The Five Transformation Factors of the Universe

Subtitle: Beyond the Lorentz Factor

Introduction

“Nature is pleased with simplicity.”

Isaac Newton

There are five fundamental Euclidean transformations in the universe, and I want to show you in this article the five transformation factors of these five Euclidean transformations. In modern relativity, we have the Lorentz transformation factor for uniform frames in special relativity and we have the Einstein’s Non-Euclidean transformations for accelerated frames in general relativity.

This is the current state of affairs, but in post-modern physics, we have only Euclidean transformations for both uniform and accelerated frames, and I want to show you the transformation factors of these Euclidean transformations.

In this article, I want to show you the derivation of these five transformation factors which shall truly take us beyond the Lorentz factor.

Conceptual Framework

I will be deriving these five transformation factors following the conceptual framework of absolute relativity and not any of the physical interpretation of modern relativity theories. So, behind the mathematics that I shall be showing you, there are profound metaphysical conceptions that you must take note of.

In these derivations, I want you to have the following metaphysical conceptions:

  • Space is absolute space which flows with regards to inertia and not physical space which we quantify using meter sticks.
  • Time is absolute time which flows regardless of inertia and not physical time which we quantify using clocks.
  • Light is not speed c, rather it is the least resistance c to uniform motion and also the maximum resistance c to accelerated motion.
  • Gravity g is the least resistance to accelerated motion. 

These are the basic understanding that I want you to have, so that you would truly understand what I am about to do, though I will refer to the physical universe when necessary. I have giving in-depth description of space and time in my other articles and even in the book.

The Ponderable Universe

The laws of absolute relativity are divided as they apply in the ponderable universe of large non-charged bodies and as they apply in the electrical universe of small charged bodies. So, I want us to begin with the large ponderable universe.

Ponderable Bodies in Uniform Motion
Preliminary 1

The diagram below depicts the uniform time transformation of a body in uniform motion according to the subtle laws of absolute relativity.

uniform time and absolute relativity

Now, before we proceed to describe the relativistic effects of the uniform motion of ponderable (non-charged) bodies, I must set a necessary background. Just as for special relativity, we are also attempting to investigate the experiment which describes the to and fro movement of a ray of light from A to B and back to A again.

However, we are doing this differently from special relativity. How? In absolute relativity, and in this article, we shall study not the physical appearance of light and of this simple experiment performed in frame K, but rather the metaphysical nature of light as the least resistance to uniform motion.

Thus, in this article, I shall be showing you how to look at the absolute nature of light and also absolute uniform time and not relative time as measured by clocks, which has been the method of investigating relativity since its inception.

Furthermore, for frame K moving in uniform motion, it moves in uniform space and not just space, and as such it carries absolute uniform velocity v which is represented below as uniform space dx over uniform time dt’.

v=\frac{dx}{dt'}\;.\;\;\;\;.\;\;\;.\;\;\;.(1)

You must understand that according to the true laws of the universe, to move in uniform motion is simply to move in uniform space. So, frame K above carries a distinct absolute quantity called absolute uniform velocity v necessary to move in uniform space dx. 

Let’s now proceed to describe uniform time dilation for ponderable bodies moving in uniform motion.

Uniform Time Dilation

For this case of uniform motion, what we call the speed of light is the proportion of least resistance in uniform space. The above diagram shows that the experiment is been carried out in frame K which is in uniform motion and offers an underlying resistance in uniform space.

Listen, for both frame K and an absolute observer in frame K’, only their uniform time moves continuously since they are in inertial states. Now, for frame K, the total uniform time light offers the least resistance to uniform motion in uniform space is,

dt_{o}=\frac{2\:dD}{c}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(2)

The above satisfies that the event occurs at the seeming uniform rest frame of frame K, since light moves in uniform path dD which is a part of the entire uniform space dx in which frame K travels. Succinctly, frame K is at seeming uniform rest with the event.

And from equation (2)  dD2 is taken as,   

dD^{2}=\frac{{c^{2}\:dt_{o}}^{2}}{4}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(2a)

Now, in frame K’ which is at uniform rest in which zero resistance is offered to uniform motion, though its uniform time dt” ever moves, the event now takes uniform time dt to occur because the uniform space or path dL is not at rest with respect to the zero uniform space of frame K’.

Succinctly, frame K’ is in seeming uniform motion with respect to the event at frame K which is truly in uniform motion with respect to frame K’. The uniform time light now travels or offers the least resistance with respect to frame K’ becomes,

dt=\frac{2\:dL}{c}=\:.\;\;.\;\;\;.\;\;\;.\;(3)

And from equation (3) dL2  becomes,      

dL^{2}=\frac{c^{2}\:dt^{2}}{4}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(3a)

In this first case of ponderable bodies in uniform motion, you must understand that both frames are governed by the absolute principle of inertia which is associated with the absolute uniform velocity and which asserts that uniform rest and uniform motion are indistinguishable.

