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For The Beginners

What prompted me to work on a new model of reality?

One of the most important reasons was the inconsistency in the construction of the current model of reality, and according to me just this inconsistency is responsible for the current, complicated model of reality.


We know that surrounding us reality four-dimensional. I hope, nobody has no doubts here (formulas of Relativity Theory allow to treat time as the fourth dimension).


In the surrounding reality the distance is calculated according to the following rules:
In two dimensional space:
(1)        s2 = x2 + y2
In three dimensional space:
(2)       s2 = x2 + y2 + z2


In four dimensional space a distance is calculated according the differnt rule:
(3)       s2 = - ( x2 + y2 + z2 ) + t2

(in this paper is applied the system of units where the speed of light c=1)

the space described by eq. 1 and 2 is named the Euclidean space while the space described by eq. 3 is named the Lorentzian space-time

You could ask - why the rules of measurement of distance in four dimensional space are different than the rules in three- or two-dimensional space?
The answer given presently by scientists says that in the four dimensional reality the observed dimensions fulfill the equation 3

In other words the answer of scientists is:


In my papers I'd like to describe this fact with more detail explanation than "BECAUSE"

Description according to the Relativity Theory

As it was written above, our reality is constructed of the four, not of the three dimensions. The notation introduced in RT allowed treating the time quite as a fourth dimension
Instead of notation x,y,z,t it is applied a four-vector x0,x1,x2,x3. Coordinate x0 denotes time t, the other three dimensions mean spatial dimensions x,y,z. Using such notation we can write the equation for a distance in the four dimensional reality in the following form (so called the covariant notation):
(4)       s2 = gikxixk
where i,k=0,1,2,3
As you can see, all the four dimensions of time and space can be treated as if they were identical. Almost....
Despite seeming similarities, time is treated differently than the other dimensions and the use of a four-dimensional vector needs the use of so-called metric tensor, which hides information about different treatment of time-dimension than the three space-dimensions. The metric tensor g_ik in the equation 4 looks like:

Finally, after applying the metric tensor, a distance in the four-dimensional space-time x0,x1,x2,x3 is computed according to the rule already showed in the introduction:
(5)        s2 = x02 - x12 - x22 - x32 (Lorentzian space-time)
There is serious inconsistency in this model because, theoretically, if the space is, at last, four-dimensional, then the distance in this four-dimensional space one should measure according to the same rules as in case of the three-dimensional one, that is, to the rules applicable to Euclidean space:
(6)        s2 = x02 + x12 + x22 + x32 (Euclidean space)

The distance in Relativity Theory is measured according the equation (5) because this is in accordance with our observations.

Finally: we observe that the 3-dimensional space is Euclidean while the 4-dimensional space-time reality is Lorentzian.

However the fact that we observe the reality as Lorentzian does not has to mean that the true reality is really Lorentzian.

Observation can give us, from time to time, a false information about the true nature of the reality.
For example, if we observe heavenly bodies in the sky, then we see that stars move along circles and planets move along certain complicated curves -see fig. 1 below.
Fig. 1 The trajectories of planets observed from surface of the Earth. Through centuries our predecessors were convinced that the planets really moves along such complicated trajectories.
Through centuries our predecessors were convinced that such complicated trajectories observed in the firmament are the true trajectories, the planets are moving along in the Universe. Theory describing these trajectories was very complicated, however it did correctly describe motions of planets. It took many centuries before our predecessors came to conclusion that the complicated shapes of routes of planets do not describe the true routes of planets but they are a result of the fact that we observe planets revolving around the Sun from a frame, which also revolves around the Sun.
Fig. 2 Complicated shapes of trajectories of planets which we are able to observe are the result of the fact that the planets which revolve around the Sun are observed from a reference system also revolving around the Sun.
Problems which met Galileo and Kopernik trying to introduce a new model of the Universe, were result, not only of its incoherence with the Bible but also, of the simple fact which we meet every day in science. Namely, before Galileo or Kopernik, worked a geocentric model describing motions of planets in correct, though a complicated way. Moreover, the Kopernik's theory, although simpler than the geocentric model, described the motions of planets less exact than the previous, geocentric, model - eventually the Kepler's model was accurate enough. Thus, many contemporary scientists thought that creating a new, less accurate, model does not make sense, when the previous - geocentric - works quite well. Similar arguments were, and still, are present in the science.

Therefore, do we not do the same mistake, assuming that the reality is Lorentzian only because we can observe it as Lorentzian, as our predecessors did, assuming that the planets move along such complicated routes because such strange routes they observed in the sky???

In my opinion, in case of description of the space-time reality we are in the point, in which was the science, before discoveries of Kopernik and Galileo. As our predecessors we think that the Universe - more precise - the dimensions creating the reality - are identical as the observed one. However, it has not to be the truth.

