Classic 4D Model Of the Discrete Universe (C3:A). I:Quantum

Este post está dedicado al capítulo 3 del libro 

Classic 4D Model Of the Discrete Universe. I:Quantum

   En dicho capítulo se demuestra que las fuerzas de largo alcance, gravitatoria y magnética son la misma fuerza. La fuerza gravitatoria es producida por una velocidad de rotación del electrón del orden de 10^-12  m/s, mientras que la fuerza magnética es producida por una velocidad de traslación del orden de 10⁺⁶ m/s. Esa diferencia de velocidades junto con la diferente orientación del campo es lo que origina que observemos los campos gravitatorio y magnético como diferentes. 

Como el capítulo 3 es bastante largo lo he dividido en dos entradas.

3. The origin of long-range forces         

The current theories are based on the assumption that the Big Bang had a unique strength, which, along with the expansion of the universe, gave rise to four forces, two of which are of infinite range. In the model developed here, there is only a single force, which is the magnetic force. Gravity and the electromagnetic force are connected at all times in the electron, both being different manifestations of the same phenomenon.

3.1 Introduction

In nature there are four interactions that are responsible for all phenomena in the universe: force or gravitational interaction, weak nuclear force, electromagnetic force, and the strong nuclear force. According to the Standard Model of Particle Physics (SMPP), the four interactions manifest themselves through an exchange of particles called bosons.

The electromagnetic and gravitational interactions have infinite extent, due to the fact that the interacting particles, photons and gravitons respectively, have zero mass. The weak and strong interactions have finite range, because the interacting particles have non-zero mass. They are the vector bosons and gluons. In the long-range forces, the time variable does not appear, suggesting that the action is performed instantaneously, i.e. at infinite speed. In turn, this implies that there is no material in between interacting bodies. That infinite speed requires the existence of the vacuum.

This action at a distance was a problem even for Newton himself: “That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance thro’ a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain laws; but whether this Agent be material or immaterial, I have left to the Consideration of my readers.” ^[20]

Current physics has solved this problem by including particles that can not be detected, such as virtual photons and gravitons. It should be noted however, that the graviton has not yet been discovered, and the photons involved in the electromagnetic force are virtual photons, which have not been discovered either. However, according to the current physics, it is accepted that virtual photons must exist because the electromagnetic force can be measured. According to the SMPP, when energy is high enough, the electromagnetic interaction and the weak interaction are combined into a single interaction called the electroweak interaction. The grand unified theories (GTU) combine the electroweak interaction with the strong nuclear force, but leave aside gravity.

       Initially, according to the SMPP, four forces were unified into a single force. Figure 3.1 shows roughly the times when the various forces separated.

Figure 3.1 Evolution of forces.

In this monograph we will see that the long-range forces such as the gravita-tional and electro-magnetic forces still remain connected, since the electric charge and mass are two different manifes-tations of the rotation of the Planck particle ^{[1, 2]}.

3.2 Black holes

In recent years a group of physicists have developed the theory that within each black hole there is a universe, and that our universe could be the result of a black hole. From a modification of the equations of Einstein's general relativity, and the analysis of the motion of particles entering a black hole, Poplawski concludes that our entire universe may have originated inside a black hole existing in a bigger universe ^[21]. He says that “the interior of every black hole becomes a new universe”. The new universe is a natural consequence of a simple new assumption about the nature of space-time ^[22].

Several other authors have also proposed cosmological scenarios in which our universe emerges from a black hole ^[23-26]. Poplawski suggests that the universe formed inside of each black hole may be due to the coupling between rotation and torsion ^[27]. Space-time with torsion prevents the formation of singularities, where the universe expands from a low, but finite, radius, which corresponds to the dynamics of matter inside a black hole ^{[28, 29]}. Pourhasan, Afshordi, and Manna suggest that our universe could be a spherical 3-brane- formed by the explosion of a four-dimensional black hole ^[30].

When a star consumes all of its fuel gravity shrinks the star. If the mass of a star is large enough gravitation can overcome the neutron repulsion. In that case, in the current model, there is nothing that can oppose the collapse. According to Susskind, “The material squeezes into an unimaginably small region called a singularity, the density inside of which is essentially infinite” ^[31].

