Collisions: The Three Luminal and Relativistic Resolutions of Resultant Mass

Introduction

Author’s Note: The author uses the term “luminal” in the title of this post because there are superluminal phenomena within the framework of absolute relativity which for now or in this article is not our concern.

In this article, we will be looking within the framework of absolute relativity at the post-modern and relativistic interpretations of the resultant mass of colliding bodies. 

Within the framework of special relativity we have the modern interpretation of the collision of bodies, however, in modern physics relativity only describes the collision of bodies moving in uniform motion.

There is no description or adequate relativistic interpretation of the collision of accelerating bodies. This is a major loophole in our understanding of the universe. This is partly because we did not have a complete understanding of light.

I have exposed the complete three essences of light and the three luminal transformations exposed in the article would be used in this article to deduce the three luminal resolutions of resultant mass.

Light has different essences for bodies in uniform motion and for bodies in accelerated motion, and so following the fundamental changes in the essence of light we can derive the resultant mass of a system of colliding bodies whether they are in uniform motion or accelerated motion.

The approach I am about to show you is rooted in absolute science and not relative science. So, I want you to give me your undivided attention throughout the course of this article. Moreover, the mathematical analysis strictly follows the mathematical methods of special relativity. So, if you understand collisions according to special relativity you will understand this article.

Background 

Before we proceed to describe the different cases of colliding masses I would like to restate the three essences of light in the universe. Listen:

  1. For ponderable bodies in uniform motion, light c is the least resistance to uniform motion.
  2. For accelerating ponderable bodies, light c is the maximum resistance to accelerated motion.

The above outlines the two essences of light in the ponderable universe. It shows the nature of light for ponderable bodies in uniform motion and for bodies in accelerated motion. Also, I indicated light as c for both cases because light offers the same magnitude of inertia for both cases but with converse essences.

two planets on collision

Two colliding planets

This underlying equal magnitude of inertia of light for both uniformly moving and accelerating ponderable bodies manifests in our physical investigation as the speed of light c which equals 299792458 m / s.

So, because we have been looking at only the speed of light which is just a manifestation and not the true reality of light we have missed the other possibilities wrapped up in special relativity and especially in the interpretation of collisions.

For electrical (charged) bodies which can only experience accelerated motion:

      3. Light is the least vertical resistance to accelerated motion.

The above essence manifests as the acceleration of light ac in the atomic world, which we have also missed for so long because we did not know the true absolute nature of light in the atomic world.

Now, it is based on these three essences of light that we would derive the three qualitatively different mathematical expressions for the collision of bodies under all conditions. Be enlightened.

Let’s begin with ponderable bodies in uniform motion.

Uniform Collision: Ponderable Bodies in Uniform Motion

Uniform collision in the ponderable universe

Absolute Relativity: Uniform Collision in the Ponderable Universe

The first case of colliding masses shown above is that of ponderable (non-charged) bodies in uniform state of motion. I call the case of colliding bodies in uniform motion uniform collision

As shown above in A for uniform collision, two ponderable bodies of equal masses m collide in such a manner that one of the bodies is moving uniformly in uniform space with absolute uniform velocity vx and the other is at uniform rest which is indicated by the blue line which shows the flow of uniform time dt.

So, we have that the absolute 4-momentum vector for the uniformly moving ponderable body becomes,   

dp_{u}=(\alpha mc,\; \alpha mv_{x},\; 0, \;0)

Where \alpha=\frac{\delta}{\sqrt{1-\frac{v_{x}^{2}}{c_^2}}

Listen, for the absolute 4-momentum vector written above, light c is the least resistance to uniform motion and vx is absolute uniform velocity. Thus, in absolute relativity, the absolute 4-momentum equals mass times absolute uniform velocity.

Also, and since the inertial factor α equals one (\alpha\;=\;1) for the ponderable body at uniform rest the absolute 4-momentum vector for the ponderable body is represented as,  

dp_{r}=(mc,\; 0,\; 0, \;0)

As shown in B in the above diagram for uniform collision, when the uniformly moving ponderable body collides with the ponderable body at uniform rest the resulting system composed of the lumped masses of the two bodies now move in uniform motion with absolute uniform velocity v’x.

