In order to describe a motion in Special Relativity Theory we apply a co-ordinates system consisting of three space and one time dimension which we can measure in our frame. The space-time construction of those dimensions is from our point of view obvious – the dimensions are those we can directly observe. Instinctively we accept the observed shape of space-time as the “true” one assuming that the reality is pseudo-euclidean.

However, the description of events in SRT is complicated; some strange similarities appear, which that couldn't have been satisfactionally explained till now. For instance: similarity of space and time with no full symmetry of the dimensions or enigmatic absence of full symmetry in Maxwell Equations, which made and still makes many authors formulate various theories treated rather as curiosities [4, 10-14].

The complication of the theory can be caused by the complicated structure of reality indeed, but the reason of the complication can be quite different.

For example, the description of motion of the planets with the assumption that co-ordinates system of the Universe is connected with the Earth, was very complicated. Trajectories of planets were described with complicated, although true, formulas. The choice of that co-ordinates system seemed to be obvious. Everyone all their life observed motion of the Sun and the stars, while the Earth was stable.

Only connecting the co-ordinates system with the Sun – inconsistent with directly observed events – caused simplification of the description of planets motion.

Therefore, we can ask the question: Is the well known, but complicated, model of the pseudo-euclidean reality a description of the “true” structure of the reality, or is the complication of the model an effect of describing some simpler hypothetical reality with improper co-ordinates system, like it took place with the mentioned above description of planets motion.

The fact that the reality is observed as pseudo-euclidean doesn't have to mean that the “true” reality is pseudo-euclidean, too. The observed character of reality can be an effect of performing the observation – we cannot observe the reality directly. We can only observe events in this reality, and still indirectly. The observation is performed through interactions carried by quantums – particles moving in some strange, from our point of view, manner.

In this paper I wanted to show that it is possible to describe the reality with a simpler hypothetical, for instance euclidean, model. The pseudo-euclidean reality would only be an effect of observation of events in this hypothetical reality – performed with quantums.

The proposed description explains e.g. the already mentioned problem of symmetry of time and space, and gives some conclusions different from those predicted by SRT.

The specific property of the time and the space dimensions is that if the frame of the observer is changed, the distance ds² described with rel. (1) is conserved.

The dimensions xyz of the euclidean reality and the dimension of time t are therefore assumed to build the pseudo-euclidean reality in which the distance is described just with the value ds². In the reality in which distance is defined with (1), change from one co-ordinate system to another, which moves with different velocity, will cause stretching of dimensions xyz and t

On the other hand, the motion is relative, so if observer A sees change of dimensions in frame of observer B, observer B can see the same change of dimensions in frame of observer A. The deformation of dimensions really takes place; it was verified in various experiments e.g. [3,5]

What will happen now, if observer B takes off in a journey and comes back, while observer A remains in rest? During the journey both will mutually observe time dilation in the frame of the other observer, but in which frame the time will really flow slower?

The problem is known as the Twin Paradox. Its usual interpretation predicts that time in the moving frame flows slower because the observer in motion has to change the direction of flight in order to return home. This change causes that frame of traveller becomes non-inertial for a while.. This interpretation has been confirmed directly in experiment with clocks travelling around the world in jet-planes and although there can be some objections to the theoretical part of the experiment [6,9], belief in this usual interpretation is so strong, that the results of the experiment have been accepted as obvious and published in the most serious journals [1,7]

However, problems connected with mutual observation of the Lorentz contraction, time dilation, relativity of the choice of the frame etc, are difficult to understand, so the Relativity Theory is known by the physicists but hardly anyone can really understand it. Many problems are difficult to interpret, which leads to appearance of incompatible opinions in literature, as for example the mentioned above [1,6]. The relativity theory itself cannot give us a unique and simple explanation for them.

Similarity of time and space dimensions allows us to write eq. (1) in a form in which time and space are treated seemingly in the same way:

"Seemingly", because tensor g_ik equals to: so the time dimension is treated differently from three space dimensions. Such shape of the tensor does not results from more fundamental laws and is accepted only because it is in agreement with observations . This shape raises new doubts. The basic one an absence of full symmetry of time and space dimensions. Efforts made in order to introduce the symmetry, for example increasing the number of time dimensions up to three [10-14] did not bring satisfactory results.

