Hypothesis of Primary Particles and the Creation of the Big Bang and Other Universes

In this paper, we have presented a new approach to the dynamics of hypothetical primary particles, moving at speeds greater than the speed of light in a vacuum within their flat spacetime, which is why we understood the reason why they have not been detected so far. By introducing a new factor, we have linked the space-time coordinates of primary particles, within different inertial frames of reference. We have shown that transformations of coordinates for primary particles with respect to different inertial frames of reference, based on this factor, constitute the Lorentz transformations. Utilizing this factor, we have set the foundations of primary particle dynamics. The results obtained for the dynamic properties of these particles are in accordance with the fundamental laws of physics, and we expect them to be experimentally verifiable. Likewise, due to their dynamic properties, we have concluded that the Big Bang could have occurred during a mutual collision of the primary particles, with a sudden speed decrease of some of these particles to a speed slightly greater than the speed of light in a vacuum, which would release an enormous amount of energy. Created in such manner, our Universe would possess a limit on the maximum speed of energy-mass transfer, the speed of light in a vacuum, which we will show after introducing the dynamic properties of these particles. Similarly, we have concluded that the creation of other universes, possessing a different maximum speed of energy-mass transfer, occurred during the collision of these particles as well, only by means of deceleration of some of these particles to a speed slightly greater than the maximum speed of energy-mass transfer in that particular universe.

than the maximum speed of energy-mass transfer in different universes k, and because of this they are in their flat spacetime, wherein the aforementioned space is homogeneous and isotropic and time is homogeneous. Simultaneously, their lower border speed equals k, i.e. they can only move at speeds that surpass the values of it u k > . In our Universe, the maximum speed of energy-mass transfer is k c = .
We have shown what the basic kinematic and dynamic properties of these hypothetical particles look like, based on the newly introduced ξ factor which links space-time coordinates between different inertial frames of reference. It is widely known that our Universe originated in the Big Bang, but that modern physics cannot explain events preceding Planck time. We expect further development of this hypothesis to clarify the Big Bang itself.
In the following section of this paper, we will discuss potential kinematic and dynamic properties of hypothetical primary particles with regard to our Universe, in which the maximum speed of energy-mass transfer is the same as the speed of light in a vacuum.
The facts known thus far are the following:  Particles that possess the rest mass can approach the speed of light by increasing their momentum and energy. Let's assume they move with v c < .  The maximum speed of energy-mass transfer is the same as the speed of light in a vacuum c.
Newly described:  Primary particles, whose speeds we will denote by u, are able to move faster than light 2) The Principle of Constancy of the speed of light: The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or observer.
3) The speeds of the primary particles u, may possess values p c u u < ≤ , ( ) p u c  , that are independent of the choice of inertial frame of reference from which observations are being made.

Time Dilation for Primary Particles
Einstein's relativity of the notion of simultaneous occurrence of some events [1] can also be extended to primary particles moving faster than light.
We will imagine how observers from the "mobile" S' and the "stationary" S frames of reference see the time between two events in the world of primary particles, through an example of the time required for the primary particle to pass a certain distance from the point of departure to the primary particle reflector ( Figure 1). Let us assume that S' moves in the positive direction of the x-axis at the speed of light c, relative to system S, because we want to find the factor Figure 1. The observer O from the S perceives that the observer O' and the reflector are moving to the right at speed of light c, which represents the lower border velocity of the primary particles movement, hence the series of these events appear different to him. By the time primary particle reaches it, the reflector moves to the right by distance ct, hence the primary particle travels the distance ut, where t represents the time required for primary particle to relocate from the point of the viewer O' to the reflector at the position R. After time 2t, the primary particle, starting from the point O' and reflecting of the reflector, returns to O' again, but observed from the S, by passing the distance 2ut. Therefore, the observer O from the S concludes that the primary particle will reach the reflector only if it leaves the point of the observer at some angle in relation to the vertical plane. Note also that observer O must possess two synchronized clocks at the departure and arrival points of the primary particle, which are immobile in his frame of reference S, and compare their display with the display of a mobile clock located in the frame of reference S'.
Thus, the observer O from the S measures the dilated time t in relation to the time τ measured by the observer O' from the S'. through which the space-time connection of possible speeds of the primary particles u with c, would be implemented. Above the observer O' and the frame of reference S', a reflector of primary particles R' is located at a certain distance, perpendicular to the path of the primary particle in that frame of reference. Observer O' measures time for which the primary particle proceeding perpendicular towards the reflector returned as 2τ , travels the distance 2uτ . Note that in order to measure this time, the observer O' requires only one clock which is permanently situated at the same location from which the primary particle starts and to which it returns.
From the shaded triangle, we can see the following: We can also introduce the ξ factor: Similarly, if these events were to play out in the S, in the manner that the pri-mary particle moved from and returned to the same place in this frame of reference, the observer O' from the S' would measure the same dilation of time, since in relation to him, the S moves at speed of light c only in the opposite direction, to the left. In accordance with the postulate on the independence of primary particle speed from choice of the inertial frame of reference from which it is being observed, for both observers it moves at the identical speed u. None of the observers O and O' have the means of determining whether or not they are moving, i.e. each of them is in a state of rest in his own frame of reference.
Therefore, the names of two frames of reference "mobile" and "stationary" are written in inverted commas.
The shortest possible time between two events, proper time τ , is measured by the observer from whose perspective they are taking place at the same location in space. We therefore conclude that the time elapsed between the two events depends on how far they have unfolded within the two observed frame of references, i.e. that a connection between spatial and time intervals exists.

