ON THE INCOMPLETEDNESS OF THE EQUIVALENCE PRINCIPLE

THE MISINTERPRETATION OF E = MC2

 
First of all I must warn that this paper is borne out of curiosity not necessity. The ideology that I mean to convene here is based on one of the most beautiful equation borne out of the ingenuity of one of the greatest physicist of the 19th century whose name has transcended throughout the ages and his name is Albert Einstein and this famous equation is stated thus;

E = mc²

The reason why I postulate the idea that this equation is indeed incomplete doesn't necessity the fact to believe that it is inconsiderable so for lack of a better word, I humbly ask that you try to see the point I intend to convey as you thread on with the intention as to think on these things.
Before I go on, I must say this, the ideas, facts and concepts being portrayed in this piece will be based in this three fronts:
 

1. Is the equation Complete?
2. Is the equation Consistent?
3. Is the equation Decisive?

 
These are the intricate questions that had to be asked before any further synopsis is to be laid down in this compendious writing. At this juncture, I would like you dear reader to pause and try to answer these questions in your mind before treading on. Now, the key terms are “Complete, Consistent and Decisive”. Tackling the questions carefully…
 

INCOMPLETE NATURE OF THE EQUIVALENCE PRINCIPLE

My main take after studying carefully the relativity pieces of Albert Einstein was that in and for everything you are trying to explain intricately, frames of reference matters and also, there are two views in which you can do that which are the general view and the special view. My frame of reference for this talk is that during the epoch and birth of the idea hence the equation, both the energy and mass were not explained in toto and I was left to ponder on the type of energy and mass. The global science community has over the years grown and has been well developed with time. So I am still left to ask what was in Einstein’s mind and what he thinking when he related the relationship between energy and mass. When you consider the energy of a moving body, you’ll get to see that the energy of that body is not just a particular or singular force but the energy of that moving body is given by:

E → ∑(∆E)

The essence and logical explanation for this is because; for a moving body, the total energy of that body is a summation of the internal and external components each possessing one or more kind of energy and based on the First Law of Thermodynamics and the Principle of Conservation of Energy stating that “energy can never be created nor destroyed but is transformed or converted from one form to another ”. Hence the delta E (∆E) and because all components are involved underlies the need for the epsilon (summation) symbol (∑). At this juncture, let me state a more concise and general equivalence stated thus:

∑(∆E) = ∑(∆M) . (c + ∂t)² → New Equivalence Principle

 
The reason for the equation is not to challenge the one that was earlier formulated but to drive home the point that recent advancement both in science and technology has brought more light to the understanding of renaissance concepts. To explain the need for the inclusion of ∆M, the truest definition of mass is this; mass, in physics, is the quantitative measure of inertia, a fundamental property of all matter. It is, in effect, the resistance that a body of matter offers to a change in its speed or position upon the application of a force. Simply put, mass is a measure of how hard it is to accelerate an object. If we are to take away the ideology that things that are of the order of the negative exponential are to negligible to be considered and consider that an object in an open system is constantly under the influence of certain unseen forces that truly the mass of an object varies over time. Also, ask yourself these questions:
 

1. Is the mass of an object before and after combustion exactly the same?

2. Why is the mass of an object smaller when compared to the total mass of its constituent particles?

3. If gravity is not constant then why should mass either given by the formulae:

m = F/g?

Regarding the (c + ∂t)² expression, my reason is simple; since so far, we haven’t been able to prove that the speed of light is constant in both directions due to the incomplete measure of the one-way speed of light.
 

INCONSISTENT NATURE OF THE EQUIVALENCE PRINCIPLE

On a personal note, explaining this is rather more challenging than I thought but who doesn’t love a challenge? So let’s dive right in… Speaking on the fickle nature of the equivalence principle, so by way of definition, the word inconsistent as used in this context in simple terms refers to a state of incoherent or illogical thoughts, explanations and actions containing incompatible elements or notions. Over the years, it has been pointed out that at present we only prove that inertial static mass and gravitational static mass are equivalent. We have not proved that inertial kinetic (i.e. moving) mass and gravitational moving mass are also equivalent. It is proved by the dynamic effect of special relativity that inertial moving mass and gravitational moving mass are not equivalent. Besides, it can be proved that the general relational principle is untenable. It is only an apparent feeling of mankind actually. Therefore, there exists serious defect in the foundation of the Einstein’s theory of gravitation. We need to refurbish our ideas of space-time and gravity. I did some research and the references to the research papers for the basis of this theory is thus:
Inertial mass as earlier spoken of is a mass parameter giving the inertial resistance to acceleration of the body when responding to all types of force. Gravitational mass, on the other hand is determined by the strength of the gravitational force experienced by the body when in the gravitational field g. A research paper written by Britannica on the title: “Gravitational fields and the theory of general relativity” revealed that in Einstein’s theory of special relativity, inertial mass is a manifestation of all the forms of energy in a body, according to his fundamental relationship E = mc², E being the total energy content of a body, m the inertial mass of the body and c the speed of light. Dealing with gravitation, then, as a field phenomenon, the weak principle of equivalence indicates that all forms of non-gravitational energy must identically couple to or interact with the gravitational field, because the various materials in nature possess different fractional amounts of nuclear, electrical, magnetic and kinetic energies, yet they accelerate at identical rates. With all these being proven true, I deem it safe to say that my indicted equation has a side to it. Now, back to the experiments the following has been proven;
 

EQUIVALENT PRINCIPLE IS NOT CONSISTENT WITH SPECIAL RELATIVITY

We point out at first that the equivalent principle is not consistent with special relativity. Einstein used the reference frame of rotational desk to show the principle of equivalence and concluded that the space-time of gravitational field was curved. As shown I Fig. 2.1, suppose that the desk K1 with radium r and perimeter 2πr is at rest in beginning. Then let the desk turn around its center in a uniform angle speed ω . According to the contraction of space-time contract in special relativity, observers on the resting reference frame of ground K0 would find that the perimeter of desk becomes;

2πr√(1- ω²r²) /c²

owing to desk’s rotation, but the radium of desk would not contract for there is no motion in the direction of radium. Therefore, the radio of perimeter and radium would be less than π and the observers on the ground would affirm that the space of rotating desk is non-Euclidean space.