This presented above very concise review of main assumptions and problems of SRT shows that although SRT describes most of events correctly, the description is complicated, sometimes not clear, and cannot explain some properties of the reality, like for example the shape of tensor g_ik which we have to assume as the fundamental property of the reality. So, is the reality really so complicated and incomprehensible - or maybe, as it was mentioned at the beginning, problems with interpretations or absence of the dimensions' symmetry are the result of improper co-ordinate system used for description of the reality?

Let's assume that the mentioned above complicated properties of the reality, like its pseudo-euclidean shape, are not the property of reality but an effect of observation of events only. These events would take place in simpler reality, probably in the euclidean one.

If the "true" reality was euclidean, the first assumption of my theory would be - similarly to STR:

However, principle of invariance of the distance ds described with equation (1) still needs one more assumption in order to satisfy the equation (1).

If we present trajectories of observed body and observer in new, euclidean reality, we can see that in conventional frame xt the dependence (1) is not satisfied - see fig.1a.

Yet the dependence is satisfied in another co-ordinates system, where x-axis of the observer is perpendicular to trajectory of the observed body -fig. 1b; we should remember that in case of observation of a real body relationship: ds² = dt’² takes place.

Therefore we have to assume:

The assumption could seem strange or illogical, but we should realise that dimensions of the new reality are not those we can indirectly observe.

Practically, it means that in the new, four-dimensional euclidean reality, direction perceived as time dimension covers trajectory of an observer, and three other directions perceived (interpreted) as space dimensions are perpendicular to trajectory of an observed object, so they have to be different for observation of each body. Thus, one and the same direction of the new reality can be interpreted either as time- and or space dimension. This depends only on choice of observer and observed body.

Some consequences of properties of the new reality, mentioned above, will be touched upon in further part of the article.

Connection of the space dimension with trajectory of an observed body, and not with the observer, results that in the new reality. Condition (1) is then automatically satisfied and there is no need write equations in form ensuring invariance of ds - it is explained in fig 2.

In other words, every equation written in the new co-ordinates system satisfies condition of invariance of the space-time interval ds !

It should significantly simplify equations of General Relativity Theory, the complication of which mainly results from the fact that notation has to conserve value ds² while the frame of an observer is being changed.

Also problem of mutual observation, e.g. of time dilation, is presented here simply, comprehensibly and uniquely (fig.3). As it is shown, the time dilation observed in frame in motion is here just effect of the observation, and not the real deformation of dimensions.

Another problem is the interpretation of the fact that space dimension is not stable in relation to the observer but it depends on choice of an observed object.

Firstly, we must consider why in a four-dimensional reality we can only see three space dimensions. The problem is new because in hitherto theory dimensions had been in advance defined as space or time ones and we didn't need to think about the meaning of the time or space. Now we have four dimensions neither of which is a time or a space one. Only process of observation makes three of the directions space dimensions and fourth - the time dimension.

We can perceive the space through interactions, so number of space dimensions, that we can observe should be equal to those dimensions only in which the interactions can propagate, regardless of the real number of dimensions of the reality. So if in the objective n-dimensional reality, interactions can propagate into three-dimensional subspace, we will only be able to observe the three dimensional space.

Moreover, we should realise that in the process of observation we are only receivers of interactions, because even if we try to interact on another object, in fact we emit particles to this object and only then we receive back information through reflected or new emitted particles.

Therefore the assumption 2, which tells us that space dimensions should be chosen perpendicularly to trajectory of observed body, can be interpreted as following:

We should therefore have two basic kinds of particles:

• particles travelling (existing?) on some trajectories

and

• particles carrying interactions - emitted perpendicularly to trajectories of those particles

Observed space- and time dimensions give us in this case, pseudo-euclidean picture of the reality, but it is not property of the reality any more. The "true" reality is still euclidean, and pseudo-euclidesn shape of the reality is only the result of the act of performing of the observation - through the particles emitted perpendicularly to trajectories of the observed bodies.

As we can see construction of the reality motivates the shape of the metric tensor in equation (2), and the possibility of interpretation of one and the same direction of reality as either time or space dimension motivates similarity of time and space dimensions.

As well dependencies of SRT are obtained here is much simpler way than before. For example the Lorentz transformation results straightforward from comparison of frames of two bodies presented in the new, euclidean reality - see appendix at the end of the article

In the new, euclidean reality frames of observer xt and observed body x't' can be shown as following - fig 4:

Space axis of the observer is chosen as perpendicular to trajectory of the observed body, Similarly, space axis of observer's frame is chosen in the same way - in order to be perpendicular to trajectory (time axis) of observer.