The total 4-momentum of the system before the uniform collision is gotten from,

dp\;=\;dp_{u}+dp_{r}\;=\;(|\alpha+1|mc,\; \alpha mv_{x},\; 0,\; 0)

After collision, the total 4-momentum of the system which moves in uniform space may be represented as,

dp_{R}=(\alpha' Mc,\; \alpha' Mv'_{x},\; 0, \;0)

Where the inertial factor \alpha'=\frac{\delta}{\sqrt{1-\frac{v'_{x}^{2}}{c_^2}}

Now the relativistic expression for the resultant mass of the uniformly moving system for uniform collision can be gotten from,

M^{2}\;c^{2}\:=\:|\alpha+1|^{2}\;m^{2}\;c^{2}- \alpha^{2}\;m^{2}\;{v_{x}}^{2}

Dividing through by c which is the least resistance to uniform motion which manifests as the speed of light we have that,

M^{2}\:=\:|\alpha+1|^{2}\;m^{2}\;-\; \alpha^{2}\;m^{2}\;\frac{{v_{x}}^{2}}{c^{2}

M^{2}\:=\:\|1+\;2\alpha+\;\alpha^{2}\;\(1-\frac{{v_{x}}^{2}}{c^{2}}\)\|\;m^{2}}

M^{2}\:=\:2\;(\alpha+1)\;m^{2}}

Thus, the resultant mass of the system of ponderable bodies for uniform collision becomes,

M\:=\:\sqrt{2\;(\alpha+1)}\;\;m \; \; \;.\;\;\;.\;\;\;.\;\;(1)

And just as special relativity teaches us, in absolute relativity the resultant mass of the system M is still greater than 2m and we know that 2m is actually the sum of their masses. This may be written mathematically as,

M\:\gt \;2\:m

The equation (1) above for the resultant mass of the system during uniform collision is mathematically similar to that deducible from special relativity, but in the case above for absolute relativity, we are looking at the resultant mass of the system or relativity through the lens of absolute space and time.

Special relativity looks at the resultant mass of the system through the lens of relative physical space and time, and herein lies the difference between the resultant mass of the system in absolute relativity and that in special relativity. Please understand this.

In special relativity, the resultant mass of the system is of the form,

M\:=\:\sqrt{2\;(\gamma+1)}\;\:m

Where γ is the Lorentz factor represented as,

\gamma=\frac{1}{\sqrt{1-\frac{{v*_{}{x}}^{2}}{c^2}

So, in the expression for the resultant mass according to special relativity light is represented as a speed limit which is 299792458 m/s but in absolute relativity, light is represented as a limit of inertia. This great insight or approach enables us to model accelerated frame in the manner in which we have modeled uniform frames above.

Let’s proceed to the collision of accelerating ponderable (non-charged) bodies so that you can see the indispensable option to understanding relativity and the cosmos that absolute relativity proffers.

Accelerated Collision: Ponderable Bodies in Accelerated Motion

Accelerated collision in the ponderable universe

Absolute Relativity: Accelerated Collision in the Ponderable Universe

The second case of colliding masses depicted above is that of ponderable (non-charged) bodies in accelerated state of motion. I call the case of colliding bodies in accelerated motion accelerated collision.

As shown above in A for accelerated collision, two ponderable bodies of equal masses m collide in such a manner that one of the bodies is accelerating in accelerated space with absolute accelerated velocity va and the other is at uniform rest which is indicated by the flow of uniform time dt.

In this case of accelerated collision, the body at rest can be taken to be at accelerated rest, remember the correspondence principle.

So, we have that the 5-momentum vector for the accelerating ponderable body becomes,   

\Delta p_{a}=(\alpha_{{p}} mc,\; \alpha_{{p}} \:mv_{a},\; 0, \;0)

Where the luminal non-inertial factor for ponderable (non-charged) bodies  \alpha_{{p}}=\frac{\delta_{c}}{\sqrt{1-\frac{v_{a}^{2}}{c_^2}}

Listen, for the absolute 5-momentum vector written above, light c is the maximum resistance to accelerated motion and va is absolute accelerated velocity. Thus, in absolute relativity, the absolute 5-momentum equals mass times absolute accelerated velocity.

Also, and since the luminal non-inertial factor αp equals one (\alpha_{{p}}\;=\;1) for the ponderable body at uniform rest the absolute 5-momentum vector for the ponderable body is represented as, 

\Delta p_{{r}}=(mc,\; 0,\; 0, \;0)

As shown in B in the diagram above for accelerated collision, when the accelerating ponderable body collides with the ponderable body at uniform rest, the resulting system composed of the lumped masses of the two bodies now move in accelerated motion with absolute accelerated velocity v’a.

