Table of Contents
A Critical Subject: The Origin of Our Notion of the Square of Time
Time and the Principle of Universal Equivalence
I have discussed the universal equivalence in some of my articles but I have cautiously refrained from talking about time and how it is related to the universal equivalence principle just like force and mass.
So, now that I have decided to do so in this article, I really hope that it imprints on you the same measure of caution I have when dealing with time and the principle of universal equivalence.
Why do I have this caution? I have this caution, because unlike force and mass, time is most transcendent. It is not as concrete as the other two even though its persistent existence cannot be denied.
I have shown you the universal equivalence equations for force and mass, and just as the universal equivalence principle applies to both of them, so it also applies to time. But before I show you how it mathematically applies to time, I want to first of all show you something about the origin of the square of time t2 in physics.
This will further help you understand my caution when it comes to the application of the universal equivalence principle to time.
Since classical physics, scientists have realized the unique quantity called acceleration, and that it can only be expressed in inverse relation to the of square of time, which is simply written as t2.
Why this is so has been unknown. Why can’t we just take our normal measurement of time t? I want to explain this mystery to you. You see, what we call acceleration in standard physics is what I call relative acceleration. And in this blog relative acceleration is denoted as a*, especially when I am discussing relative and absolute science in an article.
This relative acceleration is presented mathematically as space x over the square of time t,
The above kind of acceleration emerges from the wrong conception in classical and modern physics that there is only one form of space and time and also three states of motion in the universe.
However, there is another kind of acceleration which I call absolute acceleration, and I usually denote it as “a” without any asterisk. The absolute acceleration emerges from the right conception in post-modern physics that there exist two forms of space and time and four states of motion in the universe.
So, one of the special things about absolute acceleration a and what distinguishes it from relative acceleration a* is that it is inversely related to the product of the two forms of time. Absolute acceleration is mathematically expressed as accelerated space Δx over the product of uniform time dt and accelerated time Δt,
I want you to look closely at both equations for relative and absolute accelerations. I want you to notice their mathematical or quantitative similarities and their qualitative differences.
Following their mathematical similarities both are in m/s2, but following their qualitative differences relative acceleration a* is related to one form of time t while absolute acceleration a is related to the two forms of time dt and Δt.
In absolute science the product of the two forms of time is represented as tau time dτ and the above equation (2) in contracted form is written as,
We can have any variation of tau time so long as the letter tau is preserved in them. I want you to look at absolute acceleration until you also realize where our notion of acceleration as being related to the square of time comes from.
Our notion of the square of time comes from absolute science which shows us the true metaphysical or absolute form of acceleration. You really must understand this. It is very important if you must also comprehend my cautious application of the universal equivalence principle to time.
So, whenever in relative science we encounter the square of time, we must realize that it is as a result of the product of the two forms of time of absolute science. This is why I sometimes tell you that the physical quantities of relative science are the shadows of the metaphysical quantities of absolute science.
Your understanding of the universe will be lacking unless you come to understand the subtle relationships between the physical quantities of relative science and the metaphysical quantities of absolute science.
Also, you must understand that the distinction between the physical quantities and the metaphysical quantities is that while the physical quantities are solely quantitative the metaphysical quantities are both quantitative and qualitative. I make no other suppositions for the metaphysical quantities.
After realizing that our notion of the square of time arises from the product of the two forms of time in the universe then we can proceed to mathematically represent the universal equivalence equations for time as,
The above equation can come in different variations depending on what aspect of relative science or absolute science you want to emphasize. However, in the above case, we have the simplest mathematical representation of time and the universal equivalence principle according to relative science.
In the simplest form of the equation above, the crucial factors have been stripped of their qualitative essence and only their quantitative essence remains. The above is as the universal equivalence principle will appear in relative science.
However, you must remember that without absolute science which upholds the balance of both the quantitative and qualitative essences of the universe the above insight about the principle of universal equivalence will not be known in the first place. This is basically what I call the new scientific method.
Now, the square of time in the above universal equivalence equation for time stems from the product of the two forms of time. This should be duly noted. So, we will simply apply the universal equivalence equation for time just as I have done for force and mass in the article below:
It is important that you read the article above so that you will understand how the universal equivalence principle is applied in this blog and in post-modern physics, as I don’t so much feel the need to go over them again in this article. I will explain time and the universal equivalence principle as a continuation of the above article.
The above article will show you how the principle of universal equivalence which states that the weak and strong equivalence principles are equal arises because no accelerating body can accelerate greater than the acceleration of gravity.