Thus none of the frames, xt or x't' is not favoured here. The fact that xt frame was named the observer's frame is conventional only. We can as well name x't' frame the observer and axes in the figure 4 will be the same.

At the same time, according to SRT, axes of both frames should look differently from point of view of observer placed in xt frame - fig. 5a, and differently from point of view of observer in x't' - fig 5b.

We can see that relative velocity here has the meaning of the sinus of angle between trajectories of both bodies:

Moreover, velocity is no longer a physical property, it is only an effect of observation. Speed of light, equal 1 in this paper, corresponds to trajectory perpendicular to trajectory of the observer. It is easy to conclude that increasing of angle j up to 90^o will cause increase in the value of x dimension up to infinity; for 90^o dimension x should be parallel to time axis t of an observer. According to this, even if change of body's trajectory into perpendicular to trajectory of the observer is possible in some finite time (i.e. proper time of an accelerated body), observation of this fact should last to infinity. Velocity, speed of light, possibilities of acceleration and interstellar travels are discussed in more detail in further part of the article.

Conclusions

The assumption that the “true” reality is described with the euclidean model and not, as in hitherto models, with a pseudo-euclidean one, results in different description of some events, well known from SRT.

For example, a description of the Twin Paradox in the new, euclidean reality must lead to the conclusion that the time of the twin in motion is longer - the opposite effect than one obtained in SRT - see fig. 6. It must be longer because trajectory of twin in motion is longer. We should remember that trajectories of both observers are presented in the same scale and lengths of them are equal to proper times of observers.

This conclusion is in disagreement with hitherto interpretation of the clock paradox verified with a lot of various experiments [5]. It could suggest that the presented theory must be false. In fact most of the experiments can be explained in accordance with the presented theory. As an example interpretation of Pound and Rebka's [3] experiment is presented below:

Authors - Pound and Rebka - have measured dependence between temperature of body and frequency of emitted radiation. The change of frequency of radiation corresponded to relativistic dilation of time, which took place in frame connected with oscillating atoms of the body. Velocities of oscillating atoms, and therefore also relativistic dilation of time, were a function of temperature. The result of this experiment is given in handbooks as a proof for hitherto interpretation of twin paradox, e.g. [8].

According to the presented model, an observation of any part of trajectory of the travelling twin or of the oscillating particle in experiment [3] should give as a result a dilation of the time identical as in SRT. Therefore measurements as performed by Pound and Rebka are in accordance with the presented theory which predicts observation of the dilation of time, according to relation (4); see also fig. 4:

where j is an angle between trajectories and sinj denotes relative velocity of bodies.

The basic difference between my theory and SRT is that observation of each point of trajectory of the body must be performed in different frame and x-axis of this frame must be perpendicular to the trajectory of the observed body.

Thus although observer in rest can every moment observe time dilation in frame in motion, total time flowing in frame in motion is longer than in frame of the observer in rest. It is explained in fig. 7a.

In other words, it is not possible to calculate time flowing in frame in motion as simple integration of times observed in following points of trajectory (5).

According to my theory, only observer in motion can calculate time which flows in system in rest as an integral from observed times ( equation 6).

It can be true because in this case space axes of all co-ordinates systems chosen for observation of each point of trajectory are parallel (perpendicular to trajectory of body in rest). Observation from point of view of the observer in motion is shown fig. 7b.

It results from the above considerations, that although the observation of each following part of the trajectory of the observed body gives as a result the time dilation –as shown by Pound and Rebka - the experiment with clock positioned in a rocket and measuring time from start to landing should show that total time in the rocket was longer.

Such experiment with clocks positioned not in a rocket but in jets flying eastward and westward around-the-world was performed by Hafele and Keating [1] and its results were in accordance with the hitherto interpretation of SRT. This result is inconsistent with my theory and I can only hope that the problem has not been formulated [6] or interpreted [9] well. For example, according to [9], Hafele and Keating omitted the centrifugal force which should be an effect of eastward and westward motion of the jets. If we take this force into account we get the dependence of the gravitational effect on the direction of the jets’ flights. It should change the achieved results of the experiment by a few hundred percent.

Another result of the assumption that the space dimension of the observer’s frame depends on the observed object is that particles observed as being in the same point of space-time can be, in fact, in two different points of the new reality. Therefore, particles, observed by us in the same point of space-time, which should interact, in practice do not interact and vice versa, particles observed in different points of space-time can sometimes interact. The described effects should be increased with the increase of velocity of observed objects and the observer's distance from them. The situation described above is shown in fig 8.