The total 5-momentum of the system before the uniform collision is gotten from,

\Delta p\;=\;\Delta p_{a}+\Delta p_{r}\;=\;(|\alpha_{{p}}+1|mc,\; \alpha_{{p}} mv_{a},\; 0,\; 0)

After collision, the total 5-momentum of the system which moves in accelerated space may be represented as,

\Delta p_{R}=(\alpha'_{{p}}\:Mc,\; \alpha'_{{p}} \:Mv'_{a},\; 0, \;0)

Where \alpha'_{{p}}=\frac{\delta_{c}}{\sqrt{1-\frac{v'_{a}^{2}}{c_^2}}

Now the relativistic expression for the resultant mass of the accelerating system for accelerated collision can be gotten from,

M^{2}\;c^{2}\:=|\alpha_{{p}}+1|^{2}\;m^{2}\;c^{2}- \alpha_{{p}}^{2}\;m^{2}\;{v_{a}}^{2}

Dividing through by c which is the maximum resistance to accelerated motion which also manifests as the speed of light we have that,

M^{2}\:=\:|\alpha_{{p}}+1|^{2}\;m^{2}\;-\; \alpha_{{p}}^{2}\;m^{2}\;\frac{{v_{a}}^{2}}{c^{2}

M^{2}\:=\:\|1+\;2\alpha_{{p}}+\;\alpha_{{p}}^{2}\;\(1-\frac{{v_{a}}^{2}}{c^{2}}\)\|\;m^{2}}

M^{2}\:=\:2\;(\alpha_{{p}}+1)\;m^{2}}

Thus, the resultant mass of the system of ponderable bodies for accelerated collision becomes,

M\:=\:\sqrt{2\;(\alpha_{{p}}+1)}\;\;m \; \; \;.\;\;\;.\;\;\;.\;\;(2)

And just as special relativity teaches us the resultant mass of the system of two accelerating ponderable bodies M is greater than 2m which may be written mathematically as,

M\:\gt \;2\:m

The equation (2) above for the resultant mass of the system during accelerated collision is mathematically similar to that deducible above for the uniform collision of ponderable bodies, but in the case above for absolute relativity, we are looking at the resultant mass of the system through a different essence of light.

payoneer

For ponderable bodies in accelerated motion light becomes the maximum resistance to accelerated motion and the absolute accelerated velocity becomes the physical quantity associated with ponderable bodies in accelerated motion as they attempt to offer greater resistance to accelerated motion than light. Let this insight enlighten you.

So, in accelerated collision of ponderable bodies, we are still within the confines of the mathematical framework of special relativity, we only have to understand the underlying change in the essence of light.

Accelerated Collision: Electrical Bodies in Accelerated Motion

Accelerated collision in the electrical universe

Absolute Relativity: Accelerated Collision in the Electrical Universe

The above diagram is that for the accelerated collision of electrical bodies, and you can see that it is distinct or different from the other two collisions in the ponderable universe. 

As shown in A, two electrical bodies of equal masses m collide in such a manner that one of the bodies is accelerating in accelerated space with absolute acceleration ax and the other is at accelerated rest which is indicated by the blue and green lines which respectively shows the flow of uniform time dt and accelerated time Δt.

So, we have that the force vector for the accelerating electrical body becomes,   

\Delta F_{a}=(\alpha_{{e}}ma_{{c}},\;\alpha_{{e}}\:ma_{x},\;0,\;0)

Where  \alpha_{{e}}=\frac{\delta_{a}}{\sqrt{1-\frac{a_{x}^{2}}{a_{}_{{c}}^2}}

Listen, for the absolute force vector written above, light ac is the least vertical resistance to accelerated motion and according to relative science, this implies the acceleration of light and ax is absolute acceleration. Thus, in absolute relativity, the absolute force equals mass times absolute acceleration.

Author’s Note: The author of this article would elucidate in the nearest future the distinctions between Newtonian force and absolute force. However, you can know today about these distinctions in The Theory of the Universe which is the source of the author’s knowledge. Also, in this article, we are assuming the uniform acceleration of light ac.

And the force vector for the electrical body at accelerated rest is represented as, 

\Delta F_{r}=(ma_{{c}},\; 0,\; 0, \;0)

The above follows for the electrical body at accelerated rest since \alpha_{{e}}\;=\;1 for an electrical body at accelerated rest.

As shown in B in the diagram above for accelerated collision of two electrical bodies, when the accelerating electrical body collides with the electrical body at accelerated rest, the resulting system composed of the lumped masses of the two bodies now move in accelerated motion with absolute acceleration a’x.

