Theory of everything

A theory of everything is a physics and mathematics theory that describes the union of all known fundamental interactions. In addition, it must explain space and time, as well as the existence of fundamental elementary particles. In much of its theory, the theory of everything should be a priori. Since all the obvious variants of the theory of everything have long been considered and rejected, the true theory of everything should look completely unexpected and radically different from all previous versions.

History

After the construction at the end of the 19th century, electrodynamics, combining on the basis of equations J. K. Maxwell in a single theoretical scheme of the phenomenon of electricity, magnetism and optics, in physics there was an idea of explanation on the basis of electromagnetism of all known physical phenomena. However, the scheme has already failed to include Newton's law of global gravity. In addition, there were interactions that at first glance had nothing to do with Maxwell's equations. Thus, the original goal of merging on the basis of Maxwell's equations was finally lost.

Mathematical basics

It was possible to return to its original goal only after the creation of a fundamentally new section of mathematics, hyperanalytic functions. Their significance for the theory of everything is that they are generating functions for the intensity of fundamental interactions expressed through the famous quantum constant - the fine structure constant (FSC) - a sizeless, numerical whose value does not depend on the selected unit system. The following value is recommended at the moment: $$\alpha=7{,}297\;352\;569\;3(15)\times 10^{-3}.$$

Some equivalent definitions of α in terms of other fundamental physical constants are: $$\alpha = \frac{1}{4 \pi \varepsilon_0} \frac{e^2}{\hbar c} = \frac{\mu_0}{4 \pi} \frac{e^2 c}{\hbar} = \frac{k_\text{e} e^2}{\hbar c} = \frac{c \mu_0}{2 R_\text{K}} = \frac{e^2}{4 \pi}\frac{Z_0}{\hbar}$$

where:

• e is the elementary charge (1.602176634×10^-19 C);
• π is the mathematical constant pi;
• ħ is h/2π is the reduced Planck constant (6.62607015×10^-34 J.s/2π);
• c is the speed of light in vacuum (299792458 m/s);
• ε₀ is the electric constant;
• µ₀ is the magnetic constant;
• k_e is the Coulomb constant;
• R_K is the von Klitzing constant;
• Z₀ is the vacuum impedance or impedance of free space.

A natural hyperanalytic function occurs when considering the reticulum with increment L, in which the nodes are not yet defined objects. The distribution of object centers can be described using the reticulum function (RF): $$\mathbb{R}(x)=\frac{1}{\sigma\sqrt{2\pi}}\sum_{n=-\infty}^{\infty}e^{-\frac{1}{2}(\frac{x-nL}{\sigma})^{2}}.$$ Definitions: $$\mathbb{R}\left(0\right)=\mathbb{R}_{max}=\frac{1}{\sigma\sqrt{2\pi}}\sum_{n=-\infty}^{\infty}e^{-\frac{1}{2}\left(\frac{-n}{\sigma}\right)^{2}},$$ $$\mathbb{R}\left(1/2\right)=\mathbb{R}_{min}=\frac{1}{\sigma\sqrt{2\pi}}\sum_{n=-\infty}^{\infty}e^{-\frac{1}{2}\left(\frac{1/2-n}{\sigma}\right)^{2}}.$$ Now introduces the fine structure constant \(\alpha\) as function of \(\sigma\): \begin{equation} \alpha\left(\sigma\right)=\frac{1}{2}\frac{\mathbb{R}_{max}-\mathbb{R}_{min}}{\mathbb{R}_{max}+\mathbb{R}_{min}}. \end{equation}

The choice of name and designation of this parameter is due to the fact that \(\alpha\left(0.4992619105929628\right)=\alpha.\) The deuce left in the definition of \(\alpha\) is also present in the last formula. Thus, there can be no other mathematical constants in it by definition. Now the approximation of \(\mathbb{R}(x)\) will look like:

\begin{equation} A\left(x\right)=\frac{\mathbb{R}_{max}+\mathbb{R}_{min}}{2}(1+2\alpha cos\left(2\pi x\right)) +2\sum_{i=1}^{\infty}\alpha^{4^{i}}\left(cos\left(2i\times 2\pi x\right)-1\right)+\\ +\frac{2}{\mathbb{W}_{max}}\sum_{i=1}^{\infty}\alpha^{9{i}^2}\left(cos\left(3 \times (2i-1)\times 2\pi x\right)-cos\left((2i-1) \times 2\pi x\right)\right), \end{equation} where \(\mathbb{W}_{max}\) is a normalizing multiplier (which is equal to \(\left(cos\left(3 \times (2i-1)\times 2\pi x\right)-cos\left((2i-1) \times 2\pi x\right)\right)\) in the maximum point). Coefficient 2 for all cosinus is a consequence of symmetry \(\mathbb{R}(x)\) relative to point x = 0.