In my work velocity is not a physical property of bodies; it is only an effect of observation of trajectories of other bodies, performed with quantums. The trajectory of body is now, in four dimensional, euclidean reality the physical property - instead of velocity.

For example it could be possible to change the trajectory of the body into perpendicular to the trajectory of the observer which would be observed as the speed of light or observation of "superluminal" velocity.

According to my paper an effect of speed of light would be observed in case of particles whose trajectories are perpendicular to the observer’s trajectory. Because all trajectories in the new reality are allowed, some amount of particles would be observed as moving with the speed of light. Another problem is how to accelerate particle to this velocity. It is easy to conclude that the acceleration of a particle to speed of light in accelerator is impossible, because the field in accelerator is emitted perpendicularly to its trajectory (into the space dimensions), so the acceleration of the particle to speed of light (perpendicular to the accelerator trajectory) needs infinite time and energy (fig – 9a).

However, such acceleration can take place in case of interactions with other accelerated particles – fig 9b. In this case some incoherence with the energy conservation law should occur. According to my first estimation the incoherence should be observed in interactions involving energy even of just a 3-5 GeV.

Moreover, if the particle interacts with other particles in accelerator, it can be sometimes observed as moving with speed higher than the speed of light – see fig 9c.

According to the model presented here, none of the trajectories can be observed as corresponding to superluminal velocity, i.e. V>1 because velocity is defined as sinus of an angle between trajectories: V=sinj . However, sometimes we can define trajectories along which we can travel shorter than along trajectories corresponding to the speed of light. As an example, a travel to the stars that are running away fast can be given.

If we send the rocket with velocity almost equal to speed of light to fast running away system, the travel should last very long time (fig. 10), but it is possible to determine a much shorter trajectory, which would make possible the travel to the system and back (fig.10)

It is easy to see that observation of such travelling rocket would be very strange from our point of view. The rocked would be probably observed in various places in the same moment and its travel would be observed long time after landing.

I introduced here the proposal of another description of the physical reality.

The great advantage of the model is the simplification of description of events in euclidean reality (as shown on example of the Lorentz transformation) and the fact that the model can motivate, as the first one ever, I suppose, the signature (+ - - -) of the space-time metric. Problems of time dilation, light speed, mutual observation of clocks, distances etc. are described here simpler than in SRT and are easy to understand. Moreover, new description does not have any singularities taking place in SRT for the speed of light or in GRT on the boundary of black holes (to be published). It should thus be possible to describe some events that are difficult to describe in hitherto model of reality.

Some of the conclusions of this work, as for instance the interpretation of the Twin Paradox, are different from those predicted by SRT and from some experimental results, e.g.[1]. According to [6,9], results of this experiment had not been properly interpreted and this fact should give my theory a chance.

Many of the new conclusions need to be described in more detail, for example the problem of interpretation of fact that space dimension depends on the trajectory of observed body; also, the problem how to connect this with specific diagnostic system having stable space co-ordinates. Another problem is what are the new rules of composition of velocities, which enable us to reach speed of light. Hitherto rules did not allow us to reach this speed. Those problems are solved now and will be described soon.

Another conclusion, touched briefly now, needs to be elaborated on or needs reconstruction of the model. For example, interpretation of motion of rocket travelling along superluminal trajectory. Is it really possible to observe the flight of the rocket before its taking off or is it only the mistake of theory? And what is the meaning of the trajectory in euclidean reality?

Those and many other questions have no answer yet, but great simplicity of the model seems to be not accidental and may suggest that the idea of reality presented here can be true.

I would like to end my article with a question which was asked at the beginning of it: “is it possible to describe the space-time reality with the euclidean model?”, or more general: “are the observed time and space, the dimensions of true physical reality or some observed projections of non-observable hypothetical true dimensions?”.

In this article I introduced only the suggestion of the answer for the above questions only, and the problem is still open to discussion.

Let us consider a simple problem of two inertial bodies in the new xt’ coordinate system as described in this work. Obtaining of the Lorentz transformation in the frame xt’ proposed here is shown below.

In the frame as shown in fig. 4 let us put a point P (see fig 11). From the picture we can conclude that x coordinate of the point P is equal

then

OA=x'+ t'sinj

so - if we remember that sinj means velocity V of the body (fig 4), we can write:

In the same way the equation for t coordinate can be obtained:

OB=t'+ x'sinj

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