Now, taking that {dL}^{2}=[(\frac{1}{4}) v^{2}\:dt^{2}+d D^{2}], the equations (2a) and (3a) can be substituted for {dL}^{2} and dD^{2}, so we have that,

\frac{c^{2}\:dt^{2}}{4}=[(\frac{1}{4}) v^{2}\:dt^{2}+\frac{c^{2}\:dt_{o}\:^{2}}{4}]

c^{2}\:dt^{2}=4[(\frac{1}{4}) v^{2}\:dt^{2}+\frac{c^{2}\:dt_{o}\:^{2}}{4}]

c^{2}\:dt^{2}=v^{2}\:dt^{2}+c^{2}\:dt_{o}\:^{2}

Rearranging the terms above,

c^{2}\:dt^{2}-v^{2}\:dt^{2}=c^{2}\:dt_{o}\:^{2}

dt^{2}(c^{2}\:-v^{2})=c^{2}\:dt_{o}\:^{2}

dt^{2}=\frac{c^{2}\:dt_{o}^{2}}{(c^{2}\:-v^{2})}

Dividing the numerator and denominator of the factors on the RHS by c^{2}

dt^{2}=\frac{\frac{c^\;{2}}{c\;^{2}}\:dt_{o}^{2}}{(1\:-\frac{v^{2}}{c^{2}})

Let c2/c2 be equal to δ which is to be referred to as the uniform delta number, and which equals unity for the uniform motion of ponderable bodies because the inertia of light in uniform space is constant. The proportion of the delta number, whether it equals unity or not, is a very important and overlooked factor in modern relativity.

You would understand shortly how the proportion of the delta number underlies the relativistic principles of the motion of ponderable and electrical bodies. Now, taking the square roots of both sides of the equation above,

dt=\frac{\delta\:dt_{o}}{\sqrt{1\:-\frac{v^{2}}{c^{2}}}{}}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(4)

The above shows that dt is a greater proportion of uniform time than dto because the proportion of decreasing resistance v of frame K to uniform motion is always greater than the least resistance to uniform motion, which is light c.

It can otherwise be said that uniform time dilates because no inertial reference frame can offer equal or lesser resistance to uniform motion than light. Thus, the absolute uniform velocity of frame K cannot exceed light c which most maximizes uniform space.

The above is written in a contracted manner as,

dt=\alpha\.dt_{o}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(4a)

\alpha=\frac{\delta}{\sqrt{1\:-\frac{v^{2}}{c^{2}} represents what I call the inertial factor, and which applies to uniform time and space, and it is distinct from the Lorentz factor which applies to physical time and space. The inertial factor α is a more powerful and complete description of the relativistic transformation for uniformly moving bodies. It captures the true nature of light and its relationship with ponderable bodies in uniform motion.

Unlike the Lorentz factor which is indiscriminately applied to all kinds of bodies and to all forms of motion, the inertial factor has a qualitative essence in that it applies only to ponderable (non-charged) bodies in uniform motion.

payoneer mastercard

You would understand this new form of inertial transformation in this blog, Echa and Science, and as you proceed in your understanding of absolute relativity. Let’s now proceed to uniform space contraction.

Uniform Space Contraction 

The diagram below depicts the uniform space transformation of a ponderable body in uniform motion according to the absolute laws of absolute relativity. The diagram shows a ponderable body which moves uniformly from A and stopped at B

The space in between A and B is uniform space because, as I have told you, when a body moves in uniform motion it is simply moving in uniform space.

uniform space and absolute relativity

Now, there exists for the uniform motion of frame K’ the proportion of proper uniform space. This is the proportion of uniform space for frame K not only because frame K is at uniform rest, but also because there is a uniform time dt which is not the proper uniform time for frame K’, since events A and B occur at different uniform points.

The proportion of the proper uniform space dLcan be expressed as, 

dL_{o}=v\.dt\;.\;\;\;\;.\;\;\;.\;\;\;.\;(5)

The uniform space dL relative to frame K’ will not be the proper uniform space. This is because frame K’ is not at uniform rest with the uniform space and events A and B occur at the same uniform points.

The proportion of uniform space dL relative to frame K’ becomes,

dL=v\.dt_{o}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(6)

Dividing equation (6) by (5),

\frac{dL}{dL_{o}}=\frac{v\.dt_{o}}{v\.dt}

\frac{dL}{dL_{o}}=\frac{dt_{o}}{dt}

Substituting the transformation of uniform time shown in equation (4) for dt above, we would have the transformation of uniform space as, 

dL=\frac{\sqrt{1-\.\frac{v^{2}}{c^{2}}}}{\delta}dL_{o}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(7)

dL=\delta^{-1}\left ({\sqrt{1-\frac{v^2}{c^2}}} \right )^{-1}dL_{o} \;.\;\;\;\;.\;\;\;.\;\;\;.\;(7a)

The above equation (7) shows that dL is a lesser proportion of uniform space than dLo because the proportion of reduced resistance v of frame K’ to uniform space is always greater than the least resistance to uniform space c.

