On the Unification of Physic and the Elimination of Unbound Quantities

On the Unification of Physic and the Elimination of
Unbound Quantities
Shpëtim Nazarko1
1
Independent Researcher, Tirana, Albania
ABSTRACT
This paper supports Descartes' idea of a constant quantity of motion, modernized by Leibniz. Unlike
Leibniz, the paper emphasizes that the idea is not realized by forms of energy, but by energy itself. It remains
constant regardless of the form, type, or speed of motion, even that of light. Through force, energy is only
transformed. Here it is proved that force is its derivative. It exists even at rest, representing the object's
minimal energy state. With speed, we achieve its multiplication up to the maximum energy state, from which
a maximum force is derived from the object. From this point, corresponding to Planck's Length, we find the
value of the force wherever we want. Achieving this removes the differences between various natural forces.
The new idea eliminates infinite magnitudes. The process allows the laws to transition from simple to
complex forms and vice versa, through differentiation-integration. For this paper, this means achieving the
Unification Theory.
KEYWORDS
Energy Transformation, Principle of Least Action, Lorentz Factor, Dark Energy, Relativistic Momentum,
General Theory of Relativity, Energy State, Planck's Length, Quantum Gravitation, Schwarzschild Radius,
Unification of Physics
1. INTRODUCTION
Presentation of the General Idea Seeking the Unification of Physics:
The demand for knowledge of the fundamental laws of nature is linked to the attempt to reach
them through initially discovered laws, which are essentially derived from them. This leads to the
idea that through differentiation-integration processes, we can transition from simple to complex
laws and vice versa. The validation of this idea requires controlling proven theories in practice
and supported by the principle-mathematical apparatus-conservation laws rule. The general
theory of relativity and quantum mechanics can be considered the best examples to control the
process. It is first done for the relativistic theory.
Can we transition from the apparatus and laws of the General Theory to those of the Special
Theory and mechanics, and then achieve the opposite through the integration process?
The answer is not positive, and the reason seems not related to its apparatus or laws. They are
accurate, so the mystery should be sought in the meaning of the Principle of Relativity.
Transitioning from Galileo's Principle to the special and then general principle of relativity is seen
here as an attempt to understand the principle's meaning. The continuous search for it leads to the
observation of the most important feature of the fundamental magnitude of energy. It appears to
be independent of form, type, or speed, even that of light itself. Precisely this fundamental
magnitude, which is not recognized by classical mechanics and initially by the special theory,
International Journal of Recent advances in Physics (IJRAP) Vol.13, No1/2, May 2024
15
DOI: 10.14810/ijrap.2024.13202

seems to reveal the mystery of the meaning of the Principle of Relativity. Analogously to the
principle, it shows why laws have the same form in coordinate reference systems.
Thus, when Einstein proves that laws have the same form in coordinate reference systems, he has
not expressed the meaning of the principle of relativity itself, but the attempt that aims first to
understand through the consequences produced, the feature of the fundamental magnitude of
energy.
The effort to understand the essence of these consequences expresses the essence of the theory of
relativity. The paper sees Einstein's ideas about the principle as accurate but only in a quantitative
aspect. Therefore, it replaces the general principle of relativity with the principle of energy
conservation. The energy of the object remains constant, and with the action of force on it, it is
transformed. With speed, the object gradually changes not its energy, but only its energy state, a
process reflected by the Lorentz Factor. The process of deriving the energy state at any moment
with speed leads to the laws of impulse and force for special relativity and classical mechanics.
The part of the untransformed energy does not affect the process, so it is called dark energy. Force,
as a derivative of energy, emphasizes that it exists even at the moment of the object's rest,
reflecting its minimal energy state. It is represented here by the classical radius for objects with
small mass. For those with large mass, by the Schwarzschild radius. The minimal energy state is
multiplied up to the maximum. The transformation process continues until the object reaches a
minimal spatial parameter. It corresponds here to Planck's Length. The minimal and maximal
energy states, expressed through Planck's and Sommerfeld's Constants, also reflect the essence of
quantum mechanics. In the maximum energy state, a maximum force is derived from the object.
It weakens according to the inverse square law with distance. The process can also be realized in
reverse. It allows us to find the force at any moment at the distances we want. This enables us to
remove the difference between different natural forces. We have thus achieved the requirement to
go from a simple form of the laws of motion to the laws of a higher form. The process can also
be realized in reverse. The achievement requires the mechanism of differentiation-integration.
The presentation helps build a quantum theory of gravitation. It allows the unification of General
Relativity with Quantum Mechanics, so it is seen here as a unification achievement. The idea that
energy remains constant automatically eliminates infinite magnitudes.
Method and Its Role in Building Fundamental Theories
The paper links the achievement of the Unification Theory of physics with a fundamental
condition. It requires that based on the principle-mathematical apparatus-conservation laws rule,
we transition from one theory or theoretical model to another and vice versa, achieved through
the differentiation-integration process. Therefore, it does not follow any of the current or proposed
models to achieve the goal. Practically, the new idea should overcome the difficulty presented by
transitioning from the laws of a simple form to those of a more complicated form. The difficulties
highlighted, as well as the successes, accumulate experience to judge the possibility of revising
past or current theoretical models. Atechnique the paper calls "Revision of the research procedure
from scratch." By utilizing the achievements, it analyzes historical processes, i.e., the periods of
theory creation. This is the premise that leads to the Method of building a fundamental unifying
theory. The construction of the Method enables you to assess the value of theories as much as
theoretical models.
But how does the paper present its essence? Matter or substance is represented by the fundamental
relation energy-mass-space-time. In their dynamic interaction, the fundamental magnitudes create
invariant relationships with numerical or non-numerical character. They can be the rest-uniform
straight motion relationship of Galileo or natural constants like the speed of light, Planck's,
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Sommerfeld's, etc. Invariant relationships and natural constants serve as the basis for formulating
principles that are placed at the top of theories. Principles are accompanied by the construction of
mathematical apparatuses that faithfully reflect their meaning in quantitative terms. Fundamental
theory or theoretical models are completed with conservation laws that show the limits of the
theories' effectiveness in practice. The Method defines the primary role of fundamental
magnitudes.
Through their number, the value of other factors or the theory itself is determined. The absence
of one of the fundamental magnitudes means that we are dealing with only a theoretical model
and not a fundamental theory. Invariant relationships and natural constants, despite their
importance, can never replace the role of fundamental magnitudes or determine their behavior.
The same thing can be said for invariants, principles, or conservation laws.
2. JUDGING THEORETICAL MODELS BASED ON THE METHOD
Galileo and Newton
Isaac Newton laid the foundations of classical mechanics based solely on three fundamental
magnitudes: mass-space-time. His invariance is based on the relationship of rest-uniform straight
motion. It also serves as the basis for formulating the principle of relativity named after Galileo.
Referring to the Method, despite the quantitative successes, we are dealing with a serious
problem.
The invariant or invariant relationship can serve as the basis for creating the principle, but it can
never replace it or play its role. Asimilar situation is seen later in the special theory where Einstein
replaces the role of the principle with the invariant of the speed of light. Disregarding the rule
dictated by the Method leads to consequences. The creation of models that legitimize any
theoretical construct, considering the achievement of quantitative results sufficient. Newton, who
has very limited possibilities, does not give much importance to the principle of relativity,
considering it a healthy rule that he uses to derive the laws of impulse and force. The invariant
relationship of rest-uniform straight motion does not have a numerical character. Aspecificity that
allows Newton's principle, apparatus, and laws to have an infinite scope of action. In Newton's
theoretical construct, due to the unchanging nature of mass, dynamic interaction is missing. This
makes his dynamics have a character that contains many elements of statics. Here we can include
his Law of Gravitation, whose cause cannot be found, a task that normally belongs to dynamics.
This emphasizes that Newton's dynamics are built on simple kinematics. Which is based on the
study of motion equations through Galilean Transformations. Its form is simple. But it accurately
represents Newton's and the period's understanding of the essence of the principle of relativity.
Here we can say that the first chapter of classical mechanics named after Newton is closed. What
we can highlight as special in his work is that he maintains the same concept with Galileo for
force. Exerted on an object, it can lead its motion to infinity.
Descartes and Leibniz
The dynamic interaction of fundamental magnitudes is initially expressed in Descartes. Embodied
in the idea of "constant quantity of motion," it is valid even for the Universe seen as a single
object. With his work "Geometry" in 1637 (1), he lays the foundations of modern kinematics. But
it also helps to establish dynamics on a new foundation. However, Descartes does not have the
opportunity to advance his idea through the expression of impulse, which is only valid for low
speeds. The discovery of differential and integral calculus by Newton and Leibniz is needed to
verify Descartes' idea through a new dynamic. The well-known Cartesian-Leibniz debate, which
17

