is the universe an isolated system?. The majority of theories on the origin and evolution of the universe are based on the axiom of which it is an isolated system. No objective reason exists that it justifies this bet. In these pages I propose a new cosmological model that explores the possibility that our universe is not an isolated system.

This model introduces the concept of gravitational wavelength applied to a particle.

This model, as well as the Steady-State model of Universe gives the correct electromagnetic answer so much on the part of the future universe as of the past universe. At the same time it gives the origin of the numeric value of the electron mass, the proton mass and the quarks mass and the correct values of the Hubble Radius, the Age of the Universe and the Hubble Constant.

The new structure proposal of the space-time allows harmonizing the General Theory of Relativity and the Quantum Mechanics. From this point of view, this model describes a quantum universe.

This model discovers the holographic and multidimensional character of the universe, giving at the same time support to propose theses by David Bohm.

Previous considerations

Before enunciating the hypothesis in which this web is based, I will make some considerations around the behaviour of the matter (energy) in the proximities of a black hole. This behaviour has not still been verified experimentally in any case, although some considerations can be made. In the first place a black hole is, by definition, the geometric place in which the escape speed of a gravitational field becomes same or bigger that c (light speed), concretely, if it is considered a spherical and homogeneous mass distribution M, it would be a radius sphere r= 2GM/c2.

Applying the principle of uncertainty, a particle of mass m with regard to M should have to minimum angular moment of 1/2 ћ (mvr =1/2 n h/2π, n>0), we can consider a minimum speed intrinsic and normal v to the axis that unites. The gravitational force resultant will be: F= - GMm/r2 + mv2/r. And we can consider the gravitational field resultant as:

V = -GMm/r + n2 ћ2/(8 m r2)    (1.1)
V = -GMm/r + m c2 n2 λ 2/(8 r2)  where λ = ћ / m c    (1.1)

In the previous paragraph I have postulated that the trajectories of the particles in the gravitational field of a black hole are orbits around the center of the gravitational field in each point with a quantified angular moment L = 1/2 n ћ (n > 0). This postulate is similar to the one made by Bohr for the atom.

How to grow a black hole?
Now we can study how a black hole characterized by the radius r= 2GM/c2 grows. When growing, by definition, a black hole cannot lose its own identity of black hole. Which will the minimum quantity of energy (m) be that can absorb without losing that characteristic and in what minimum time can it take place? Since this energy will be characteristic of the black holes, it will be the same one every time.

Let us consider the new radius r1 = 2G (M+m)/c2 resulting of the absorption of m and let us calculate the difference with the radius previous r0:

r1 - r0 = 2G (M+m)/c2 - 2GM/ c2

r1 - r0 = 2Gm/ c2

On the other hand, this energy increment should complete the uncertainty principle:

mc2 Δt >= ћ/2 y Δt (minimum) = ћ/ 2 mc2

If we consider that c is the limits for the speed of expansion of the black hole we obtain that c = r1 - r0 / Δt (for the minimum time) and in consequence m2 = c ћ / 4 G, of this expression, you certainly calculate the value of m that coincides with the value of 1/2 Planck Mass, m = (c ћ/ G)1/2 / 2, r1 - r0 = lp y Δt= tp. Therefore we can consider that a black hole grows absorbing quantum of energy for value of 1/2 Planck Mass. During any time the black hole will accumulate energy in the external of its events horizon until arriving to the quantity 1/2 Planck Mass, growing in that moment a wavelength of the Planck mass in a Planck Time. We can say that the mass of a black hole is worth N mp/2, being N a number that indicates the order of the last process of absorption and the radius of a black hole will be N lp.

In the previous paragraph I have considered to c like maximum limit of speed of expansion of a black hole, implicitly I have also considered that it is the minimum limit of expansion speed in each process of absorption, this limit is justified when also considering to the horizon of event subject to the condition of escape speed of a black hole similar to c.

We see that the form of growing a black hole is with quantums of energy of value 1/2 mp c2 each Planck Time. However this event or interaction between the black hole and the rest of the universe don't have reason to be continuous, since the matter contribution around the hole is not continuous (you can have isolated black holes). If the matter contribution is abundant the growth will go becoming from growth pulsatile to a continuous growth to the light speed like maximum (c = lp/ tp). The density of a black hole you can also calculate easily:

Density = N mp / (8/3) π N3 lp3  ó  3 c5/ 8 π N2 h G2 g/cc    (1.2)

Since N lp is the radius of the black hole, (1.2) shows that the density of a black hole coincides with the critical density ρ = 3 c2 / 8 π G R2.

We can also calculate the density of the following spherical cap that will be absorbed by the black hole:

Density surface = mp / (8 π N2 lp 2) lp g/cc   ó   mp / (8 π N2 lp 3) g /cc    (1.3)

And the potential energy of the particle that enter in the black hole. If in the expression m c2 n2 λ 2/(8 r2) that appears in (1.1) we substitute m for 1/2 mp, we obtain :

V = - G mp mp / 4lp + 1/4 mp c2 = 0     dado que G mp / lp = c2     (1.4)

We see that all the particles go with the same potential energy 0. If we introduces an integration constant with the value -1/2 mp c2 (choosing the level 0 for the gravitational potential in an appropriate way) and since all the particles go with relativity energy 1/2 mp c2 we could affirm that all of them enter with total mechanical energy 0

A black hole, therefore, is totally defined with a whole number N.