The Transformation of Space-Time Coordinates for Primary Particles
Since primary particles moving at speeds higher than the speed of light u c > , it is necessary to introduce new transformations of space-time coordinates between inertial frames of reference. They must apply to all speeds of these particles of u which is slightly higher than c to p u . As we can see (Figure 2), the same event has different coordinates in two different inertial frames of reference.

, , x Cx Dt t Kx Lt
where C, D, K and L represent constants to be determined. If we observe the movement of a primary particle along the x-axis, it will, from the perspective of the frame of reference S' at time moments 1 t′ and 2 t′ , possess the spatial coordinates 1 x′ and 2 x′ , and its shift will be ( ) ( ) The time interval in the S', during which the movement occurred is Based on this, the velocity of the observed primary particle moving along the x-axis equals: Relative to the frame of reference S the velocity of that same point is and the relation of these two velocities is given via expression .

Cu D u
Ku L In order to determine the constants C, D, K and L in this expression, we will consider several special cases of motion. Journal of Modern Physics , , , x y z t ′ ′ ′ ′ . It is necessary now to find new coordinate transformations that would also apply at the higher relative velocities of frames of reference, than the speed of light. Along the y and z axes, no movement S and S' occurs, and as in the cases of Galilean and Lorentz transformations, y y ′ = , z z ′ = , applies. In order to determine the functional connection between the remaining two coordinates, one of space and one of time, we have to acknowledge that it should preserve the properties of space and time. The basic properties of the space are homogeneity and isotropy, and the basic property of time is homogeneity, which is directly related with the conservation laws in mechanics. Therefore, the coordinate transformation law we are searching for has to be linear, hence the interconnection of the coordinates is linear.
We will first observe the border case. The primary particle is idle relative to S', i.e. is located in its own frame of reference, at its lowest possible velocity in relation to S. In this case, 0 u′ = while u has slightly greater value than c, i.e. u c → . Therefore, observed from a "stationary" frame of reference, the primary particle moves at the same velocity as the "mobile" frame of reference. Thus, expression (6) becomes 0 , Cc D Kc L + = + and the following applies Vice versa, due to relativity of motion, when the primary particle is idle relative to S i.e.
We will now use the third postulate according to which the possible primary particle velocities appear identical, observed from all inertial frames of reference and if we substitute this in (6) using (7) and (8) Equations (2), after replacing the values D, K and L, become in which only the constant C remains unspecified. According to the principle of relativity, a complete equality of the observed frames of reference exists. Which means that for an "stationary" frame of reference we can take S' and consider that the frame of reference S moves at velocity "−ω" in relation to it. Based on that, equations that connect x and t with x' and t' read When we replace (12) in (11) we get 2 2 , from which we can see that i.e.