The total force of the system before the accelerated collision is gotten from,

\Delta F\;=\;\Delta F_{a}+\Delta F_{r}\;=\;(|\alpha_{{e}}+1|ma_{{c}},\; \alpha_{{e}} ma_{x},\; 0,\; 0)

After collision, the total force of the system which moves in accelerated space may be represented as,

\Delta F_{R}=(\alpha'_{{e}} Ma_{{c}},\; \alpha'_{{e}} Ma'_{x},\; 0, \;0)

Where the luminal non-inertial factor for charged bodies \alpha'_{e}=\frac{\delta_{a}}{\sqrt{1-\frac{a'_{x}^{2}}{a_{}_{{c}}^2}}

Now the relativistic expression for the resultant mass of the accelerating system for accelerated collision can be gotten from,

M^{2}\;a_{{c}}}^{2}\:=\:|\alpha_{{e}}+1|^{2}\;m^{2}\;a_{{c}}^{2}- \alpha_{{e}}^{2}\;m^{2}\;{a_{x}}^{2}

Dividing through by ac which is the least vertical resistance to accelerated motion which manifests as the acceleration of light we have that,

M^{2}\:=\:|\alpha_{{e}}+1|^{2}\;m^{2}\;-\; \alpha_{{e}}^{2}\;m^{2}\;\frac{{a_{x}}^{2}}{a_{{c}}^{2}

M^{2}\:=\:\|1+\;2\alpha_{{e}}+\;\alpha_{{e}}^{2}\;\(1-\frac{{a_{x}}^{2}}{a_{{c}}^{2}}\)\|\;m^{2}

M^{2}\:=\:2\;(\alpha_{{e}}+1)\;m^{2}}

Thus, the resultant mass of the system of electrical (charged) bodies for accelerated collision becomes,

M\:=\:\sqrt{2\;(\alpha_{{e}}+1)}\;\;m \; \; \;.\;\;\;.\;\;\;.\;\;(3)

And similar to special relativity, the resultant mass of the system of electrical bodies M is greater than 2m which may be written mathematically as,

M\:\gt \;2\:m

In the equation (3) you begin to see the harmony of the universe I have been telling you is founded on Euclidean geometry. We have applied the same mathematical and conceptual framework to describe ponderable or macro bodies and the collision of electrical bodies or particles.

The unified description of the universe lies in the mathematical framework of special relativity. The expression for the resultant mass of a system of colliding bodies for the luminal transformations, whether in the atom or outside the atomic world is the same.   

The above mathematical expression above for the collision of two electrical or charged bodies is very important in particle physics and especially in our study of the motion of particles in our accelerators. 

accelerator

Inside of a Particle Accelerator

As we proceed deeper into the operations of the atomic world in this blog you would come to understand the true operational principles of our particle accelerators which we use to collide energetic particles or electrical bodies.

Summary

This article exposes the three mathematical representations of resultant mass according to the subtle principles of absolute relativity. In special relativity, we have only one of such mathematical representations. This is because of our incomplete understanding of light. We wrongly think according to classical and modern physics that light has a single essence as a speeding wave.

In post-modern physics, we come to realize the triune nature of light and due to this triune nature of light, we come to have three relativistic and mathematical representations that fit the three conceivable analysis of collision shown in this article.

Due to the non-consistency of the essence of light, you would realize that in this article we dealt with the uniform collision of ponderable bodies applying the absolute 4-momentum vector and for the accelerated collision of ponderable bodies we applied the absolute 5-momentum vector, and for the accelerated collision of electrical bodies, we applied the absolute force vector.

the theory of the universe

More so, in this article, I have mostly let the maths speak for itself. If you look closely at the similarity of the three deduced equations you will begin to have a grasp of the unity of the universe. The universe, my friend, is amazingly simple when we ascend to absolute metaphysical science.

And contrary to what you may have thought absolute metaphysical science is also mathematical just like relative science, we only need to alter qualitatively our understanding of the objects of our study. To put it better, we only need to understand the metaphysical nature of reality. Mathematics cuts across both absolute metaphysical science and relative physical science.

We have applied this great truth in this article to mathematically elucidate the three possible outcomes for the three different conceivable collisions of bodies.

Don’t grope in the dark.

– M. V. Echa

Author’s reference: The Theory of the Universe: Absolute Relativity by M. V. Echa.



M. V. Echa

M. V. Echa

My message is the universe, my truth is the universe, and this blog contains all you need to know about the universe, from the true nature of reality to the long-sought unity of the cosmos — which is the big picture!