In other words,  uniform space contracts because the absolute uniform velocity of frame K’ cannot exceed light c which most maximizes uniform space. The uniform space contraction above could be abridged in relation to the inertial factor as,

dL=\alpha^{-1}dL_{o}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(7b)

Where \alpha^{-1}=\delta^{-1}\left ({\sqrt{1-\frac{v^2}{c^2}}} \right ).

Ponderable Bodies in Accelerated Motion

Let’s now investigate the gravi-electrodynamic principles that govern accelerating ponderable (non-charged) bodies. In modern physics, this would be the point we move over to general relativity in order to understand accelerated frames. But in this article, and in post-modern physics, we won’t be doing that any longer.

Rather we shall stick to the conceptual framework of absolute relativity, which now informs us that just as ponderable bodies in uniform motion move in uniform space with respect to the electromagnetic wave (light), in like manner do accelerated frames move in accelerated space with respect to gravi-electromagnetic wave.

This is the simple step missing in modern relativity and which has spun the current crisis in physics. So, we won’t be doing that. Also, know that the existence of accelerated space as the space for gravi-electromagnetic comes with accelerated time which captures the dynamics of gravi-electromagnetic motion.

Preliminary 2

The diagram below depicts the accelerated time transformation of a ponderable (non-charged) body in accelerated motion according to the subtle laws of absolute relativity.

accelerated time and absolute relativity

Now, before we proceed to describe the relativistic effects of the accelerated motion of ponderable (non-charged) bodies, I must also set the necessary background like I did above for uniformly moving ponderable bodies.

Also, just as for special relativity and above for uniformly moving ponderable bodies, we are also attempting to investigate the experiment which describes the to and fro movement of a ray of light from A to B and back to A again.

However, we are doing this differently from the case for uniform motion. How? We now know in absolute relativity and in this article, that for all ponderable bodies in accelerated motion, light is the maximum resistance to accelerated motion.

So, we shall study not the physical appearance of light and of this simple experiment performed in frame K, but rather the metaphysical nature of light as the maximum resistance to accelerated motion.

Thus, in this sub-section on accelerating ponderable bodies, I shall be showing you how to look at the absolute nature of light and absolute accelerated time, which is what really transforms alongside accelerated space for all accelerating ponderable bodies. 

Now, for frame K moving in accelerated motion, it moves in accelerated space and not (just space or) uniform space, and as such it carries absolute accelerated velocity va which is represented below as accelerated space Δx over uniform time dt’.

v_{a}=\frac{\Delta x}{dt'}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(8)

You must understand that according to the true laws of the universe, to move in accelerated motion is to move in accelerated space. So, frame K above carries a distinct absolute quantity called absolute accelerated velocity va which is qualitatively different from absolute uniform velocity v, and which is the absolute quantity necessary for a ponderable body to move in accelerated space.

Let’s now proceed to describe accelerated time dilation for ponderable bodies moving in accelerated motion.

Accelerated Time Dilation and Contraction

For this case of accelerating ponderable bodies, what appears as the speed of light in the physical, is the maximum resistance in accelerated space in the metaphysical.

The above diagram shows that the experiment is been carried out in frame which is in accelerated motion and offers resistance in accelerated space, and for both frame K and an observer in frame K’, their uniform and accelerated times move continuously since they are in non-inertial states.

Now, for frame K, Δto is the accelerated time light offers the maximum resistance in accelerated space ΔD to and fro its path from point A to B.

You must understand that the proportion of the maximum resistance in accelerated space and least resistance in uniform space are the same and are denoted simply as c. So, the proper accelerated time relates to the accelerated space in frame K as,

\Delta t_{o}=\frac{2\:\Delta D}{c}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(9)

The above satisfies that the event occurs at the seeming accelerated rest frame of K, since light moves in accelerated path ΔD which is a part of the entire accelerated space Δx in which frame K travels. Succinctly, frame K is at seeming accelerated rest with the event.

And from equation (10) ΔD2 is taken as,    

\Delta D^{2}=\frac{{c^{2}\:\Delta t_{o}}^{2}}{4}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(9a)

Since ponderable bodies move in uniform and accelerated spaces, it can be said that they satisfy the correspondence principle, which states that uniform rest and accelerated rest are indistinguishable.

Therefore, frame K’ can be taken to be at accelerated rest offering zero resistance in accelerated space, and as shown, its accelerated time ∆t” flows alongside its uniform time dt”.

payoneer

The event for frame K’ now takes accelerated time ∆t to occur, since the accelerated space or path ∆D is not at accelerated rest with respect to frame K’. Succinctly, frame K’ is seemingly in accelerated motion with respect to the event.