Three-dimensional RF \(\mathbb{R}\left(x,y,z\right)\) can be obtained from the definition: \begin{equation} \mathbb{R}\left(x,y,z\right)=\mathbb{R}_{max}^{2}\mathbb{R}\left(x\right). \end{equation} Thus, the approximation of the three-dimensional RF is also the series of the fine structure constant \(\alpha\) along any axis of the reticulum three-dimensional space, and the constant itself is a function of the dimensionless parameter \(\sigma\), which is equal to quotient of the "diameter" of some physical object, located in each cell, to the grid step L.

To quantize the time the direct use of the lattice idea is too formal. It is therefore appropriate to use a definition of derivative with respect to time but without moving to the limit. Let \(\mathbb{R}\left(t\right)\) is RF on a unit interval \(\left[-T/2,T/2\right]\) and \(\tau=\sigma\) и \(T=1\): \begin{equation} \mathbb{R}\left(t\right)=\frac{1}{\tau\sqrt{2\pi}}\sum_{i=-\infty}^{\infty}\left[\exp\left(-\frac{1}{2}\left(\frac{t+T/4-i}{\tau}\right)^{2}\right)-\exp\left(-\frac{1}{2}\left(\frac{t-T/4-i}{\tau}\right)^{2}\right)\right]. \end{equation}

\(\mathbb{R}\left(t\right)\) is also a hyperanalytic function, as the next approximation takes place: \begin{equation} \alpha_{eff}\left(t,\tau\right)=\sum_{k=0}^{\infty}\left(-1\right)^{k+1}\alpha^{(2k+1)^{2}}sin\left(2\pi\left(2k+1\right)t\right) \end{equation} Just as in the case of space, it is possible to generalize the resulting decomposition for a three-dimensional time because there are no formal limitations for a similar generalization. However, based on the principle of conformity, one-dimensional time should be generalized to the cylindrical "right-left" particle time, in which the discrete transition "forward or backward along the axis of time" is consistent with "turning right or left around the axis of time at 180⁰". The need for such a generalization is due to the fact that out (5) follows: \(\sin\left(2\pi t\right)\simeq-\frac{\alpha_{eff}\left(t,\tau\right)}{\alpha}.\) At the same time, the definition of \(\mathbb{R}\left(t\right)\) shows that the lowest-frequency pair is approximated as follows: $$\sin\left(\pi t\right)\simeq- m\left[\exp\left(-\frac{1}{2}\left(\frac{t+1/4}{\tau}\right)^{2}\right)-\exp\left(-\frac{1}{2}\left(\frac{t-1/4}{\tau}\right)^{2}\right)\right],$$ where \(m\) is a rationing multiplier. From this you can see that the actual "local frequency" \(\mathbb{R}\left(t\right)\) half the "group frequency" observed \(\alpha_{eff}\). In addition, the generalization of the "right-left" time allows you to see that the change \(\mathbb{R}\left(t\right)\) in time is actually caused by both the movement along the t axis and the simultaneous rotation around this axis.

Interaction № 1 or Space

As can be seen from the approximation of the \(\mathbb{R}(x)\) the final form of the permanent member of the decomposition of the RF is equal to 1. It was therefore useful to consider its importance in relation to the second member ratio. In this case, the reverse value of the permanent member of the decomposition will have a known physical value $$\frac{q_{S}}{q_{e}}=\frac{q_{N}}{q_{p}}=\frac{1}{2\alpha},$$ where \(q_{S}\) and \(q_{N}\) — Dirac's magnetic monopoly charges, \(q_{e}\) — electron charge and \(q_{p}\) — posiron charge. Since there are charges of particles and antiparticles in the denominators, we can expect that in the numerators there are also charges of particles and antiparticles!

It follows that the spatial grid used to build a hyperanalytic function is formed by Dirac's monopolies. The model of space of this kind was first described in the article. Thus, in the proposed theory, the strong interaction is the magnetic interaction described by Maxwell's equations.