divided the great minds of Europe, including Kant, sides with Leibniz in a qualitative view
through the concept of "Vis Viva" or "Living Force" (2). However, in a quantitative view,
Leibniz's idea is realized not with the formula 𝑚𝑣2
but with 𝑚𝑣2
2
⁄ . The Cartesian-Leibniz
debate gradually leads to the presentation of two forms of energy, kinetic and potential. Then to
Lagrange's Function in 1790 and a bit later to Hamilton's Function in 1830.
L = T – V (L-Lagrangian, T-Kinetic Energy, V-Potential) (1)
H = L + V (Where H is the Hamiltonian) (2)
Subsequent processes seem to materialize the initial idea of "constant quantity of motion."
Expressed by a formula that is a contribution of Mayer, Joule, Colding, etc.
𝑚𝑔ℎ + 𝑚𝑣2
2
⁄ = 𝑐𝑜𝑛𝑠𝑡 (3)
The formula, which takes a general form from Kirchhoff in 1870 with the "Virial Theorem (3),"
completes in its final form the ideas initiated by the Cartesian-Leibniz debate. In this sense, it
seems to inspire Helmholtz, who emphasizes that here we can say that the unification process of
theoretical physics is completed, and its study should be concentrated only on the study of
conservative forces acting along the centers of objects (4) . We have, therefore, the conclusion of
the second chapter of classical mechanics. Hence, we can draw some conclusions. They are based
on the ideas that in this period are developed not under the sign of Newton.
The force, which is the foundation of Newtonian dynamics, does not have the same role as given
by his definition. It more than increases the magnitude of motion, only transforms it. The force
that also has the function of measuring motion leaves it to kinetic energy, which, regardless of its
magnitude, is expressed through the formula 𝐸𝑘 = 𝑚𝑣2
2
⁄ . The potential energy form, initially
seen as an auxiliary concept, becomes increasingly important. Lagrangian and Hamiltonian can
easily solve all mechanics problems. Showing as a product that modernizes kinematics and
dynamics, it allows the analysis of all forms of motion. Lagrange's Function reduces the
importance of using Galileo's Apparatus. From the perspective of the paper that values the control
of the transition of laws from top to bottom and vice versa through the differentiation and
integration process, it seems that we have a clear realization of the process.
𝑚𝑣2
2 ⇆
⁄ 𝑚𝑣 ⇆ 𝑑𝑝 𝑑𝑡
⁄ (4)
From what has been presented above, classical mechanics, initially formulated by Newton and
then modernizing its kinematics and dynamics, resembles a small but regular house. Meanwhile,
in the post-Newtonian period, physics operates again only with three fundamental magnitudes
mass-space-time, replacing energy with its forms. But it mistakenly thought that with the terms
of kinetic and potential energy, it also defined the term of energy. Practically, it had reached only
the formula of work. Regardless of the units, work is not the same as energy. This principal error
marks the beginning of significant problems in physics.
Maxwell and Lorentz:
In a general definition, despite the advantages of Lagrangian and Hamiltonian, some weaknesses
are attributed to them. For the paper, its main weaknesses are expressed this way. They cannot be
used in the case of high speeds due to the limited value of the kinetic energy formula. A limitation
shown by Einstein in the Special Theory. The second and most fundamental limitation comes
from the fact that Lagrangian and Hamiltonian analyze energy forms, not the energy itself. The
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problems created in electrodynamics that lead to Maxwell's field laws and those in
thermodynamics that lead to Planck's law are related to energy as an inherent characteristic of the
problem, not its forms. The difficulty of using Lagrangian and the non-recognition of energy as
an inherent characteristic of the object impose solving problems using natural constants. Initially
considered as auxiliary elements or for respecting physical units (as we see in Newton's law where
the gravitational constant is placed a century later), they now occupy a central place in theoretical
constructs. The apex is reached with the Constant of the speed of light in Maxwell and Planck's
Constant, which stands at the foundation of Quantum Mechanics. In Maxwell, we see this idea
directly in the formula that presents the speed of light (5) .
𝑐 =
1
√𝜖0 𝜇0
(5)
Referring to the Method, which calls invariants a product of the dynamic interaction of
fundamental magnitudes, the question here is straightforward. To whom do the invariant of the
speed of light or Planck's belong? The study poses the problem, starting from its main goal. The
demand to achieve through differentiation -integration processes the transition from high-form
laws to lower ones or vice versa. So, can we transition from Maxwell's field laws to Newton's
laws or vice versa? Referring to the rule that emphasizes the dependence of principle-
mathematical apparatus-conservation laws, the signs seem positive. From Lorentz's Apparatus,
we can go to Galileo's. From the latter, as Lorentz shows, we can only reach the former with
modifications. This process seems to be experienced even in the conservation laws of energy. The
fundamental difficulty according to the Method here lies in the fact that energy is considered
massless, whereas the object is assumed not to have energy. In a general plan, unification stands
in constructing physics based either on matter represented by mass or on energy. The conclusion
aimed at unification in this form is clearly described by Einstein a long time after constructing
the Special Theory. (6)
The paper assesses the situation based on the "Revision of the research procedure from scratch."
For it, the control of the unifying idea can only be done after we reach the conclusion that energy
has mass and the object has energy. These facts are not recognized only at the time when Clerk
Maxwell formulates the field laws but also later after Einstein presents the Special Theory.
Einstein.
Uncertain about the meaning of the invariant of the speed of light, Maxwell sees it as an
electromagnetic wave that propagates in a vacuum at the speed of light. Einstein sees it as the
maximum speed in nature. He elevates the invariant to the rank of principle by placing it alongside
Galileo's Principle. (7) Which is considered valid in mechanics, but now also in electromagnetic
and optical phenomena. Einstein thus canonically raises a serious theory, which has at its head
the Special Principle of Relativity and the Postulate of the speed of light. They are accompanied
by Lorentz's Apparatus, which he formulates independently of Lorentz. Along with the
conservation laws presented in the article "Electrodynamics of Moving Bodies," Einstein
constructs the scheme principle-mathematical apparatus-conservation laws. The paper judges the
Special Theory of Relativity referring only to the Method, without being influenced at all by the
quantitative results.
Einstein briefly shows at the beginning of the article the compatibility of the Special Principle
with the Postulate of the speed of light. This through a simple example. A spherical light wave
emitted along a moving axis retains the same spherical shape even at its end. The invariant
represented by the speed of light has a numerical value. For the paper, it merely reinforces the
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invariant relationship rest-uniform straight motion, which does not have a numerical value. It does
not seem difficult to understand in mechanics that precisely this character of it allows the
development of events to infinity. A possibility that is limited by the new invariant with a
numerical character. Referring to the Method, we check the factors determined by it in
constructing a theory. Despite the importance of the invariant, it, like the principle, cannot replace
or play the role of fundamental magnitudes. Even more so that through it to determine the line of
behavior of these magnitudes. We are dealing with a principal error, which leads to a presentation
of the apparatus and laws that carry on their back the consequences of breaking this rule. Einstein's
initial conclusions expressed in a popular form are: With speed, the mass of the object increases
continuously and takes an infinite value if we reach the speed of light. The time measured for an
object in motion, from an observer at rest, seems to move slower. It stops completely when we
reach the speed of light. For the same conditions for the observer at rest, the length of the object
in motion with the reaching of the speed of light becomes zero. The processes are described below
through the well-known Fitzgerald-Lorentz Factor.
.
𝑚0
√1−𝑣2 𝑐2
⁄
(6) 𝑙 = 𝑙0 (√1 − 𝑣2 𝑐2
⁄ ) (7) 𝑡 =
𝑡0
√1−𝑣2 𝑐2
⁄
(8)
Where the Fitzgerald-Lorentz Factor is equal to;
1/ √1 − 𝑣2 𝑐2
⁄
The initial judgments are initially accompanied by a set of masses with strange names like
longitudinal mass, transverse mass, rest mass, motion mass, electromagnetic mass, relativistic
mass, etc. It is understood that from the perspective of the "Revision of the research procedure
from scratch," we are dealing with an epistemological weakness, dressing the mass with a set of
names, a burden that it cannot bear.
It is Einstein himself who withdraws from this idea by returning to Newton. Forty-three years
after the Special Theory, in a letter he sent to Lincoln Barnett, he expresses himself exclusively
as follows.
It is not good to use the concept of mass M = m √1 − v2 c2
⁄
⁄ for a moving object, all the more
so when we cannot give a clear definition for it. It is better to use the concept of rest mass m.
Instead of M, it is good to use the concept of momentum or the energy of the object in motion.
(8)
The conclusion is accurate. But with the new kinematics that leads to new dynamics and naturally
to new physics, Einstein can practically only reform classical mechanics. The reason is simple.
By keeping, like Newton, the idea that it is based on three fundamental magnitudes, he cannot
achieve qualitative results, only quantitative ones.
Today it is accepted that we should only talk about Newton's mass, i.e., the rest mass. Einstein's
initial explanation is still held in a few texts, and this is for didactic reasons. Wheeler sees the
difficulties of the problem differently from him in the geometric properties of space-time. (9)
20