Since accelerated time flows regardless of inertia, the accelerated time light travels or offers the maximum resistance to accelerated motion in accelerated space ∆L with respect to frame K’ becomes,

\Delta t=\frac{2\:\Delta L}{c}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(10)

\Delta L^{2}=\frac{{c^{2}\:\Delta t}^{2}}{4}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(10a)

In this second case of accelerating ponderable bodies, both frames are experiencing the strong manifestation of the principle of non-inertia which is associated with the absolute acceleration and which causes accelerated rest and accelerated motion to be indistinguishable,

How the absolute acceleration comes into the transformations of accelerating ponderable bodies would become clear to you soon. This is important because I have told you in the preliminary one above that accelerating ponderable (non-charged) bodies carry only and distinctly absolute accelerated velocity va.

Now, while Δto is the accelerated time light offers the maximum resistance in accelerated space ΔD, by the orthogonality principle, it is also related to the superluminal motion of gravi-electromagnetic wave in accelerated space.

This orthogonality is represented by what would be referred to as the proper inertia or speed of gravi-electromagnetic wave  uo with respect to frame K as, 

u_{o}\:^{2}= c^{2}+ g^{2}\Delta {t_{o}\:^{2}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(11)

From which light c becomes,

c^{2}= u_{o}\:^{2}- g^{2}\Delta {t_{o}\:^{2}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(11a)

Substituting equation (11a) above for c2 into equation (9a) for ΔD2, we would, therefore, have that,

\Delta D^{2}=\frac{(u_{o}\:^{2}- g^{2}\Delta {t_{o}\:^{2})\:\Delta t_{o}}^{2}}{4}

\Delta D^{2}=\left ( \frac{1}{4}\right )u_{o}\:^{2}\Delta {t_{o}\:^{2}-\left ( \frac{1}{4}\right )g\:^{2}\Delta {t_{o}\:^{4}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(12)

And also for ΔL2

\Delta L^{2}=\frac{(u_{o}\:^{2}- g^{2}\Delta {t_{o}\:^{2})\:\Delta t^{2}}}{4}

\Delta L^{2}=\frac{u_{o}\:^{2}\Delta t^{2}- g^{2}\Delta t^{2} \Delta {t_{o}\:^{2}}}{4}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(13)

Taking that \Delta L^{2}=[(\frac{1}{4})v_{a}\:^{2}\:\Delta t^{2}+ \Delta D^{2}], the equations (12) and (13) can be substituted for \Delta D^{2} and \Delta L^{2}, so we have that,

\frac{u_{o}^{2}\Delt t^{2}-g^{2}\Delt t^{2}\Delt t_{o}^{2}}{4}=[(\frac{1}{4})v_{a}^{2}\Delt t^{2}+\left ( \frac{1}{4}\right )u_{o}^{2}\Delt t_{o}^{2}-\left ( \frac{1}{4}\right )g^{2}\Delt t_{o}^{4}]

Multiplying through by 4 we would have that,

u_{o}\:^{2}\Delt t^{2}-g^{2}\Delt t^{2}\Delt t_{o}^{2}=v_{a}\.^{2}\Delt t^{2}+u_{o}\:^{2}\Delt t_{o}^{2}-g^{2}\Delt t_{o}^{4}

Rearranging the above gives,

u_{o}\:^{2}\Delt t^{2}-v_{a}\.^{2}\Delt t^{2}=u_{o}\:^{2}\Delt t_{o}^{2}-g^{2}\Delt t_{o}^{4}+g^{2}\Delt t^{2}\Delt t_{o}^{2}

\Delta t^{2} (u_{o}\.^{2}-v_{a}\.^{2})=(u_{o}\.^{2}-g^{2}\Delt t_{o}^{2}+g^{2}\Delt t^{2})\Delt t_{o}^{2}

Since c= uo2 – g2Δt2

\Delta t^{2}( u_{o}\:^{2}- {v}_{a}\.^{2})=(c^{2}+ g^{2}\Delta t^{2}) \Delta t_{o}^{2}

The relation c+ g2Δt2 represents the relation of gravi-electromagnetic wave u’ with respect to frame K’ since accelerated time Δt is that for frame K’. This relation would be referred to as the transformed inertia or speed of gravi-electromagnetic wave or G-wave relative to frame K’

This shows that even if the inertia of light c and that of gravity g are the same for both frames, by the absolute relativistic operations of the universe for accelerated time, the inertia or speed gravi-electromagnetic wave cannot be the same for both frames.

Unlike uniform frames discussed above, where the inertia of light is the same for both frames, the non-equality of the inertia of gravi-electromagnetic wave has crucial implications which will be elucidated in this blog.