Just as we have for force rest force Fr and inertial force Fi , and for mass, rest mass Mr and inertial mass Mi, we also have for time, rest period Tr and inertial period Ti. In the equation (3) above, the rest period Tr is related to the components of rest gravity gr, while inertial period Ti is related to the components of acceleration a.
While you are familiar with rest mass and inertial mass and with rest force and inertial force from classical physics, you may never have heard of rest period and inertial period before. This should be an entirely new concept to you.
This is also why I have set aside this article to talk about time and the principle of universal equivalence, and to make sure that I show you all the subtleties involved. I want you to now realize that our notion of rest force and mass and also inertial force and mass are because of the formerly hidden principle of universal equivalence.
We just didn’t know these things until now. But then I want you to have this basic understanding of the rest and inertial properties of the above quantities, which is that rest properties are simply related to a rest frame or rest gravity gr, while the inertial properties are simply related to an accelerating frame or to acceleration a. Nothing more, nothing less.
Let’s look again at the motion of the Moon (which is arbitrarily chosen as it can be any other revolving body) around the Earth. The rest period Tr applies to a frame at rest on the Earth surface while the inertial period Ti applies to the Moon revolving around the Earth.
And just as for the cases of force and mass, the rest period Tr and inertial period Ti only differs when the moon deviates from free fall. Let me just write down the three equations for the principle of universal equivalence,
During free fall we have the following three very important conditions:
You must have the above three conditions at the back of your mind when analysing or studying free fall. Free fall is a special condition where the rest geomephysical properties and inertial geomephysical properties of interacting bodies under investigation are equal. Free fall is an equilibrium state.
However, when the Moon deviates from free fall, we have the following three conditions:
So, the realization that the rest period Tr is not equal to the inertial period Ti when the Moon deviates from free fall is not an independent realization. It follows with the new facts that the Moon revolves around the inertial mass Mi of the Earth and not the rest mass of the Earth Mr, and also that the Moon experiences the inertial force Fi due to the inertial mass of the Earth Mi and not the rest force Fr due to the rest mass of the Earth Mr.
Let’s begin with the Moon’s frame, choosing arbitrary values for the acceleration of the Moon and its radial distance away from the Earth. If the moon were to non-gravitationally accelerate at 30 m/s2 and at a radial distance of 4 × 109 m, then the inertial period of the Moon becomes,
The observer must realize that this inertial period Ti is caused by the inertial mass of the Earth which produces the acceleration of the Moon. This is the basic understanding of inertia interaction.
The observer must realize that the Moon is not moving across the rest mass of the Earth which he is experiencing but across the inertial mass of the Earth which he is not experiencing. The fundamental dissociation in the experience of the Earth by the observer on Earth and by the Moon must be duly noted.
So, the period above is valid with respect to the frame of the Moon which the observer is trying to take into account. The observer being at rest on the Earth surface experiences the rest period which is related to rest gravity gr. This is the description of rest interaction in relation to time.
Rest gravity gr is related to the constant rest mass of the Earth Mr and its value around the region of the Moon at the radial distance of 4 × 109 m. At this radial distance rest gravity gr is,
From the above value of rest gravity at the radial distance of 4 × 109 m we may calculate the rest period of the Moon, which as you may already know is not related to the acceleration a of the Moon. Now,
Substituting 4 × 109 m for R and 2.49 × 10-5 m/s2 for gr, we will have that,
I want you to learn now how Newton’s description of gravity is modified and advanced in post-modern physics. The above is the rest period of the Moon, but the Moon does not experience it because it cannot accelerate greater than the acceleration of gravity.
The Moon experiences inertial period. However, listen, it is only when the Moon undergoes free fall that its inertial period Ti will be equal to the rest period Tr, both calculated at the radial distance of 4 × 109 m above.
This is because during free fall, the proportion of acceleration a would equal the proportion of rest gravity gr. I have talked about this in Absolute Relativity and in my other articles on gravity and the principle of universal equivalence.
(Please read them. They will help you to completely understand this new principle, especially my e-book. My ebook on Absolute Relativity will expose to you how the principle of universal equivalence emerges from the new conceptual framework of gravi-electrodynamics.)
Free fall is the only time the conditions of rest interactions and those for inertial interactions are equal. Furthermore, the observer at rest on the Earth surface who has no acceleration experiences rest gravity gr which is related to the rest mass Mr of the Earth and his radial distance from the Earth’s center.