Suppose that the universe is formed by discrete atoms, of four spatial dimensions, and that the particles also have four spatial dimensions with a diameter equal to the Planck radius r_p=(Gℏ/c³)^1/2. Of the four dimensions, three are observed as space (x, y, z), and the fourth dimension (u = ct) is observed as time. These are the atoms of space and time from Smolin [3].

Therefore, in every atom we have the potential due to Planck's gravitational field, or any other field, to consider:

Here, m_p is the Planck mass, r_p the Planck radius , G the gravitational constant, and c is the speed of light. To compress the atom of space-time (Figure 3.2) we need to apply the force of Planck (Equation (2.3),F_p=c⁴/G ).

Figure 3.2 Atom of space and time (u=ct).

If we suppose that a star of mass M has surpassed the neutronica repulsion its radius is reduced until it reaches the Schwarzschild radius R, which we can write as:

Dividing Equation (3.2) by the radius squared (R²), and multiplying by the Planck mass (m_p), gives us

In Equation (3.3) the first term represents the gravitational force exerted by the mass M of the star, in gravitational collapse, on the Planck mass located on the surface of star of radius R.

It is possible to write the second term of Equation (3.3) as

We obtain an equation corresponding to the Heisenberg Uncertainty Principle

UGP is the Planck potential that exists in the past (t = R / c), at the distance R in the forth-dimension being R the radius of mass M observed in three-dimensional space.

Therefore, from the Heisenberg Uncertainty Principle, the same relationship to the radius of a black hole (or Schwarzschild radius) is obtained.

3.3 Quantum universe

Suppose a quantum fluctuation in energy occurs, that verifies the Heisenberg Uncertainty Principle, so that

where E_i, is the initial energy, t_p is Planck time, and ħ is the reduced Planck constant.

If, in addition to the quantum fluctuation, an expansion of space formed by discrete space-time atoms, of four dimensions, with diameter equal to the Planck wavelength, is produced (Figure 3.4).

where U_po is the Planck potential at the origin, R = ct is the radius of the universe at time t and U_p is the Planck potential that exists in every atom of space-time.

At the initial time, there is a quantum fluctuation that produces mass m (E_i). The expansion of space (Figure 3.4) causes that gravitational potential energy of the mass m, from the origin (O point), to decrease. The gravitational potential energy of the mass m, with respect to Planck´s potential at the origin, will be

Here m_p is the Planck mass, and c is the speed of light.

Considering the gravitational potential energy of the mass m, with respect to the Planck potential Up, local energy is obtained

The principle of conservation of energy implies that, at any time, the total energy, E(t), of the universe must be equal to the initial energy, E_i, therefore

where M is the total mass of the universe at time t. From this:

This equation corresponds to the Schwarzschild radius of a black hole.

As the radius of the universe increases to the speed of light, the gravitational potential energy with respect to the origin decreases. This generates an increase in mass to compensate for the decrease the energy. 

At all times, the total gravitational energy of the universe, with respect to the origin, verifies the Heisenberg Uncertainty Principle.

If we consider the gravitational potential of the mass m, with respect to the Planck potential that existed in the past, then the potential energy is less than or equal to the energy given by the Heisenberg Uncertainty Principle.

Moreover, considering the discrete four-dimensional space formed by atoms whose diameter is the Planck radius, the radius of the universe will always be an integer multiple of the Planck radius

Substituting Equation (3.18) in Equation (3.17), the mass of the universe can be expressed as:

Therefore, the mass of the universe can only take discrete values, equal to half integer multiples of the Planck mass. That means that, for each time increment of Planck time, an increase, equal to half a Planck mass, in the mass of the universe, occurs. It can be considered that at every Planck time, a quantum fluctuation occurs, of amount half of a Planck mass, and that instead of disappearing, it persists in time due to the expansion of space. This causes a decrease in the total gravitational potential energy. The Planck’s fluctuation, mass  length  time and energy, creates an expanding universe that at all times is a cosmological quantum black hole. This converts  Planck’s fluctuation into the cosmological Planck’s fluctuation (the Universe today) ^[32] of length  and  time.