 
The problem now is what the observer resting on the rotating desk thinks about. Einstein and almost textbook of general relativity took a mistake here. It were though that because the speed of tangent direction caused length contraction, when these observers used their rulers to measure the perimeter of desk, the perimeter becomes

2πr√(1- ω²r²) /c²

, longer than that of resting desk. But when they use their rulers to measure the radium of desk, the length is unchanged. So the ratio of perimeter and radium is big than π . However, this result is wrong, for it is based on the premises that desk is at rest and observer and his ruler move. But in this case desk rotates actually so that the perimeter of desk and the rulers of observers contract synchronously. So the observers who are at rest on desk can not find the change of desk’s perimeter actually by using their rulers. Secondly, let’s show that the principle of equivalence contradicts with the concept of space-time relativity. There are two problems here. The first is that according to the common understanding of special relativity, space-time’s contraction is caused by relative speed, which has nothing to do with acceleration.
Or speaking strictly, the effect of acceleration is too small comparing with the effect of speed so that it can be neglected. So according to space-time relativity, for observers resting on rotating desk, K1 is at rest but ground reference frame K0 moves around K1 shown in Fig. 2.2. In this way, the observers resting on desk would think that the rulers on their hands are unchanged so that they can not conclude that space-time of desk is curved. Instead, they would think that space-time of ground reference frame K0 should be curved for K0 is moving around K1. Of course, this result can not be accepted. Therefore, if the concept of space-time relativity holds, we can not conclude that the space-time of gravitational field is curved. Conversely, if the space-time of gravitational field is curved and the principle of equivalence holds, the principle of space-time relativity would be violated.
The second problem is that in light of general recognition of special relativity, space-time contract is a purely relative effect, having nothing to do with acceleration. But according to the equivalent principle, space-time contraction should be relative to force and interaction, not a purely relative effect. It is obvious that the principle of equivalence contradicts with the principle of space-time relativity. Because the principle of equivalence is regarded as the foundation of the Einstein’s theory of gravitation, It can be said that special relativity is not consistent with the Einstein’s theory of gravity. Only way for us to get rid of this paradox is to give up the relativity of space-time, and admit that space-time contraction is a kind of effect caused by accelerating processes. The rational result should be that the perimeter of rotating desk contracts and the radio of perimeter and radium is less than π . No matter who are on rotating desk or on ground, observer’s viewpoints are the same.
 

INERTIAL & GRAVITATIONAL MOVING MASS ARE NON-EQUIVALENT

Let’s discuss the problem of equivalent principle itself. The principle can be divided two parts, one is weak equivalent principle and another is strong equivalent principle. The weak equivalent principle indicates that gravitational mass is equivalent with inertial mass, or gravity is equivalent to inertial force locally. We fist discuss the equivalence of gravitational mass and inertial mass. Then discuss the equivalence of gravity and inertial force, as well as the problems of space-time contraction in gravitational field and non-inertial reference frame and so do. At present, the experiments to prove the equivalence between inertial mass and gravitational mass is the so-called type of experiments. It can be pointed out that this type of experiments can not expose the equivalence of inertial moving mass and gravitational moving mass actually. According to the second law of Newtonian, the force acting on an object is F = mi0a, where mi0 is the inertial static mass and a  is the acceleration. In a uniform gravitational field, the formula of force can also be written as F = mg. Here mg is gravitational static mass and g = constant is the strength of the gravitational field. So we have; should be constant for any material. In this way, the acceleration of an object falling in this uniform gravitational field would also be a constant. This result has an obvious defect, i.e., the object’s speed would surpass light’s speed in a vacuo at last when the object falls in the gravitational field. In order to avoid this problem, the dynamic relation of special relativity should be considered. We have:
If gravitational resting mass is equivalent with inertial resting mass, the ratio mg0 = mi0 should be constant for any material. In this way, the acceleration of an object falling in this uniform gravitational field would also be a constant. This result has an obvious defect, i.e., the object’s speed would surpass light’s speed in a vacuo at last when the object falls in the gravitational field. In order to avoid this problem, the dynamic relation of special relativity should be considered. We have:
  and
Because the effect of speed on gravitational force is still unknown at present, we suppose;

 The function f(V) is waited to be determined. Suppose we still have F = mgg, Eq.(2.1) becomes;
As long as, the acceleration is not a constant  again (The fraction above is 3/2). When V → c, we may have a → 0, so that the falling speed would not surpass light’s speed. It is obvious that when an object moves in a gravitational field, the effect of special relativity should be considered.
 

INDECISIVENESS OF THE EQUIVALENCE PRINCIPLE

At this point what do you think? The sincere but bitter truth is that my equation bring a whole new light and exposé to the understanding of the energy-mass relationship and also taking invariability into consideration. On a final note, my newly found equation is a better approximation. What say you?

DISCLAIMER:

I stand corrected on the accountability of my ideas portrayed hitherto.

Psst! Email your thoughts, questions on the concepts to me at azunobicaleb@gmail.com