Both explanations, whether that of Einstein or Wheeler, are inaccurate. We say that the problem
is not didactic. They should be sought in the new formula of mass.
𝑚 =
𝑚0
√1−𝑣2 𝑐2
⁄
(9)
The formula that explains Einstein's initial interpretation expresses a principal problem. The
change in the form of laws can lead to a change in the qualitative properties of fundamental
magnitudes, but not their quantitative ones. The discovery of energy as an inherent characteristic
of the material object expressed through the formula 𝐸 = 𝑚𝑐2
, does not improve the initial
explanation. Presented simply, its formula is reached by multiplying both sides of the above
equation by 𝑐2
.
𝐸𝑡𝑜𝑡 =
𝑚𝑜𝑐2
√1−𝑣2 𝑐2
⁄
= 𝑚0𝑐2
+
1
2
𝑚0𝑣2
+ ⋯ (10)
The general energy formula consists of two factors, rest energy, and kinetic energy. If the speed
reaches that of light, the total energy becomes infinite. For the judgment given here, it is not
logical to see the energy formula as the product of two factors where one of them, the rest energy,
is an inherent characteristic of the object, and the other, the kinetic energy, is only a form of
energy. How can the quantitative results achieved by the Special Theory be explained despite the
criticism? In the last formula that differs from Einstein's initial one based on mass, there is a
fundamental difference. He has now introduced energy represented by the formula 𝐸 = 𝑚𝑐2
.
Precisely energy, not mass, allows presenting the new and reformed formula of kinetic energy.
Einstein did not know the energy formula 𝐸 = 𝑚𝑐2
at the time of constructing the Special
Theory.
It is a fundamental absence that does not allow him to present events with Lagrange's Function.
The Lagrangian is placed later in the Special Theory. As mentioned, the Lagrangian is based on
the analysis of motion equations that include energy forms and not the object's energy itself. But
its placement emphasizes that it is as much an indicator of the modernization of his theory as the
fact why it cannot be placed earlier. The defects shown seem to be eliminated after Dirac's new
formula in 1928 (10). He presents the general energy formula of the object with speed, combining
momentum and energy.
𝐸𝑡𝑜𝑡
2
= 𝑚0
2
𝑐4
+ 𝑝2
𝑐2
(11)
or
𝐸2
− 𝑝2
𝑐2
= 𝑚0
2
𝑐4
(Energy, momentum and mass are given with the numerical value of their squares.)
The formula, which stands at the base of Quantum Mechanics but also of all physics, shows the
difficulty of transitioning from the laws of a lower form to those of a higher form. The elegance
of the formula lies, among other things, in two elements. It first shows that whatever energy value
you take in the experiment, the difference in its numerical value with the momentum gives the
value of the rest energy, which remains constant. The second element is that the relativistic
momentum is expressed here in a form that respects the idea presented by Einstein in 1948.
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𝑝 =
𝑚0.𝑣
√1−𝑣2 𝑐2
⁄
(12)
The formula gives the idea that momentum is a direct product of energy, and from Dirac's idea,
we can transition with derivation processes to the one started from the general energy. Feynman
does not give any importance to presenting the momentum in this form. Emphasizing that Einstein
modifies both it and the magnitude of the force starting from the correction of Newton's mass
with speed. Therefore, he presents the formula of relativistic momentum as follows (11)
𝑝 = (
𝑚0
√1−𝑣2 𝑐2
⁄
). 𝑣 (13)
Feynman's presentation does not lead to the laws of mechanics through the derivation process
from those of the Special Theory. But this goal, which is fundamental for the study, does not say
anything about theoretical physics, which is satisfied only with achieving quantitative results.
From Dirac's formula, we go to Einstein's formula of the total energy of the object:
𝐸𝑡𝑜𝑡 =
𝑚𝑜𝑐2
√1−𝑣2 𝑐2
⁄
(14)
Dirac's formula shows a significant improvement achieved by using four-vectors or Minkowski's
space-time continuum. However, the idea that it leads to the laws of impulse and force of Classical
Mechanics and the Special Theory through derivation is not a principal form. It is not difficult to
see that Dirac's formula also contains the initial and inaccurate idea of Einstein about the change
in mass with speed.
Theoretical physics ultimately legitimizes Dirac's new formula as the representative of the total
energy. It also presents the unification in one formula of energy and momentum. The possibility
of unification in a single formula of the law of impulse with that of energy is another point that
the paper views with skepticism. Accepting this conclusion is analogous to that of force, which
states that its increase leads to an increase in the object's energy. We can only accept that through
impulse, we transition to the expression of force, the formula of which is based on that of kinetic
energy. But in this case, we would accept that the formula of the total energy of Dirac, as well as
that of Einstein, is a formula that only reforms that of kinetic energy. Despite the progress, a
product of the introduction of Minkowski's space-time continuum, which Einstein, like energy of
the material object expressed by the formula 𝐸 = 𝑚𝑐2
, did not know at the time of constructing
the Special Theory, Dirac's presentation does not close the problems created by the idea that
assumes the increase of mass. Referring to the Postulate of the speed of light, which states that
the object never reaches its magnitude, the Special Theory allows any value close to its speed that
the parameters space and time can take in the process of measuring the movement. For this theory,
it is enough not to violate the Postulate of the speed of light, a conclusion that cannot be complete
if we accept Planck's Length as the minimum in nature. In today's practice, efforts lead to attempts
to avoid the problem, which require the construction of a theory that reconciles the Special Theory
with the condition imposed by Planck's minimum Length. Such is presented by Giovanni Amelino
Camelia, who names his effort "The Double Theory of Relativity." Referring to the Method, the
problem is not solved by constructing a new apparatus. The mathematical apparatus faithfully
represents in quantitative terms the meaning of the principle, so the issue is not resolved without
first understanding the axiomatic character of the principle of relativity. The presentation of the
difficulties of Classical Mechanics or the Special Theory given by Dirac's formula or Camelia's
attempt is given in the two figures below, which express the change in the energy state of the
object with speed (12).
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Newton Einstein
Figure 1 Kinetic energy according to Figure 2 Kinetic energy according
Newtonian mechanics to Special Relativity.
The graphical presentation of the figures shows, firstly the fundamental weakness of the idea that
seeks to express energy and its formula through energy forms and not from this fundamental
magnitude itself, which is an inherent characteristic of the material object. This is the most
important difference from the study's perspective, which constitutes the basis of the criticism for
the generally accepted judgment of the situation at the time. The practical consequence of thinking
differently is clearly seen in points zero and c in the Special Theory of Relativity, where kinetic
energy takes the values zero and infinity. Einstein's idea of attributing a certain energy to the
material object at point zero, which he calls rest energy in a theoretical plan, seems to reinforce
his accepted conclusion today that the 𝐸 = 𝑚𝑐2
is a consequence of the Special Theory of
Relativity. The consequences of the relativistic interpretation for rest energy are transmitted to all
new theories based on the conservation law of energy of the Special Theory. They are clearly seen
in the works of de Broglie and Schrödinger. The rest energy given in the Special Theory of
Relativity cannot be measured. It must be accepted by deduction, so in the above works, the idea
is imposed that attributes to point zero the wavelength infinity and to point c, zero. The practical
successes and the impossibility of determining the energy state at points zero and c cement in
physics the infinite magnitudes. This problem is the same one reflected by Classical Mechanics.
It seems that mathematical techniques, despite the partial successes achieved, cannot remove
them. Meanwhile, theoretical physics, which continues endlessly the efforts for this task, seems
never to have asked the question of their real cause. In a general statement, it seems that only
Niels Bohr emphasizes that the law of conservation of energy of the Special Theory of Relativity
is a suit that is too tight for theoretical physics. (13)
The above conclusions for the paper are reflected first by the theoretical apparatus. Lorentz's
Apparatus is valid for the field laws and the Special Theory. Modified, it is also valid for classical
mechanics. Based on the connection apparatus-law, we could not expect to go from the initial
laws of the Special Theory, which are conservation laws of mass, to those of Maxwell. But it
seems that we cannot go from Maxwell's laws to those of the Theory with the derivation process
either. The logical justification of the conclusion seems evident. The energy represented by the
field is considered massless, while the object with mass is assumed to have no energy. To expect
the transition with the differentiation-integration process to realize the transition of laws from one
theory to another, you need to have the common factor of both theories in hand. That is, to have
the conclusion that the object has energy and light has mass. The first fact, Einstein discovers it
only after constructing the Special Theory and presents it in the article where we see the formula
𝐸 = 𝑚𝑐2
, in 1905. The idea that light has mass in addition to energy, he discovers after
23