Proceeding with the deductions we, therefore, have that,

\Delta t^{2}(u_{o}\:^{2}- {v}_{a}\.^{2})=u'_\;\;^{2} \Delta t_{o}^{2}

From the above and as aforesaid, u’ would be referred to as the transformed inertia or speed of gravi-electromagnetic wave or G-wave relative to frame K’. Then,

\Delta t^{2}=\frac{u'_\;\;^{2} \Delta t_{o}^{2}}{(u_{o}\:^{2}- {v}_{a}\.^{2})}

Dividing the numerator and denominator of the factors on the right-hand side by uo2 gives,

\Delta t^{2}=\frac{\frac{u'_\;\;^{2}}{u_{o}\:^{2}} \Delta t_{o}^{2}}{\left (1- \frac{v_{a}\;^{2}}{u_{o}\:^{2}} \right )}

Let uo2/u’2 be equal to δo which is to be referred to as the accelerated delta number for accelerating ponderable bodies, and which importantly does not equal one or unity in all conditions, because the inertia of light of gravi-electromagnetic wave in accelerated space is not constant.

And taking the square root of both sides, 

\Delta t=\frac{\delta_{o} \Delta t_{o}}{\sqrt{1-\frac{v_{a}\;^{2}}{u_{o}\:^{2}}}

\Delta t=\frac{\delta_{o} \Delta t_{o}}{\sqrt{1- \left 1 \frac{v_{a}\;^{2}}{c_^{2}}+\frac{v_{a}\;^{2}}{g\:\:^{2}\Delta t_{o}\:^{2}}}}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(14)

The above equation (14) is a very crucial point you need to look at. The above shows us how absolute acceleration comes into the transformation of accelerating ponderable bodies even though they directly carry only absolute accelerated velocity va.

This is why I stated afore that frame K and frame K’ are experiencing the strong manifestation of the principle of non-inertia because of the absolute acceleration. The absolute acceleration is what causes accelerating ponderable bodies not to sense inertia while the absolute accelerated velocity is what causes them to sense inertia.

So, because the absolute accelerated velocity vover accelerated time Δto equals absolute acceleration a, we now have that, 

\Delta t=\frac{\delta_{o} \Delta t_{o}}{\sqrt{1- \left 1 \frac{v_{a}\;^{2}}{c_^{2}}+\frac{a\;^{2}}{g\:\:^{2}}}}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(14a)

The non-inertial factor γp for accelerating ponderable bodies becomes,

\gamma_{p}=\frac{\delta_{o}}{\sqrt{1- \left 1 \frac{v_{a}\;^{2}}{c_^{2}}+\frac{a\;^{2}}{g\:\:^{2}}}

The electromagnetic and gravitational components of the non-inertial factor above can be represented as,

\gamma_{p}=\frac{\delta_{o}}{\sqrt{1- \beta_{c}\:^{2}+\beta_{g}\:\:^{2}}}

Where βc2=va2/c2 is the electromagnetic component and βg2=a2/g is the gravitational component.

Now, one finds from accelerated delta number δo that the transformed accelerated time Δt is inseparably on both sides of the equation. This is because for all accelerating ponderable bodies, gravi-electromagnetic wave is inseparable from accelerated time. Thus, this importantly applies for both frames K and K’.

So, one is left to infer from equation (14a) that accelerated time Δt is a greater or lesser proportion of accelerated time than Δto depending on whether the electromagnetic component βc2 is lesser or greater than the gravitational component βg2This is the gravi-electrodynamic principle that applies exclusively to accelerated frames.

Representing the three conditions for the transformation of accelerated time and for the accelerated delta number δo which fundamentally arises because of the orthogonality principle and the gravi-electrodynamics of accelerated frames, we have that:

  1. Accelerated time Δt dilates and the accelerated delta number δo  is greater than 1 when βc2 > βg2
  2. Accelerated time Δt contracts and the accelerated delta number δo  is less than 1 when βc2 < βg2
  3. Accelerated time Δt  becomes stable or static and the accelerated delta number δo  is equal to 1 when βc2 = βg2

You should now understand that while uniform time can only dilate because of the principles of electrodynamics which apply for uniformly moving ponderable bodies, accelerated time can dilate, contract and be stable because of the principles of gravi-electrodynamics which apply for accelerating ponderable bodies.

Gravi-electrodynamics is the proper extension of electrodynamics and not general relativity. This is why we have not been able to unify physics so far.

Accelerated Space Contraction and Expansion

The diagram below depicts the accelerated space transformation of a ponderable body in accelerated motion according to the subtle laws of absolute relativity. The diagram shows a ponderable body which accelerates from A and stopped at B

The space in between A and B is accelerated space because, as I have told you, when a body moves in accelerated motion it is simply moving in accelerated space.

accelerated space and absolute relativity

Now, there exists for accelerated motion the proportion of proper accelerated space ΔLo. This is the proportion of accelerated space for frame K not only because frame K is at accelerated rest, but also because there is an accelerated time Δt which is not the proper accelerated time for frame K, since for frame K events A and B occur at different accelerated points.