Four-Dimensional Formulation of Coordinate Transformations for Primary Particles
Similar to Minkowski space [2], we shall introduce a real four-dimensional space in which we will present transformations of coordinates of the primary particles as transformations of coordinates of that very space. Points in that space are position vectors where x σ represent contravariant components of the vector x at basis The metric of this space is identical to the metric of Minkowski space x gx ut x y z y z Within spacetime of the primary particles, we associate each contravariant vector to covariant components using the metric Below, we will use Einstein summation convention, which implies summation when an index is repeated twice in a single term, once as upper index and once as lower index, without writing the sum sign. Therefore, the previous form is summed by the index ς , and the following applies  where I represents an identity matrix. Numerically, we easily get

A g A g A g A g A g A A A g A g A g A g A g A A
However, tensors The square of the length of vector x is calculated via ( ) and for differential of the square length between the points x and Boost along x-axis for primary particles, which is similar to the Lorentz boost, we will record in the form of where 4 4 × matrix represents the transformation matrix σ ς Σ , in which the index σ represents the row index and index ς is the column index. The matrix Equation (27) in component notation is Lorentz transformations are those linear transformations of the coordinates x x ′ = Λ , where Λ represents the real matrix 4 4 × , which does not alter the square of length of the four-vector, i.e. the following applies to them 2 Therefore, every real 4 4 × matrix that satisfies the condition (29) is a Lorenz transformation. Hence, we see that our boost matrix along x-axis is a Lorentz transformation, and it can be easily shown that the boost matrices along y-axis and z-axis are also Lorentz transformations, as well as the three matrices of rotation of the coordinate system.

Time Dilation as a Result of a Transformation of Coordinates for Primary Particles
We have already derived the time dilation formula for primary particles based on postulates that apply to primary particles. We will now demonstrate how it is obtained by applying the transformations of the coordinates of the primary particles. Imagine the clock being located at the coordinate start of the inertial frame of reference S'. It will show time S' in t' and its coordinates in S' would be 0 x y z ′ ′ ′ = = = . If we replace those values of time coordinates with expressions for transformation of the space-time coordinates of primary particles (15), we get the coordinates of the clock from "stationary" frame of reference S in relation to which S' moves at velocity u:  in relation to which it remains immobile, equals less than the time measured in frame of reference S, that is, in this case, time t' represents own time.

The Velocity-Addition Formula for Primary Particles
We will continue to observe that S as a "stationary" frame of reference in relation to which S' moves at velocity ( ) , , x y z u u u = u . Primary particle with the velocity of ( ) , , According to the Equation (14), the differential dx′ and the differential dt′ are while the velocity represents their ratio x component of velocity relative to S, we have Figure 3. The dependence of total relativistic energy of the particle on speed v (red curve), the speed of light in a vacuum c (green line) and dependence total energy of the primary particle on speed u; according to the primary particles hypothesis (blue curve).
We will introduce homeokinetic energy H.
Conversely with kinetic energy increment that accompanies increase of the speed of particles possessing rest mass in classical and relativistic physics, homeokinetic energy of primary particles increases as they decelerate during mutual collisions, consequently increasing their total energy t E . .
It is obvious that these particles would not interact with matter via four known interactions due to the speed of their motion u c > , so primary particles therefore exist in their flat spacetime, while the non-interaction of these particles with matter is the reason why they have not been detected so far. So, in order for these particles to mutually interact, a need for a new kind of interaction expanding faster than the speed of light arises. For homeokinetic energy, from (40), (41) and (42) we get third postulate as well, according to which the values of the speeds of these particles are independent of the choice of inertial frames of reference from which they are being observed. In a thought experiment, we realize that dilation of time is the greatest while these particles are moving at speeds close to lower border speed, i.e. the speed of light c within our Universe, and get a ξ factor that corresponds to Lorentz γ factor. The same value of ξ factor was obtained via transformations of space-time coordinates for primary particles. We have shown that these transformations are Lorentz transformations. Based on the ξ factor, we have developed the dynamics of particles moving faster than light. We have proved that the assumed properties of these particles satisfy the fundamental laws of physics, which we have postulated. We recognized that the explanation of the Big Bang could be made from the standpoint of primary particles speed reduction during their mutual collision, during which the energy of the Big Bang would be released, simultaneously limiting the maximum speed of energy-mass transfer in our Universe to speed reached in that collision, c. The creation of other universes could be explained in a similar manner. Hence, the limitation to maximum speed of energy-mass transfer within them, as well as reached speed reduction of primary particles during big bangs in which those universes were created, would instead of c have various values k.

The Need for Development of a Primary Particle Hypothesis and Their Experimental Proof
It is clear that in this paper we have only made a logical assumption about some properties of primary particles. Thus, we believe their further study may lead to a major shift in physics, as well as our philosophical view of the world. Based on the described properties of primary particles, we expect their indirect experimental proof to be possible through successful explanation of the Big Bang, via further scientific work on the hypothesis of primary particles.

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