constructing the General Theory in 1915. The idea of raising the laws of conservation of the
Special Theory, based on the role that Einstein gives to the invariance of the speed of light, seems
difficult to accept. Invariants are a ratio that comes from the dynamic interaction of fundamental
magnitudes. And they cannot play their role or determine their line of behavior.
In the above reasoning, there was no talk of the fundamental magnitudes of space and time. It
seems that in the central equation of Lorentz, they directly express the invariance of the speed of
light.
𝒍𝟏
𝒕𝟏
=
𝒍𝟐
𝒕𝟐
= ⋯
𝒍𝒏
𝒕𝒏
= 𝒄 (15)
The parameters l and t represent space and time even in the case of light which is considered to
have no real physical dimensions. Hence, concepts such as wavelength, frequency, etc., are
attached to it. The changes in their values express light with different energy and mass. The
invariance of the speed of light represents a ratio of the dynamic interaction of the fundamental
magnitudes, but at the time of the Special Theory, the reasoning cannot be done, because light
was considered massless. In the analysis that Einstein makes of the magnitudes of space and time
in the Special Theory, his great difference from Newton's classical physics is emphasized. The
work takes a different stance here. As emphasized above, the change in the form that the laws
take and the measuring instruments has a purpose which should be considered achieved, only
when this change in their form also preserves the invariance of the fundamental magnitudes. The
continuous reformulation of the form taken by space and time is related to the demand for
reaching the final form of the conservation law. In that case, we should see how the graphical
curve of the conservation law of energy corresponds to the graphical curve of space-time. At the
current point of discussion, this task and its achievement are very far away. This is also because
in this case, the magnitudes of space only serve a conservation law that represents a principle
based on the invariance of rest-uniform straight-line motion. The work tries to prove below that
the content of the Lorentz Central Equation is fully clear in Quantum Mechanics. There we can
easily see why its laws are valid even for Classical Mechanics. Or in other words, why the laws
of the latter are derived from it. Concluding on the Special Theory, we can say that it cannot lead
us through the processes of derivation-integration, neither to Maxwell's laws nor to those of
Classical Mechanics.
Referring to the Method, the principal defects of the Special Theory can be summarized in this
form. The invariance of the speed of light is only a product of the interaction of the fundamental
magnitudes. It cannot condition their behavior. The invariance can be the basis for formulating
the principle, but it cannot play its role. The role given and the properties assigned to it are
reflected in the conservation laws, which make infinite magnitudes inevitable. The formula for
the general energy as the sum of the rest energy and kinetic energy, which is a form of energy, is
a fundamental inaccuracy. It expresses the addition of content with form. The second and more
important problem arising from this perspective is that it leads to the incorrect conclusion that we
can increase the energy of an object through force.
3. DERIVATION OF THE LAWS OF CLASSICAL MECHANICS AND THE SPECIAL
THEORY OF RELATIVITY
The work utilizes the conclusions of Poincaré (1900), Hasenöhrl (1904), and Einstein in 1905,
which present the formula 𝐸 = 𝑚𝑐2
. The idea that it is a consequence of the Special Theory seems
difficult to accept.
24

This would imply that through force, we change the energy of the object, which is a principal
inaccuracy for the paper. The paper maintains the idea that the action of force on an object never
changes its energy but only transforms it. What changes is its energy state. The energy of the
object remains constant. The action of force and the counteraction of the object against it is
reflected by the Principle of Least Action. So if the process of action-counteraction force-object
occurs at the speed of light, the quantitative value of the transformed energy is shown by the value
taken by the Fitzgerald-Lorentz Factor. The role given to it is different from that attributed by the
Special Theory. It merely reflects the process of energy transformation. The Factor accompanies
all laws and also the measuring tools, which are space and time. These latter are considered
accurate in their task only in one case. When the form of the graph curve that reflects them fully
coincides with that of the law of conservation. If the law of conservation is in its final form, even
the forms of the measuring tool have the same character. The paper fundamentally differs from
the Special Theory by accepting first that the energy of the object is constant, and the Fitzgerald-
Lorentz Factor only reflects the process of its transformation. Based on these objections, we
present the new form of the law of conservation by proving directly how the laws of Mechanics
and the Special Theory are derived from it.
The paper revitalizes the idea of the Cartesian-Leibniz debate, which states the transformation of
motion from one form to another. But now it does not operate with the forms of kinetic or potential
energy but with the energy itself. The magnitude of it at rest is the same in numerical value and
at point c.
𝐸𝑝 – is considered by the paper, the total energy of the material object. It is equal to the rest energy
𝐸 = 𝑚0𝑐2
given by the Special Theory of Relativity. So;
𝐸𝑝 = 𝑚0𝑐2
= 𝑐𝑜𝑛𝑠𝑡 (1)
The total energy is considered the rest energy. It is the sum of two energies, the exposed and the
unexposed, which change at the expense of each other with the Lorentz Factor.
𝐸𝑝 = 𝐸𝑒𝑥 + 𝐸𝑝𝑒𝑥 = 𝑚0𝑐2
= 𝑐𝑜𝑛𝑠𝑡 (2)
The unexposed energy at rest has the value of the total energy. With the change in speed, it
continuously decreases and becomes equal to zero at the speed of light.
𝐸𝑝𝑒𝑥 = 𝑚𝑐2
(√1 − 𝑣2 𝑐2
⁄ ) (3)
The exposed energy is given as the difference between the total energy and the unexposed energy;
𝐸𝑒𝑥 = 𝐸𝑝 − 𝐸𝑝𝑒𝑥
or
𝐸𝑒𝑥 = 𝑚𝑐2
(1 − √𝑣2 𝑐2
⁄ ) (4)
At rest, the exposed energy has a value of zero. At the end of the transformation process, we have
taken the value of the initial energy of the object that was unexposed at rest. The graph curve that
graphically represents the exposed energy against speed corresponds to Einstein's known
asymptote, obtained through reasoning as follows. From formula 3, we see that the curve of the
25