So, the proportion of the proper accelerated space can be expressed as,

\Delta L_{o}=v_{a}\Delta t\;.\;\;\;\;.\;\;\;.\;\;\;.\;(15)

The accelerated space ΔL relative to frame K’ will not be the proper accelerated space. This is because frame K’  is not at accelerated rest with the accelerated space, and events A and B occur at the same accelerated points. The proportion of accelerated space relative to frame K’ becomes,

\Delta L=v_{a}\Delta t_{o}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(16)

Dividing equations (16) by (15) above results in

\frac{\Delta L}{\Delta L_{0}}=\frac{v_{a}\Delta t_{o}}{v_{a}\Delta t}

The accelerated velocity cancels, and the substitution of equation (14) for Δt above results in the transformation of accelerated space shown below:

\Delta L=\delta_{0}}^{-1} \left ( \sqrt{1-\left \frac\frac{v_{a}\;^{2}}{c\:^{2}}+ \right +\frac{a\;^{2}}{g\:^{2}}} \right ) \Delta L_{o}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(17)

\Delta L=\gamma_{p}}^{-1}\Delta L_{o}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(17a)

The above shows that ΔL can be a greater or lesser proportion of accelerated space than ΔLo depending on whether the electromagnetic component βc2 is lesser or greater than the gravitational component βg2This is the gravi-electrodynamic principle that applies exclusively to the transformation of accelerated space for accelerated frames.

Representing the three conditions for the transformation of accelerated space and for the accelerated delta number δo which fundamentally arises because of the orthogonality principle and the gravi-electrodynamics of accelerated frames, we have that:

  1. Accelerated space ΔL contracts and the accelerated delta number δo is greater than 1 when βc2 > βg2
  2. Accelerated space ΔL expands and the accelerated delta number δo is less than 1 when βc2 < βg2
  3. Accelerated space ΔL becomes stable or static and the accelerated delta number δo is equal to 1 when βc2 = βg2

The three relativistic transformations of accelerated space above are the converse of the three relativistic transformations of accelerated time afore shown to you.

The Electrical Universe

Let’s now describe or investigate the relativistic principles that apply in the atomic world. Today when we, physicists, want to investigate the atomic world we employ quantum mechanics. This is because we did not have any appropriate conceptual framework which describes the atomic world.

The continuous application of quantum mechanics when investigating the atomic world has caused us not to understand the atomic world and the unity of all things. Now, this predicament is over! We need not employ a hugely limited and flawed theory like quantum mechanics because we now have absolute relativity

A Galaxy

I want to show you how gravi-electrodynamics which is the appropriate framework for understanding the atomic world shows us the true nature of the relativistic principles that apply in the electrical universe.

Electrical Bodies in Accelerated Motion
Preliminary 3

Just as I have done for the ponderable universe, I want you to have the first understanding of the electrical world of atomic bodies. Now, unlike ponderable (non-charged) bodies that can move in uniform motion and accelerated motion, electrical bodies cannot. Electrical bodies can only move in accelerated motion.

They are bound to move ever and only in accelerated motion, because both light and gravity accelerate in the electrical universe. There is no way you can impact any form of motion on electrical bodies and all kinds of bodies beyond the true and absolute form of motion of light and gravity.

I will exclusively discuss this soon. 

Now, for frame K moving in accelerated motion in the electrical world, it moves in accelerated space and not (just space or) uniform space, and it carries the absolute acceleration a which is represented below as absolute accelerated velocity va over accelerated time Δt’.

a=\frac{v_{a}}{\Delta t'}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(18)

You must understand that according to the true laws of the universe, to move in accelerated motion is simply to move in accelerated space. So, frame K which is an electrical body carries a distinct absolute quantity called absolute acceleration which is qualitatively different from absolute uniform velocity v and absolute accelerated velocity va. And which is the absolute quantity necessary for an electrical body to move in accurate space.

Before I proceed, I must let you know that electrical bodies are electrical bodies not just because they have charge, but also because they alone can carry absolute acceleration. It is this understanding that is applied in this article and in the two proceeding diagrams to give you an in-depth understanding of the atomic world.

I think I would have to write a separate article on this particularly important distinction between charged and non-charged bodies in the future.  

Accelerated Time Dilation and Contraction

The diagram below shows the transformation of accelerated time for accelerating electrical bodies.

accelerated time and electrical bodies

To deduce the transformation of accelerated time for frame K in the electrical universe is very simple. All you need to know is that in the atomic world, light becomes the least vertical resistance to all accelerating electrical bodies. This absolute essence of light in the physical universe implies that light begins to accelerate in the atom.