Basis of a new model of reality

For every day we live surrounded by objects which determine our idea of the reality. We can see three dimensions of space and we feel the time flow. However, all these objects determining our idea of reality, move much slower than the light, so they are not relativistic Therefore, all the world, we can perceive by our senses, is not relativistic and if we construct new models of reality, we try instinctively reproduce the picture of reality observed on a daily basis and not the relativistic one.
And now let's imagine that we are living in quite empty space. Nothing can be seen. In this quite empty space we are not able to determine the number of space dimensions, where is top, where is down etc. And now in this empty space a particle emerges. We can observe this particle with the help of waves sent by it. Thus a direction of propagation of these waves we interpret as the space-dimension. In addition, if we assume that the particle sends the waves in a particular direction, then this direction will be interpreted by us as the space-dimension, because the waves, received by us, are the only information, available to us, about the existence of other particles.
Assume now that each particle moves in the space along a certain trajectory, and sends waves in a direction perpendicular to its trajectory. Then, what we perceive as the space-dimension is the direction of propagation of the wave emitted by a specific particle - so the direction of propagation of the wave, which is perpendicular to the trajectory of particle, we perceive as the space-dimension. The true space-dimensions, creating the reality (they will be further denoted by letters a,b,c,d), cannot be observed, because the dimensions do not emit any waves or signals, which we are able to register - Fig. 3. If the direction perpendicular to the trajectory of the observed particle is perceived, by an observer, as the space-dimension, then the length of the path traveled by the particle along its trajectory will be a measure of the its proper time. In other words we can order the events of the particle's history along positions of the particles on its trajectory (a more detail explanation one can find in further chapters). As a result, the particle perceives certain directions, of the reality, as dimensions of time or space. However these directions observed by the particle, as dimensions, are different than the dimensions, that create the true reality. Moreover, the observed dimensions are not constant but depend on the currently observed particles - it is presented in the Figure 3
Fig. 3 Example of the model of observation: Two bodies move in space described by the dimensions a and b, where none of them has the meaning of time- or space-dimension. In the space ab are the observer and the observed particle. In the figure to the left it is the observed particle A, in the figure to the right it is the observed particle B. The observer and the particle interpret their trajectories as the time axes of their coordinate systems t, t'A, t'B . The existence of space can be noticed by the observer only by observations of surrounding particles. If the particles emit signals/waves in directions perpendicular to their trajectories, then the observer interprets the direction perpendicular to the trajectory of a specified particle directions as the s pace-dimension. The observer during observation of particle A interprets different direction as its space dimension than during observation of particle B. The description quoted here is shortened and imprecise. The problem is described exactly in the following sections.
Notice, that if now we observe the non-relativistic world around us, then the space-dimensions (the directions being perpendicular to the trajectories of observed objects) are perpendicular to the time dimension (the trajectory of an observer). It is result of a fact that all the trajectories of non-relativistic objects surrounding us are practically parallel to the observer's trajectory - fig. 4.
Fig. 4 In the non-relativistic world in which we live, trajectories of almost all bodies are parallel to the observer's axis of time t. If we assume that the directions, perceived as the space-dimensions, are perpendicular to the trajectory of an observed body, then it turns out that practically all these directions (interpreted as the space-dimensions) are perpendicular to the time-axis of our reference system.
The appearance of relativistic particles changes this picture and we begin to interpret as the space dimension the directions not being perpendicular to the axis of time of observer - Figure 5. However, in the Theory of Relativity one tries to keep the perpendicularity of space dimensions to the dimension of time, known from observations of the surrounding non-relativistic world - Figure 4. The observer, convinced that the dimensions for relativistic and non-relativistic objects are identical, has to assume the deformation of the dimensions during the relativistic motion. It causes the introduction of complicated metrics (Eq. 5) which is difficult to understand, difficult to use, and it is easy to come here to various false conclusions and paradoxes.
Fig. 5 In case when the relativistic particle appears, the trajectory of such particle (the blue one) is inclined to the trajectory (time-axis) of the observer. The observer during observation of the relativistic particle, interprets the directions perpendicular to the trajectory of the observed particle as the space dimensions -Xr,Yr. These directions differ from the directions perceived as the space dimensions when the observer observes non-relativistic objects XnYn. However, the observer convinced that the space dimensions are fixed (identical as for observation non-relativistic and relativistic objects), will have the impression that the dimensions XrYr for the relativistic particle are being deformed.
Application of the model of Euclidean Reality in which we assume that the directions interpreted by us, as the dimensions of time and space are not fixed but depend on the currently observed body and the true reality is Euclidean (described by equation 3) - Figure 3 - causes that the relativistic physics becomes simple and understandable. Those who know better relativistic physics may ask - if there is no deformation of the dimensions then where does the time dilation in GPS satellite systems come from, and how to justify constancy of the speed of light in systems moving at different speeds? In the new model, such explanations require certain new assumptions but thus, such problems as the constancy of speed of light or twin paradox have clear and understandable explanation, and they do not cause such doubts as the explanations of Relativity Theory.

So I invite you to read more

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