unexposed energy (normalized by 𝑚𝑐2
against speed (normalized by c) is a quarter circle with a
radius of 1. After minimal algebraic manipulations, the formula is written;
(
𝐸𝑒𝑥
𝑚𝑐2
)
2
+ (
𝑣
𝑐
)
2
= 1 (5)
By varying the speed v from zero to c, we obtain a quarter circle in the first quadrant of the
coordinate system (Figure 3). On the other hand, if in equation 3, we divide both sides by 〖𝑚𝑐2
and replace 𝐸𝑝 from equation 1, we will have:
2
2
1
mc
E
mc
E xp
une
xp
e
−
= (6)
Therefore, we can obtain the curve of the exposed energy (normalized by 𝑚𝑐2
) from the curve of
the unexposed energy (normalized by 𝑚𝑐2
) by making a reflection about the horizontal axis -
changing the sign - and a vertical shift by one unit.
Figures 3 and 4 show the exposed and unexposed energy and their respective impulses.
Deriving the exposed energy with respect to speed gives us Einstein's expression for momentum:
𝑑𝐸𝑒𝑥
𝑑𝑣
=
𝑚.𝑣
√1−𝑣2 𝑐2
⁄
(7) 𝑝 =
𝑑𝐸𝑒𝑥
𝑑𝑣
=
𝑚.𝑣
√1−𝑣2 𝑐2
⁄
(8)
For low speeds in the paper, Classical Mechanics and the Special Theory, the momentum takes
the well-known value m∙v. By deriving the momentum with respect to time, we get the expression
for force:
𝑑𝑝
𝑑𝑡
=
𝑚.𝑎
(1−𝑣2 𝑐2 )3
2
⁄
⁄
(9) 𝐹 =
𝑚 .𝑎
(1−𝑣2 𝑐2
⁄ )3
2
⁄
(10)
The derivation process can be done using the Lagrangian. From it, we first go to the law of
momentum or quantity of motion and then find the force.
𝐿 = (1 − √1 − 𝑣2 𝑐2
⁄ ) 𝑚𝑐2
− 𝑉(𝑥) (11)
26

Einstein, as mentioned, could not initially present the Lagrangian in the Special Theory. We
present the general form of the object's motion equations through the new Lagrangian. The new
Lagrangian in the paper does not have the minus sign as the one presented in the Special Theory.
(12)
For (ß«1) we go from the standard Lagrangian used in Classical Mechanics.
(13)
From the above relation, we go to the formula of relativistic kinetic energy.
(14)
By replacing the force in the given equation above, we write:
(15)
Through minimal algebraic manipulations and replacing u= 𝑣2
𝑐2
⁄ , which leads to du = 2
𝑐2 𝑑𝑣
⁄ ,
and following other complementary steps, we reach the formula of Kinetic Energy.
(16)
The idea allows us to easily derive Classical Mechanics laws of Newton and Einstein's Special
Theory laws. The conclusion is verified by the paper's Lagrangian. Its analysis shows that for low
speeds, the graph curve representing the law of energy conservation has an elliptical form. This
shows an analogy not only with the natural motion of planets. It also takes us back to the period
of analyzing Maxwell's laws when Heaviside, who reformulates them, emphasizes the elliptical
form of the electrostatic field in motion. It seems that the law of energy conservation is also the
universal law of nature. The fact that unexposed energy does not influence our measurements
might create the idea of the absence of mass or energy. But the fact that it exists in reality in the
untransformed form explains the phenomenon of dark energy. The new law of energy
conservation is not final. The reason is simple. Energy is considered continuous, which is evident
in points zero and c. Here, momentum and force seem to take undetermined values. Therefore,
we say that through exposed and unexposed energy, we can only represent events based on the
idea that the energy of the object is a continuous magnitude. For the physics structure to be
functional, it is necessary to determine the force values at points zero and c. Here, the paper
F
P
dt
d
x
V
P
dt
d
x
L
v
L
dt
d
=
=


+
=


−








0
0
1- b2
( )
1
2
» 1- 1
2
b2
( )
  ( )
( ) ( )
x
V
KE
x
V
c
v
mc
L
x
V
mc
L
−
=
−









−
−
−

2
2
2
2
2
2
1
2
1
1
1 
KE
dx
v
E
t
Fdx =


















=
 
exp
( )
   
=
=
= mvdv
dt
dx
mdv
dx
dt
dv
m
dx
ma 3
3
3
3




( )
 =
−
= KE
mc
mvdv 2
3
1


27

utilizes the idea that force is the derivative of energy. A conclusion not known to traditional
concepts. But being the second derivative of energy, the force seems to exist even when the object
is at rest. A fact that we see not only in Coulomb's law, which is reflected by the electrostatic
force. The force is also reflected by Newton's Law of Gravitation, but in a more complicated form.
At point zero, the force expresses the minimal energy state and at point c, the maximal energy
state of the object. The energy state is an inherent characteristic of the object and reflects the
field's intensity at any moment.
4. DEFINING THE BOUNDARIES OF CLASSICAL MECHANICS AND SPECIAL
THEORY
The discovery of energy not only imposes its central placement in theories but also demands its
association with the redefinition of their operational boundaries. This work analyzes not only the
zero points and c but also the intersection points of the curves where exposed and unexposed
energy intersect, where both rest energy and relativistic kinetic energy are equal. To clarify the
idea, we construct a figure analogous to that of the energy curves. Exposed and unexposed energy
are replaced by kinetic and potential energy, which again represent energy forms, but now
expressed solely through the term 𝑚𝑐2
Figure 5 The table presents the transition of lows from quantum mechanics to the special theory and then
to classical mechanics.
In the zero point for the work, the energy of the material object has the value of the total energy,
but it is all unexposed. In the zero point, the kinetic energy has a value of zero for Classical
Mechanics. For Special Theory, the zero-point energy is expressed by the value of the rest energy,
𝑚0𝑐2
. But what nature does this energy have, which Einstein emphasizes that the object has as
its own and which he considers "a kind of energy"? At the intersection of the curves, it equals the
rest energy at the speed √3 2
⁄ c. The Special Theory does not give any importance to this point.
At this point, in analogy with Classical Mechanics, we have the equality of kinetic energy with
potential energy. The difference is that here we have the equality of two energies and not their
forms. The kinetic energy of classical mechanics is valid regardless of the values of the speeds.
As we will see below, it has the same value even at point c. There, the value given for what is
called the Schwarzschild Radius is provided. But this precise result in the quantitative plane is
inaccurate in the qualitative one. It shows that its value is limited as Einstein shows in the Special
Theory. The analogy with this formula serves for something else. The points around zero show
the upper limit of the application of classical mechanics. For the Special Theory, it is the lower
limit of its operational field. But as we showed above through the derivation of the law of
conservation of energy, we can go from the limit of the Special Theory to that of Classical
28