So, from equation (14) below for the transformation of accelerated time in the ponderable universe, we can deduce the accelerated transformation for frame K and frame K’ in the electrical universe. 

\Delta t=\frac{\delta_{o} \Delta t_{o}}{\sqrt{1- \left 1 \frac{v_{a}\;^{2}}{c_^{2}}+\frac{v_{a}\;^{2}}{g\:\:^{2}\Delta t_{o}\:^{2}}}}

Now, I will substitute ac2Δto2 for c2 in the above, where ac is the acceleration of light. This method of substitution factor shows you that accelerated time is the crucial factor necessary for the change in the essence of light. Thus,

\Delta t=\frac{\delta_{o} \Delta t_{o}}{\sqrt{1- \left 1 \frac{v_{a}\;^{2}}{a_{c}\:^2\Delta t_{o}\:^{2}}+\frac{v_{a}\;^{2}}{g\:\:^{2}\Delta t_{o}\:^{2}}}}

Now, because of the introduction of the acceleration of light into the above expression, frame K and frame K’ now transform according to tau time which is the product of uniform and accelerated times and not just accelerated time like ponderable bodies.

The tau time transformation relative to frame K’ becomes, 

d\tau=\frac{\delta_{a} \:d \tau_{o}}{\sqrt{1- \left 1 \frac{a\;^{2}}{a_{c}\:^2}+\frac{a\;^{2}}{g\:\:^{2}}}}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(19)

Where dτ = dtΔt and dτo = dtΔto

One finds from above that the accelerated delta number δa for accelerating electrical bodies becomes unity because we have been able to separate the transformed accelerated time Δt from the right-hand side of the equation.

This is further made possible because light accelerates just like gravity for all accelerating electrical bodies. Thus, this importantly applies for both frames K and K’. Also, because of frame K and frame K’ transform according to absolute acceleration a, they never sense inertia. They are governed by the strong phase of the principle of non-inertia.

The non-inertial factor γe for accelerating electrical bodies becomes,

\gamma_{e}=\frac{\delta_{a}}{\sqrt{1- \left 1 \frac{a\;^{2}}{a_{c}\:^{2}}+\frac{a\;^{2}}{g\:\:^{2}}}

The electromagnetic and gravitational components of the non-inertial factor above can be represented as,

\gamma_{e}=\frac{\delta_{a}}{\sqrt{1- \beta_{a}\:^{2}+\beta_{g}\:\:^{2}}}

Where βa= a2/ac 2 is the electromagnetic component and βg= a2/g is the gravitational component.

So, from equation (19), tau time dτ is a greater or lesser proportion of tau time than o depending on whether the electromagnetic component βa2 is lesser or greater than the gravitational component βg2This is the gravi-electrodynamic principle that applies exclusively to accelerated frames.

Representing the three conditions for the transformation of tau time and for the accelerated delta number δa which fundamentally arises because of the orthogonality principle and the gravi-electrodynamics of accelerated frames, we have that:

  1. Tau time dτ dilates when βa2 > βg2
  2. Tau time contracts when βa2 < βg2
  3. Tau time becomes stable or static when βa2 = βg2

You can see from the above three conditions for the transformation of tau time in the atomic world that the accelerated delta number δa is not mentioned. This is because it equals unity for all three conditions above, unlike those for accelerating ponderable bodies.

This is a great realization: for just as the delta number δ for uniformly moving ponderable bodies equals unity, so does the accelerated delta number δfor accelerating electrical bodies equals unity. This is very fundamental, and I shall discuss this great realization in this article.

Furthermore, just as uniformly moving ponderable bodies possess only one absolute quantity, which is the absolute uniform velocity, so also do all accelerating electrical bodies possess only one absolute quantity, which is the absolute acceleration.

Unlike uniformly moving ponderable bodies and accelerating electrical bodies, accelerating ponderable bodies possess two absolute quantities which are the accelerated velocity and the absolute acceleration. It is very vital that you understand this.

Accelerated Space Contraction and Expansion

The diagram below depicts the accelerated space transformation of an electrical body in accelerated motion and carrying absolute acceleration a. The diagram shows an electrical body which accelerates from A and stopped at B

The space in between A and B is accelerated space, because, as I have told you, when a body moves in accelerated motion it is simply moving in accelerated space. This cannot be overemphasised. 

accelerated space and electrical bodies

The transformation of accelerated space between frame K and K’ is simply shown below:

\Delta L=\delta_{a}}^{-1} \left ( \sqrt{1-\left \frac\frac{a\:^{2}}{a_{c}\:^{2}}+ \right +\frac{a\;^{2}}{g\:^{2}}} \right ) \Delta L_{o}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(20)

\Delta L=\gamma_{e}}^{-1}\Delta L_{o}\;.\;\;\;\;.\;\;\;.\;\;\;.\;(20a)

The above shows that ΔL can be a greater or lesser proportion of accelerated space than ΔLo depending on whether the electromagnetic component βa2 is lesser or greater than the gravitational component βg2This is the gravi-electrodynamic principle that applies exclusively to accelerated frames.