Any body at rest experiences rest gravity and rest interaction, while any body in accelerated motion experiences acceleration and inertial interaction. An observer at rest on the Earth must know that just as the experiences of force and mass between him and the Moon are different, so also is the experience of time.
Inertial interaction was applied in the article below in order to resolve the flyby anomaly. This article will further assist you to understand one of the practical implications of the principle of universal equivalence.
What is this dissociation? The observer on Earth experiences the rest geomephysical properties of the Earth while the moon experiences the inertial geomephysical properties of the Earth. Please remember this.
Why are all these things happening? Why do we have the principle of universal equivalence? I have said it often times, it is because no accelerating body can accelerate greater than the acceleration of gravity, recognizing that gravity is just a component of gravi-electromagnetic wave.
I want you to understand that the reason why the results of the universal equivalence principle are unobservable is that gravity is a component of the gravi-electromagnetic wave which transcends the speed or the inertia of light.
All these effects are not really communicated by gravity but by gravi-electromagnetic wave. Now, when the Moon deviates from free fall, an observer at rest on the Earth surface can still apply the inverse square law to the non-gravitational motion of the Moon.
My Personal Criticism of the Extension of the Universal Equivalence Principle to Time
Remember I have told you that I am very cautious about how I apply the universal equivalence principle to time, and I sometimes wish that I can avoid it. One of the crucial reasons is a practical criticism.
I want to proceed with it and I hope that you may have a better understanding of the universal equivalence principle and also share your own ideas with me. What is this practical criticism?
While the universal equivalence principle emerges from absolute science, there is still need to relate it to relative science as I have so far done. The universal equivalence equations for time is different from the other two for force and mass because time is on both sides of the equations.
Let’s look at the equation below which shows the relationship between orbital period and the motion of the Moon,
An observer who wants to practically apply the above equation will use the time in his frame to check the acceleration a of the Moon and by extension determines the inertial orbital period Ti of the Moon.
One of the implications of the universal equivalence principle is that the observer on the Earth surface and the Moon are experiencing rest interaction and inertial interaction respectively. So, the observer’s time does not apply to the Moon.
If he uses his clock or time to determine the acceleration a of the Moon, he becomes further tempted to use his time to directly determine the orbital period of the Moon and the time he measures using his clock and directly observing the motion of the Moon may differ from that deduced from the equation for the inertial period Ti above.
This possibility seems to question how I apply the universal equivalence principle in relative science. I am unperturbed by this and I am open to further criticism of this method, and I will also like to know what you think about it.
The principle of universal equivalence is fundamentally an a priori principle, so when we bring it into the domain of a posteriori science we have to compromise in order to achieve an approximation of it that is close to reality.
The observer at rest on the Earth’s surface should not be tempted to apply his clock to the inertial period Ti of the Moon. Just as he applies the inertial force and inertial mass that he does not experience to the Moon, so also should he apply the inertial period Ti to the Moon.
He should act as though he cannot experience or determine directly the inertial period of the Moon just as he cannot experience the inertial force and mass of the Earth. He should view the inertial period Ti as some sort of Earth inertial time just like Earth’s inertial force Fi and Earth’s inertial mass Mi.
His clock or time should only be applied in determining or estimating only the acceleration a of the Moon, from this he can proceed to determine using the universal equivalence equations the inertial force, inertial mass and inertial period of the Earth that the Moon experiences.
The principle of universal equivalence cannot be exhausted in an article, for now, I think as we progress in its application, both theoretically and practically, we may arrive at a different and more preferable method of applying this principle.
Volume and the Principle of Universal Equivalence
Now, the universal equivalence principle extends even to the radius and the volume of the Earth. The entire geomephysical properties of the Earth is not constant relative to the Moon.
The rest radius and volume of the Earth is constant for an observer at rest on the Earth surface, but for the Moon, the inertial radius and volume of the Earth can vary if the Moon deviates from free fall.
However, one must realize that for both the rest interaction and inertial interaction, the density of the Earth is constant. I have concluded that the variations in the inertial mass and inertial volume of the Earth relative to the Moon occurs in such a manner that the inertial density ρi of the Earth always equals the rest density ρr of the Earth.
This may be written mathematically as,
In most cases, I still represent the density of the Earth as just ρ without any subscript. The figure below simply shows an observer on the Earth surface experiencing the rest volume Vr of the Earth, and which is the generally accepted volume of the Earth.