Mechanics. The opposite is impossible. The analogy with the formula of kinetic energy thus
serves to determine the upper limit of the application of the Special Theory and the general one.
This is because both theories see energy as a continuous quantity. We can say here that the upper
limit of the application of both theories is found at the intersection of the curves. Beyond this
point, we can continue with modifications to obtain results in the quantitative plane, but they are
difficult to comment on in the qualitative aspect. They express at the same time the impossibility
of eliminating infinite quantities. Therefore, phenomena after the intersection are analyzed only
by Quantum Mechanics. From the intersection to point c, the phenomena express quantum
character and virtual spatial and temporal parameters. At point c, we have the limit of the
application of all physical theories. Here, the energy state of the object takes its maximum value.
The final removal of singularities through the concept of the Energy State
Based on the formula 𝐸 = 𝑚𝑐2
and the idea of its transformation, the work does not make any
difference between matter and field. It considers matter as a large concentration of energy. In this
approach, the object in space is seen as a field moving at its speed. It is an idea that Einstein sees
as the core of unification but calls it very difficult to realize mathematically. The work emphasizes
the conceptual aspect as such. (14)
For the realization of the idea, the work utilizes the central equation of Lorentz, l/t = c = cons,
which here expresses not the invariance of the speed of light, but that of energy. The difference
from the traditional perspective is expressed as follows; The energy state of the object after the
exertion of force becomes at the speed of light, but the quantitative value of its change is given
by the Fitzgerald-Lorentz Factor. This conclusion emphasizes why it is necessary to find the
minimal energy state of the material object.
The maximum values of (l) and (t) express the energy state of the object at the zero point. Whereas
the minimal values express it at point c. The maximum energy state is characterized by a value of
(l) that seems to correspond to the minimal length of Planck. With the concept of the Energy State,
we not only reinforce the quantum character of energy. Its main contribution here is related to the
possibility it provides for the removal of infinite quantities, not only in the law of energy but also
in momentum and force. Through the Energy State, the functional structure of physics is sought
to be realized. Which allows, at the level of the laws of energy-momentum force, to ascend and
descend through the known mathematical processes, derivation-integration.
5. UNIFICATION
The values of the Energy State of the object at points zero and c and the removal of the
singularity
The absence of energy seems to be the fundamental factor that causes the laws of Newtonian
Gravitation and Coulomb's laws to be considered as laws described through the concept of force.
This process of presentation is complicated in Maxwell's Field Laws where the mechanism of
force changes from that of Newton in terms of quantitative value, as noted by Lorentz. The work
solves the issues raised by the above laws through the law presented earlier. The elliptical form
that the graphic curve of this law takes is the one presented by Kepler. This can easily lead us to
Newton's law of gravitation. But through the new law of energy conservation, Maxwell's laws
can also be described. The source of the electromagnetic field is simply the electron that
transforms its energy with speed. This shows the elliptical form that it takes expressed in
Einstein's language or the electrostatic field spoken in Heaviside's language, who reformulates
Maxwell's equations in canonical language. The work starts from the idea that the above laws are
29

not expressed with the concept that sees energy as a continuous quantity. This feature is expressed
in the laws of Newton, Coulomb, and Maxwell. The work utilizes the fact that force is the second
derivative of energy and exists even in rest. This fact allows us to remove from the scene the
Boltzmann Constant, as well as the concept of charge. The work similarly acts with Newton's
gravitational constant. But it does not follow the path proposed by Einstein in the General Theory.
Despite appreciating the quantitative results achieved by him, it considers it insufficient. Firstly
because its values are limited in what is called the Schwarzschild Radius, which is very far from
Planck's Length. Secondly, and this is the main problem, Einstein's idea of space-time curvature
is artificial and a product of the lack of a final law of energy conservation. As noted above, the
forms that the measuring tools of space and time take are dependent on the form of the law of
energy conservation. Therefore, the graphic curve of space-time should match that of the graphic
form that describes the law of energy conservation of the object regardless of the size of the mass
it represents. This description seems necessary even for achieving a unified theory for theoretical
physics that describes macro and micro.
The work presents the laws of gravitation and electricity formulated by Newton and Coulomb not
as laws of force, but of energy. The formulas below, through the "Classical Radius" (𝑟𝑘𝑙) and
"Schwarzschild Radius" (𝑟𝑠ℎ𝑣) express the minimal energy state of objects with smaller and larger
mass than that of Planck. The energy state at rest, in analogy with the Special Theory, is the
smallest multiple of the Exposed Energy of the material object.
𝑘𝑒2
𝑟𝑘𝑙
= 𝑚𝑐2
(17)
2𝐺𝑚2
𝑟𝑠ℎ𝑣
= 𝑚𝑐2
(18)
Knowing the fact that 𝑒2
𝑐
⁄ = 𝑎ℎ, we divide both sides of Coulomb's law by c. We get the
equation 𝑚𝑐𝑟 = 𝑎ℎ, with the units of angular momentum. It expresses its character as a constant
quantity and is valid for any material object regardless of its mass.
𝑚𝑐𝑟 = 𝑎ℏ = 𝑐𝑜𝑛𝑠𝑡 (19)
The work does not make distinctions between matter and field. The energy state of the object
changes with the speed of light, but the quantitative value of this change is expressed by the
Lorentz Factor. Therefore, we use the general form of Lorentz's equation, distance/time = c, or r/t
= c. Which was constructed to express the invariance of the speed of light, but here it expresses
that of energy. We find here the force that originates from the electron itself, which defines its
energy state at rest as the smallest multiple of the Exposed Energy.
𝐹𝑚𝑖𝑛 =
𝑚𝑐2
𝑟𝑚𝑎𝑥
(20) ose 𝐹𝑚𝑖𝑛 =
𝑚𝑐
𝑡𝑚𝑎𝑥
(21)
Here 𝑟𝑚𝑎𝑥, expresses the "Classical Radius" for objects with small mass, such as the electron, and
the "Schwarzschild Radius" for those with large mass, such as the Earth. The conclusion reiterates
that the formulas for the laws of Coulomb and Newton conceived as laws of energy and not force,
express through the Maximum Radius, the minimal energy state of the object at rest.
The maximum energy state or the maximum exposed energy is given in an analogous form;
𝐹𝑚𝑎𝑥 =
𝑚𝑐2
𝑟𝑚𝑖𝑛
(22) or 𝐹𝑚𝑎𝑥 =
𝑚𝑐
𝑡𝑚𝑖𝑛
(23)
30

In general form, the above equations are expressed by the formula Force x radius = 𝑚𝑐2
= 𝑐𝑜𝑛𝑠𝑡.
The formula that seems paradoxical and simply inaccurate based on known formulations, has its
origin in the ratio 𝑟 𝑡 = 𝑐
⁄ It is based on the concept of the Energy State, which by representing
the Exposed Energy, removes from the theoretical scene the Kinetic Energy. This imposes that
the description of events analyzed through the parameters of space and time should have a
quantum character. The situation is analogous to Quantum Mechanics, which replaces the role of
Kinetic Energy with that of operators. We preliminarily state here that if the value of the force
measured from the quantitative perspective is the same regardless of the technique used, the
space-time parameters can have a virtual character, as we will see below when analyzing the
situations created at and beyond the limit of the applicability of the General Theory of Relativity.
The minimal radius is achieved using the help of the concept of the Energy State, which is seen
as the ratio of the exposed energy to the unexposed energy. Continuing to see the energy of the
material object still as a continuous quantity with a temporary character description, we write the
formulas for energy and momentum.
𝐸𝑚𝑖𝑛𝑒𝑥 =
1
𝐸𝑚𝑎𝑥𝑒𝑥
ose 𝐸𝑚𝑖𝑛𝑒𝑥 =
1
𝑚𝑐2
ose 𝐸𝑚𝑖𝑛𝑒𝑥. 𝐸𝑚𝑎𝑥𝑒𝑥 = 1 (24)
The results correspond to the part of the work where the exposed energy collected with the
unexposed energy has the value 1. In an analogous way, we write the formula for momentum.
𝐼𝑚𝑖𝑛𝑒𝑥 =
1
𝐼𝑚𝑎𝑥𝑒𝑥
ose 𝐼𝑚𝑖𝑛𝑒𝑥 =
1
𝑚𝑐
ose 𝐼𝑚𝑖𝑛𝑒𝑥. 𝐼𝑚𝑎𝑥𝑒𝑥 = 1 (25)
The concept of the Energy State as a continuous quantity is auxiliary; it only serves to determine
the maximum momentum. Whereas the real momentum of the object is always mc, so like energy,
it is a constant quantity. Reaching this seemingly paradoxical determination is expressed as
follows. The maximum energy state is the product of multiplying the state of rest. What changes
with speed in any energy state are the time and space parameters? Whereas the ratio between
them, which is always equal to c, expresses the fact that what really changes with speed is the
force. Therefore, momentum as a ratio of energy to speed, which is a ratio of space-time
parameters and equal to c, expresses this constant quantity for any Energy State analyzed. The
determination of the maximum momentum allows us to find the minimal radius, which represents
the maximum exposed energy.
𝑟𝑚𝑖𝑛𝑒𝑥 =
𝐼𝑚𝑎𝑥𝑒𝑥
𝑎ℏ
(26)
The minimal radius is multiplied by 2𝜋, which respects the ideas of the Descartes-Leibniz debate
that emphasizes the closure of the motion process, as well as reflects the circular character of the
energy graphic curve. The concept is not in contradiction with quantum mechanics. The reduced
constant is usually used to illustrate the Heisenberg Principle, and the one with full value to
characterize the minimal state of the object when talking about its spatial dimensions.
The fundamental space-time quantities have the same character in the representation of the
transformation of energy. We determine here the maximum and minimum radii of the material
object.
𝑟𝑚𝑎𝑥𝑒𝑥 =
𝑚𝑐𝑚𝑖𝑛𝑒𝑥
𝑎ℏ
(27) dhe 𝑟𝑚𝑖𝑛𝑒𝑥 =
𝑚𝑐𝑚𝑎𝑥𝑒𝑥
𝑎ℎ
(28)
31