Representing the three conditions for the transformation of accelerated space which also fundamentally arises because of the orthogonality principle and the gravi-electrodynamics of accelerated frames, we have that:

  1. Accelerated space ΔL contracts when βa2 > βg2
  2. Accelerated space ΔL expands when βa2 < βg2
  3. Accelerated space ΔL becomes stable or static when βa2 = βg2

The three relativistic transformations of accelerated space between frame K and frame K’ in the atomic world above is the converse of the three relativistic transformations of accelerated time for electrical bodies afore shown to you. 

So, in the absolute relativistic principles that apply for accelerating electrical bodies, they transform according to tau time and accelerated space, unlike ponderable bodies that transform according to accelerated time and accelerated space. You can look again at the accelerated motions of ponderable and electrical bodies above to fully understand this.

The Five Transformation Factors

The five transformation factors in the universe are divided into the three fundamental factors and the two derived transformation factors. The three transformation factors derived so far are the three fundamental factors in the universe.

The Three Fundamental Transformation Factors

The three fundamental transformation factors are the inertial factor α for uniformly moving ponderable bodies, the non-inertial factor γp for accelerating ponderable bodies and the non-inertial factor γe for accelerating electrical bodies. Let’s mathematical present them again:

\alpha=\frac{\delta}{\sqrt{1\:-\frac{v^{2}}{c^{2}}

Where δ = 1

\gamma_{p}=\frac{\delta_{o}}{\sqrt{1- \left 1 \frac{v_{a}\;^{2}}{c_^{2}}+\frac{a\;^{2}}{g\:\:^{2}}}

Where δo ≠n 1 (≠means does not necessarily equal unity)

\gamma_{e}=\frac{\delta_{a}}{\sqrt{1- \left 1 \frac{a\;^{2}}{a_{c}\:^{2}}+\frac{a\;^{2}}{g\:\:^{2}}}

Where δa = 1 

Notice that δ = δa

The Two Derived Transformation Factors

There are two derived transformation factors which proceed from the electromagnetic or luminal components of the non-inertial factor γp for accelerating ponderable bodies and from the non-inertial factor γe for accelerating electrical bodies.

They first derived transformation factor deduced from the non-inertial factor γp for accelerating ponderable bodies is written as,

\alpha_{p}=\frac{\delta_{c}}{\sqrt{1- \left 1 \frac{v_{a}\;^{2}}{c_^{2}}

Where δc = 1 

They second derived transformation factor deduced from the non-inertial factor γe for accelerating electrical bodies is written as,

\alpha_{e}=\frac{\delta_{a}}{\sqrt{1- \left 1 \frac{a\;^{2}}{a_{c}\:^{2}}

Where δa = 1

I represent the delta number for the derived inertial factor above to be the same as the one for the fundamental non-inertial factor because they both equal unity.

The Three Fundamental Transformation Factors and Fundamental Principles

The diagram below captures how the components of the three fundamental transformation factors are related to the principle of inertia and the principle of non-inertia.

the three transformation factors

The electromagnetic component of the inertial factor for uniformly moving ponderable bodies is connected to the (absolute) principle of inertia. However, accelerating ponderable bodies are governed by the weak phase of the principle of non-inertia.

As such, the electromagnetic component of their non-inertial factor is connected to the weak manifestation of the principle of non-inertia which causes them to sense inertia, while the gravitational component of their non-inertial factor is connected to the strong manifestation of the principle of non-inertia which causes them not to sense inertia.  

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Accelerating electrical bodies are governed by the strong phase of the principle of non-inertia, and as such, both the electromagnetic and gravitational components of their non-inertial factor are connected to the strong manifestation of the principle of non-inertia which causes them to never sense inertia.

I would like you to have this diagram in your memory, for they capture the qualitative nature of the universe as revealed in the inseparable connection between the components of the fundamental transformation factors and the absolute principles of the universe.

Summary

This article has shown you how to derive from first principles the five absolute transformation factors of the universe, and they are all Euclidean in nature. These five transformation factors are the respective bases of five transformations of which some have been shown to you in this blog.

These five transformation factors are made possible because of the two kinds of non-mechanical waves in the universe, which are the electromagnetic wave which governs inertial reference frames and the gravi-electromagnetic wave which governs non-inertial reference frames.

I want you to now know that the five transformation factors are the background of absolute relativity, and they constitute the new unified framework of post-modern physics.

Until next time.

I remain your man,

– M. V. Echa



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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!