The Singularity of the Big Bang Can Be Described in Greater Depth than the Limits of the Planck Time and Length

Slobodan Spremo

Mathematical Grammar School, Belgrade, Serbia.

DOI: 10.4236/jhepgc.2023.91005                

Abstract

In this paper, we determine the frequency, energy and momentum of the primordial spherical wave at the birth of our universe, which are consistent with the fact that the total energy of our universe was created in the hot Big Bang. With this, we also indirectly demonstrate the consistency of previous works on the hypothesis of primary particles, by using their results. We obtain a hyper-high initial frequency of the spherical wave, which is not in contradiction with string theory.

Keywords

Flat Space and Time, Primary Particles, Quantum of Speed, Spherically Wave

1. Introduction

In our four previous works, continued here, we obtained physical quantities that could describe the moment of the Big Bang itself.

In our hypothesis [1] we postulated the existence of primary particles in their ground state and in flat space and time, moving relative to each other at speeds much higher than the speed of light in a vacuum. We concluded that these particles would in some way have properties symmetrical with the properties of the particles of our Universe. The energy and momentum of these primary particles would thus increase sharply when slowing down during mutual collisions, as opposed to the increase in energy and momentum of the particles of our Universe that occurs when their speed increases. This description of the dynamic properties of these particles logically imposed the possibility of describing the very origin of the Big Bang. During some of these collisions therefore, the speed of one of these two particles could drop to a speed very slightly higher than the limit speed c. The energy and momentum thus acquired would tunnel through the Big Bang into our Universe, creating our energy and matter in our space and time.

We took a very important piece of data, the speed, very slightly higher than the limit speed c, to which the primary particle could be slowed in order to cause the Big Bang, from [2], where we saw a logically introduced new term in physics: the “speed quantum” $\epsilon ={\epsilon }_u\approx 2.38\times {10}^{-114}\text{m}\cdot {\text{s}}^{-1}$. This notion allowed us to understand that there is little difference between the actual speed of light in a vacuum and the limit speed c. For most purposes, the very small difference between these two speeds is not important, but we needed precisely this “speed quantum” to determine in [3] the energy of the primary particle in its ground state $E_p=m_p{c}^2\approx 1.22\times {10}^{19}\text{GeV}$, and therefore the mass attributed to the energy of

the primary particle $m_p=m_P=\sqrt{\frac{\hslash c}{G}}\approx 1.22\times {10}^{19}\text{GeV}/c^2\approx 2.18\times {10}^{-8}\text{kg}$, which

is equal to the Planck mass $m_P$. The Planck mass therefore took on this new meaning. From [2] we also took the data on the total energy generated in the Big Bang $E_t=E_U=m_U{c}^2\approx 1.55\times {10}^{70}\text{J}$, and obtained complete agreement with our hypothesis [3] according to which

$E_t=E_U=\frac{m_p{c}^2}{\sqrt{1-\frac{c^2}{{\left(c+{\epsilon }_u\right)}^2}}}.$ (1)

This energy corresponds to the energy equivalent of the total mass of the universe $m_U\approx 1.73\times {10}^{53}\text{kg}$ and includes all types of mass (baryonic and dark matter) and the mass contained in all types of energy (photons, dark energy, etc.).

Then, in [4], we also described the Big Bang quantitatively through physical quantities that describe the initial moment of the Big Bang. We obtained a value for the time corresponding to the initial moment of our universe $t_B\approx 9.51\times {10}^{-114}\text{s}$ that is much shorter than the Planck time, and another for the resulting radius of the Big Bang itself $r_B\approx 2.85\times {10}^{-105}\text{m}$ that is much smaller than the Planck length.

In paper [5], we used modified uncertainty relations, which correspond to the spherically symmetric, very initial moment of the Big Bang, to obtain a constant ${\upsilon }_p=1.48\times {10}^{-43}\text{J}\cdot \text{s}$ corresponding to the reduced Planck’s constant.