Due to numerical values, the ratio 1/mc expresses for masses greater than zero, the minimal
momentum, and for smaller than zero, the maximum exposed momentum. Whereas mc, for
masses greater than zero, the maximum momentum, and for smaller, the minimal exposed
momentum. The table below generalizes the conclusions reached from the formulas through
examples.
Table 1 The table gives the results for the "Schwarzschild Radius" which correspond 97.6% to the General
Theory.
However, we see results that do not correspond with it, which if accurate, enable us to find the
limit of the applicability of the General Theory. Secondly, they help to create a new law of
gravitation, the field of application of which corresponds to Planck's Length.
We construct tables that graphically express the correlation force-radius mass
It is noted that for masses below the Planck Mass, the force does not depend on the mass of the
object.
The table below expresses in general form the correlation momentum-force-energy.
Table 2 The formulas for the calculation of space parameters and the forces.
m < mcrit m > mcrit
𝑟𝑚𝑎𝑥 =
𝛼ℏ
𝑚𝑐
2.1
Original domain
Impulsi = (mc)
𝑟𝑚𝑖𝑛 =
𝛼ℏ
𝑚𝑐
2.2
Mass (kg) 𝑟𝑚𝑎𝑥 (m) 𝑟𝑚𝑖𝑛 (m)
Electron 9.11 × 10−31 2.83 × 10−15
𝟏. 𝟑𝟐 × 𝟏𝟎−𝟓𝟕
Plank’s mass 1.33 × 10−9
1.93 × 10−36
𝟔𝟏. 𝟗𝟑 × 𝟏𝟎−𝟑𝟔
Universe 1 × 1053
𝟏. 𝟒𝟔 × 𝟏𝟎𝟐𝟔 2.58 × 10−98
32

𝑟𝑚𝑖𝑛 =
2𝜋𝛼ℏ
1/𝑚𝑐
= 2𝜋𝛼ℏ(𝑚𝑐) 3.1
Inverse domain
Impulsi = 1/(mc)
𝑟𝑚𝑎𝑥 =
2𝜋𝛼ℏ
1/𝑚𝑐
= 2𝜋𝛼ℏ(𝑚𝑐)
3.2
Fmax = mc2
/rmin = c/(2πaħ)
4.1
Fmax = mc2
/rmin = m2
c3
/aħ 4.2
𝐹𝑚𝑎𝑥𝑙𝒎𝒊𝒏_𝒓𝒆𝒂𝒍
2
= 𝐹(𝑟)𝑟2
5 .2
𝐹(𝑟) =
𝐹𝑚𝑎𝑥
𝑟2
𝑙𝒎𝒊𝒏_𝒓𝒆𝒂𝒍
2
⁄
=
𝑐
(2𝜋𝛼ℏ)
2
𝑟2 6.1 𝐹(𝑟) =
𝐹𝑚𝑎𝑥
𝑟2
2
⁄
=
𝑐3
𝛼ħ
𝑚2 𝑙𝒎𝒊𝒏_𝒓𝒆𝒂𝒍
2
𝑟2 6.2
Determining the Limit of the Applicability of Theoretical Physics
To achieve this goal, the work is based on two pillars. Firstly, it considers energy as a constant
quantity with a fully defined value, which gives it a quantum character. Secondly, through the
Energy State represented by the minimal and maximal radii, it determines the energy values at
every point including zero and c, which gives the overall table a fully quantum character. The
realization of the main idea begins with the clear determination of the limit of the applicability of
the General Theory and then that considered as final and supposed to be represented by Planck's
Length.
Determining the Limit of the Applicability of the General Theory of Relativity
From observing the energy curves, the Exposed Energy equals the Unexposed Energy at the
intersection, or at the speed √3 2
⁄ x c. Referring to the figure that presents the energy curves, the
work seeks to show first that the limit of the applicability of the General Theory is located
precisely at the intersection of the energy curves. The General Theory cannot analyze the
transformation process after the intersection or the radius that characterizes it up to the minimal
radius corresponding to Planck's Length. The calculation of the value of the Energy State at this
point is done by first determining the quantitative value of the energy that is partially transformed.
𝐸𝑝𝑖𝑘𝑝 =
𝑚𝑐2
2
(29)
At the intersection where the Exposed Energy becomes equal to the Unexposed, we have
presented, if speaking in the language of the Descartes-Leibniz debate, the partial transformation
of the energy of the object expressed through the Exposed Energy. The process is analogous to
that of Classical Mechanics which is given by the formula 𝐸𝑘𝑖𝑛 + 𝐸𝑝𝑜𝑡 = 𝑐𝑜𝑛𝑠.. The difference
given by the central equation of the work from the formula 𝐸𝑒𝑥 + 𝐸𝑝𝑒𝑥 = 𝑚𝑐2
= 𝑐𝑜𝑛𝑠, is that
now we are not talking about forms of energy, but about the energy of the material object itself as
a quantity that remains constant. The value of the radius of the intersection according to the
reasoning, comes by dividing the Schwarzschild Radius, or the maximal radius, by 2. How is this
value determined? Referring to the language of the work, the General Theory cannot answer the
question. It limits its field of application to the zero point and not to the intersection. Speaking
again in the language of the work, the Special Theory has very little interest in the intersection
and emphasizes that here the rest energy equals the relativistic kinetic energy and the rest mass
increases by 2 times, a result that is verified in accelerators.
33

Therefore, the limit of the applicability of the General Theory is located at the intersection of the
curves, where the radius is 2 times smaller. For verification, we first calculate the radius of the
intersection.
𝑟𝑝𝑖𝑘 = 𝑟𝑠ℎ𝑣 2
⁄ = 𝑟𝑚𝑎𝑥 2
⁄ (30)
The intersection of the curves expresses a situation analogous to where the rest energy equals the
relativistic kinetic energy. A situation after which Einstein's conclusions for its evaluation from
the quantitative perspective are accurate, but not in the conceptual aspect. The work proves that
the situations created after the value given by the Schwarzschild Radius, emphasize the quantum
character of the space and time parameters that are beyond the intersection, only virtual.
We draw the first conclusion from the radius of the intersection that replaces the Schwarzschild
Radius;
𝑟𝑝𝑖𝑘 = 𝑟𝑠ℎ𝑣 2 =
𝐺𝑚
𝑐2
⁄ (31)
The conclusion emphasizes that the maximum rotation speed of what the General Theory calls a
Black Hole is at the intersection of the curves and has the value √3 2 . 𝑐
⁄ , a value that marks the
limit of the applicability of this theory, which is still far from the limit speed of light.
Unlike the General Theory, the work uses the concept of force and not that of the curvature of
space-time. It remains faithful to the idea of building a functional theory based on the scale of
energy-momentum-force laws. Therefore, it uses the force-radius correlation given by the formula
𝐹𝑜𝑟𝑐𝑒 𝑥 𝑟𝑎𝑑𝑖𝑢𝑠 = 𝑚𝑐2
= 𝑐𝑜𝑛𝑠 in solving problems. We provide through this formula the ratio
of the force of the intersection and the Schwarzschild Radius or the minimal force.
𝐹𝑝𝑖𝑘
𝐹𝑠ℎ𝑣
=
𝐹𝑝𝑖𝑘
𝐹𝑚𝑖𝑛
= 2 (32)
Einstein makes a distinction between them because he does not consider energy as a constant
quantity.
Referring to the concept of curvature, he expresses the deflection of light in strong gravitational
fields through the angle of deviation, which for the work is simply an expression of the ratio of
the force originating from the object on the light. Regardless of the concepts, the results are the
same in both cases.
From the above, 𝑟𝑠ℎ𝑣 = 2𝑟𝑝𝑖𝑘and knowing that r_shv = 𝑟𝑠ℎ𝑣 = 2𝐺𝑚 𝑐2
⁄ , the angle of deviation
expresses the values of the ratio of the Schwarzschild Radius to the Radius of the intersection.
𝛼𝑑𝑒𝑣 = 4𝐺𝑚 𝑟𝑐2
⁄ = 4𝑟𝐺 𝑟
⁄ (33)
where 𝛼𝑑𝑒𝑣- Angle of deviation 𝑟𝐺- gravitational radius, r - distance planet-object
𝑟𝐺 - in the language used by the work, corresponds to the value of the Radius of the intersection.
Physics reflects the problem with the phenomenon called the Shapiro effect. The work considers
the ratio of the force of the intersection to the distance from the given object. The ratio of the
Radius of the intersection to the Schwarzschild Radius is seen as the ratio of the force that
34

