4. Quantum Universe

Abstract

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. In this work, from an expanding space of four dimensions, formed by atoms of space and time, and Heisenberg’s uncertainty principle, we conclude that our universe is an expanding black hole. At the same time, the universe is a white hole, where matter increases with time.

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1.Introduction

Both physicists and mathematicians have asked if it is possible that space and time are discrete? Many modern theories that try to unify the gravity with the standard model of the particle physics, as for example the string theory, propose the existence of a minimum length [1, 2].

“… a fundamental (minimal) length scale naturally emerges in any quantum theory in the presence of gravitational effects that accounts for a limited resolution of space-time. As there is only one natural length scale we can obtain by combining gravity (G), quantum mechanics (h) and special relativity (c), this minimal length is expected to appear at the Planck scale” [3].

“… we learned already from the development of relativity and quantum mechanics that Nature can impose restrictions on our measurements because of two universal constants: the velocity c and the quantum of action h.

Could Nature impose a third restriction, resulting from the existence of a universally constant quantum of length a and a universally constant quantum of time a/c?” [4].

Discrete space–time is used as a model by other authors to present the solution of the Schrödinger equation for a free particle [5] or for electromagnetic waves and the Helmholtz equation [6]. Also Smolin, says that the universe is formed by space-time atoms that cannot be decomposed into anything smaller, [7] so that the minimum value of

volume, length or area, is measured in Planck units.

Theories related to quantum gravity, such as string theory and doubly special relativity, as well as black hole physics, predict’s the existence of a minimum length [8-10].

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 [11]. He says that “...the interior ofevery black hole becomes a new universe that expands from a nonsingular bounce” [12].

Several other authors have also proposed cosmological scenarios in which our universe emerges from a black hole [13-16]. Poplawski suggests that the universe formed inside of each black hole may be due to the coupling between rotation and torsion [17].

Conclusion

From the Heisenberg uncertainty principle or the Einstein field equation the same relation is obtained for the radius of a black hole or Schwarzschild radius.

The hypothesis of a universe formed by fourdimensional Planck atoms and application of the principle of uncertainty of Heisenberg solves the formation of singularities inside a black hole, because a force is needed to compress the atoms of space and time. The before mentioned force is also deduced from the Schwarzschild radius.

On the other hand, the energy of mass m, can be considered as a gravitational potential energy. Thus, the ratio rp / R allows to refer to the potential energy with respect to the distance R in the past. This distance is equidistant to each of the atoms of space and time that make up the mass. R can be the radius that occupies themass, as in the case of black holes and the Universe, or R can be any distance between the radius of Planck and the radius of the Universe. If we consider the potential energy of mass m, with respect to Planck Up potential, we obtain the local or absolute energy E = mc²

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Conclusion

From the Heisenberg uncertainty principle or the Einstein field equation the same relation is obtained for the radius of a black hole or Schwarzschild radius.

The hypothesis of a universe formed by fourdimensional Planck atoms and application of the principle of uncertainty of Heisenberg solves the formation of singularities inside a black hole, because a force is needed to compress the atoms of space and time. The before mentioned force is also deduced from the Schwarzschild radius.

On the other hand, the energy of mass m, can be considered as a gravitational potential energy. Thus, the ratio rp / R allows to refer to the potential energy with respect to the distance R in the past. This distance is equidistant to each of the atoms of space and time that make up the mass. R can be the radius that occupies themass, as in the case of black holes and the Universe, or R can be any distance between the radius of Planck and the radius of the Universe. If we consider the potential energy of mass m, with respect to Planck Up potential, we obtain the local or absolute energy E = mc²

In discrete space-time, neither the renormalization nor singularity are necessary, since the infinites disappear. 

On the one hand the universe behaves like a white hole due to the increase of its mass and energy and on the other hand the universe behaves like a big black hole since its radio coincides with the radius of Schwarzschild. In addition the increase of the mass of the universe causes that the density of mass of the universe coincides at any moment with the density of critical energy