2. In the Big Bang, a Spherical Wave of Hyper-High Frequency Is Created

We treated time symmetrically with the other coordinates, in agreement with Dirac’s relativistic quantum mechanics, in which he gave a precise and well-defined derivation of this symmetry [6]. We now complete our hypothesis by showing that in the hypothetical collision of two primary particles, in which one of them has slowed to the limiting velocity c for our universe, a spherical wave was created with a wavelength equal to the radius of the Big Bang $r_B\approx 2.85\times {10}^{-105}\text{m}$ and a period equal to the time of creation of the Big Bang $t_B\approx 9.51\times {10}^{-114}\text{s}$. Quantifying the spherical wave created at the very moment of the Big Bang, given by the constant ${\upsilon }_p=1.48\times {10}^{-43}\text{J}\cdot \text{s}$, gives a result for its momentum

$p=\frac{{\upsilon }_p}{r_B}\approx 5.19\times {10}^{61}\text{kg}\cdot \text{m}/\text{s}$ (2)

and energy

$E={\upsilon }_{p}f={\upsilon }_p\frac{c}{r_B}\approx 1.55\times {10}^{70}\text{J}.$ (3)

Thus, this spherical wave would have a frequency of

$f=\frac{c}{r_B}\approx 1.05\times {10}^{113}\text{Hz}.$ (4)

This hyper-high frequency is only unusual at first glance: String theory assumes that Lorentz covariance implies the perfect symmetry of our universe [7]. If this is true, it would mean that a photon is allowed to have an arbitrary energy, even greater than that limited by the Planck length.

3. Results and Discussion

The values obtained for the impulse, energy and frequency of the spherical wave created at the very moment of the Big Bang complete our hypothesis. According to the Big Bang theory, our universe began as an extremely hot and extremely dense state, which matches our results. The values for the obtained physical quantities related to our previous, and this work, are given quantitatively. According to the value that we use for the mass of the universe, we would obtain a corresponding value for the speed quantum [2]. This would not affect the mass of the primary particles, whose mass is equal to the Planck mass [3]. Furthermore, this work affords a very approximate value for the frequency of the spherical wave.

It is clear that our new approach to the explanation of the Big Bang through the hypothesis of primary particles is significantly different from previous approaches, but it opens up a new possibility for describing the universe from its very beginning to the period of the very early universe. We thus consider the hypothesis interesting for further scientific work.

Conflicts of Interest

The author declares no conflicts of interest regarding the publication of this paper.

References

[1]	Spremo, S. (2019) Hypothesis of Primary Particles and the Creation of the Big Bang and Other Universes. Journal of Modern Physics, 10, 1532-1547. https://doi.org/10.4236/jmp.2019.1013102
[2]	Mercier, C. (2019) Calculation of the Mass of the Universe, the Radius of the Universe, the Age of the Universe and the Quantum of Speed. Journal of Modern Physics, 10, 980-1001. https://doi.org/10.4236/jmp.2019.108065
[3]	Spremo, S. (2021) Determination of the Energy of a Primary Particle in Accordance with the Hypothesis of Primary Particles and Another Meaning of Planck Mass. Journal of High Energy Physics, Gravitation and Cosmology, 7, 144-148. https://doi.org/10.4236/jhepgc.2021.71007
[4]	Spremo, S. (2021) On the Possibility of Describing the Origin of the Big Bang According to the Hypothesis of Primary Particles. Journal of High Energy Physics, Gravitation and Cosmology, 7, 551-558. https://doi.org/10.4236/jhepgc.2021.72031
[5]	Spremo, S. (2022) On the Uncertainty Relations That Would Be Used in the New Description of the Big Bang According to the Hypothesis of Primary Particles. Journal of High Energy Physics, Gravitation and Cosmology, 8, 978-982. https://doi.org/10.4236/jhepgc.2022.84068
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[7]	Becker, K., Becker, M. and Schwarz, J.H. (2006) String Theory and M-Theory: A Modern Introduction. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511816086