The rest volume Vr of the Earth above can be gotten from,
Where Mr equals 5.972 × 1024 Kg and ρ equals 5515.3 Kg/m3
The above is the exact value of the Earth’s volume experienced by an observer at rest on the Earth’s surface. It conforms to the generally accepted value of the volume of the Earth, and should in light of the universal equivalence principle be called the rest volume of the Earth.
Now, for the Moon which had been assumed to have deviated from free fall with an acceleration of 30 m/s2 and at a radial distance of 4 × 109 m, the inertial mass Mi of the Earth becomes,
So, from the value for inertial mass Mi above, the inertial volume Vi of the Earth relative to the Moon becomes,
For the chosen arbitrary values of the acceleration of the Moon and its radial distance from the Earth, the inertial volume Vi of the Earth relative to the Moon is greater than the rest volume Vr of the Earth relative to the observer.
The figure below captures the above result for inertial volume, and it shows that inertial volume is greater than rest volume. Altering the acceleration and radial distance between the Moon and the Earth can produce a case in which inertial volume is lesser than rest volume. So, in essence, the inertial geomephysical properties of bodies are dynamical.
The universal equivalence principle brings to your understanding the new fact that while the rest geomephysical properties of bodies such as the Earth are fundamentally constant, the inertial geomephysical properties of bodies such as the Earth are not fundamentally constant.
It is this variation in the inertial geomephysical properties of bodies that reveal to us how the continuum produces accelerated motion by inertial interaction. This interaction between accelerating bodies and the inertial geomephysical properties of other bodies is what is called inertial interaction.
In your keen mind, you may be wondering how all these variations are possible and also unobservable. Firstly I have mentioned that these variations are superluminal events governed by the gravi-electromagnetic wave.
In my future articles I will be showing you more about gravi-electrodynamics, and by then you will completely understand the new fact that the principle of universal equivalence arises because no accelerating body can travel faster than gravi-electromagnetic wave.
The gravi-electromagnetic wave and not light (or the electromagnetic wave) is the limit of motion for all accelerated frames. The electromagnetic wave is only the limit of motion for uniform frames.
The wave nature of the universe is very real. And as I have told you, the universe is a standing gravi-electromagnetic field. What we call matter are simply nodal points in the sea of gravi-electromagnetic wave.
Having this understanding of the inseparable connection between matter and gravi-electromagnetic wave, you will realize how possible it is for gravi-electromagnetic to alter the geomephysical properties of bodies.
I often tell you that the gravi-electromagnetic wave is the wave of creation. It is different from gravitational waves predicted by general relativity which is assumed to be produced by intense conditions that are far from our common experience.
The effects of gravi-electromagnetic wave, though for now are unobservable, come home to us. They are real experiences we have every day. Whenever you accelerate in your car or through any other means, you are interacting with the inertial geomephysical properties of the Earth.
We are all living in a real waving field. The universal equivalence principle is strongly associated with the wave nature of the universe without which its proposed dynamical description of matter will be impossible. Also, the universal equivalence principle applies the same even inside the atom.
I want us to now become serious about harnessing the energy potentials of gravi-electromagnetic wave. The gravi-electromagnetic wave is a non-mechanical wave just like light, and I think that just like light, it is also harnessable.
We just haven’t known about the gravi-electromagnetic wave even though the mysteries of dark energy and dark matter were pointing to its existence. All these unaccountable excess energies in the universe all inform us that there is another non-mechanical wave in the universe besides light.
So, now we know about this and what the wave really is, let’s proceed to harness it. In one of my future articles, I will inform you about one of the important consequences of the universal equivalence principle for practical purposes.
Also, the principle of universal equivalence is the principle now required after the lately proposed principle of strong equivalence by Albert Einstein in 1915. The principle of universal equivalence is a fundamental principle in the new theory of gravity required to resolve the already growing cosmological mysteries.
I want you to read all my articles on the principle of universal equivalence so that you will get a complete understanding of what I am showing you in this article. In the universe, there is so much going on right under our noses.
What we need is a kind of science that establishes the method by which we can truly investigate these subtleties. All that I have shown you in this article and in this blog comes from absolute science which is the science that unravels to you the subtleties of the universe that can hardly be directly observed.
The principle of universal equivalence is a very subtle principle, and I am so glad that it has come down to us in this new era of physics. It completes our task to understand the existence of the weak and strong equivalence principles.
The universal equivalence principle proves that these two principles first distinguished by Einstein really exist. The principle of universal equivalence changes forever how we view and understand force, mass, time, volume and other geomephysical properties of bodies.
Until next time.
Always remember that WEP = SEP.
– M. V. Echa