represents the limit of the applicability of the General Theory to that of the limit of the
applicability determined by Newton's classical mechanics. The results achieved are the same as
those of Einstein's General Theory.
𝐹𝑝𝑖𝑘
𝐹𝑠ℎ𝑣
= 2 (34)
The ratio can determine the deviation of Mercury's perihelion from Newton's law of gravitation
calculated by Einstein in a similar way to that given in the formula of light bending. If the angle
of deviation is expressed in Newton's law, for example, with the value x, referring to the ratio of
forces, the real deviation different from that given by Newton is 2 times more,
The value found emphasizes that the correction should be made for every planet but considering
first the distance where the events occur. In general terms, we can say as follows;
𝛼𝑑𝑒𝑣 =
2 𝛼𝑑𝑒𝑣 𝑁𝑗𝑢𝑡𝑜𝑛
𝑟
(35)
Specific quantitative calculations are not the subject of this work. What we can still emphasize
for this problem is that both Newton's elliptical motion, or Einstein's rosette-type for Mercury, in
principle, express the way of the existence of the material object. Or expressed differently, the
motion described by them reflects the law of energy conservation whose graphic curve according
to the work is circular. Therefore, the different forms of Mercury's motion or any planet during
their existence period are forced to follow this curve. This life process developed in a spiral form,
thus tends towards the natural circular motion, which is hypothetically emphasized by
Copernicus. The conclusion emphasizes that the calculations on deviation from the law may need
to consider also the value of the Energy State of the planet or otherwise that of the exposed energy.
It determines the specific form of the energy curve which increasingly approaches the circle over
time.
Whether Newton or Einstein describes the process quantitatively, they cannot emphasize why the
planets move in forms that increasingly approach the circular one. This is because they lack the
law of energy conservation that expresses this form of presentation.
Eliminating Newton's Gravitational Constant and Charge in Coulomb's Law
In the explanations given, there seems to be no reason for the use of the Gravitational Constant.
The masses of the objects analyzed were larger than Planck's. The consideration of the problem
for masses smaller than Planck's considers the use of charge unnecessary.
The reasoning above leads to the conclusion that the values of the radii given in the results table
and converge with those of the Schwarzschild Radius should be divided by 2. This operation
encounters a difficulty in cases of objects with a mass smaller than Planck's, for example, the
electron. By determining the Schwarzschild Radius for all objects regardless of their mass with
the formula 𝑟𝑠ℎ𝑣 = 2𝐺𝑚 𝑐2
⁄ , physics attributes to the electron a radius 𝑟𝑠ℎ𝑣𝑒𝑙 = 1,321 .10 −57
𝑚.
But meanwhile, it emphasizes that the result found should not be considered physical reality,
because these dimensions are in contradiction with Planck's Length. Is this really the cause, or
does the problem have a principled character? The General Theory to find the Schwarzschild
Radius uses only the formula 𝑟𝑠ℎ𝑣 = 2𝐺𝑚 𝑐2
⁄ . If it applies it to all objects regardless of their
mass, it must first adhere to Schwarzschild's reasoning, which through extrapolation, assumes that
the object is at rest. This conclusion does not correspond to the case of the electron. At rest, it has
35

the Classical Radius, the value of which is 2,81 .10−15
𝑚. This value corresponds to the
Maximum Radius. The formula of the General Theory, which determines only one type of radius,
that of the Schwarzschild Radius, according to the work, confuses the roles of the Schwarzschild
Radius with the Classical Radius, determining the former as the Maximum Radius and the latter
as the Minimal Radius.
We write below the correction of the values of the radius of the electron.
𝑟𝑠ℎ𝑣𝑒𝑙 = 𝑟𝑘𝑙𝑒𝑙 = 𝑟𝑚𝑎𝑥𝑒𝑙 = 2.81 𝑥 01−15
𝑚 (36)
Referring to the ideas of the work that emphasizes that at the intersection we have the limit of the
applicability of the classical theory of electromagnetism, the Classical Radius should be divided
by 2. As a result of the confusion of the Schwarzschild Radius with the Classical Radius by
calculating through the Schwarzschild formula, it is the division between gravitation and
electromagnetism. The idea of uniting them into one theory is not successful, as proven by
Einstein and costing him half a century of effort. The difficulty presented above, where the
Schwarzschild Radius is confused with the Classical Radius, is clearly reflected in the theoretical
practice. Thus, the radius of the electron is determined sometimes with the value of the Classical
Radius, and sometimes divided by 2. Showing that in the second case, the explanation takes into
account that the value found is reflected based on the principles of Quantum Mechanics.
For the work, this result is logical and corresponds to what was analyzed above for the limit of
the applicability of the General Theory. The correction of the values is done as follows;
𝑟𝑝𝑖𝑘𝑒𝑙 = 𝑟𝑚𝑎𝑥𝑒𝑙 2
⁄ (37)
Respecting, but only formally, the presented table which emphasizes the correspondence of the
results with the General Theory, the work divides by 2 what is called the Schwarzschild Radius
for the electron, thus formally accepting it as the Maximum Radius. Meanwhile, recognizing the
situation, the correction is made in the actual calculations that help determine the final limit of
physical theories, a limit that corresponds to Planck's Length. The correction is valid for removing
the distinction of gravitational forces from electromagnetic ones, but also for constructing a new
law of quantum gravitation. Through the curves of exposed and unexposed energy that intersect
at points zero and c, we can conceptually present here an idea analogous to that of Dirac for matter
and antimatter. For the case of the electron, when the curve of Exposed Energy goes to point c,
we have the maximum energy state of it, where it can also be seen as a positron. The correction
given through the figures emphasizes first the results achieved from the work that uses the
concepts of the Minimal and Maximal Energy State, expressed through the Maximal and Minimal
Radius, and the General Theory, which uses only the concept of the Schwarzschild Radius.
The conclusion of the above analysis, which seems foreign to physics, is based on the graphic
curves of energy, which by defining it as a constant quantity, gives a completely quantum
character to the table through the concept of the Energy State. The work emphasizes here the idea
that the issue presented above is not the domain of theories that see energy as a continuous
quantity. These theories cannot precisely define the lower and upper limit of the applicability of
the laws, which as analyzed, is reflected only by the values of the Maximum and Minimum Radii.
Unifying Gravitation with Electromagnetism and the New Quantum Nature Law of
Gravitation, the Field of Application of Which Corresponds to Planck's Length.
36

Theoretical physics accepts the concept of the Schwarzschild Radius, but considers it a physical
reality only for objects with mass larger than Planck's. Meanwhile, it excludes other values, based
on the reason that space-time parameters are in contradiction with Planck's Length. Although
there is no theoretical proof that legitimizes this condition coming from Planck's table or
Wheeler's hypothesis, the work analyzes the situation after it is easily noted that many of the
values of the radii it provides contradict the condition. It determines the situation when the
Maximum Radius with speed reaches the value of the Minimal Radius where we have the
Maximum Exposed Energy.
The first step is presented by the force-radius correlation written as follows;
𝐹𝑚𝑎𝑥
𝐹𝑚𝑖𝑛
=
𝑟𝑚𝑎𝑥
𝑟𝑚𝑖𝑛
(38)
Using the formulas of the maximum and minimum radii, for example, those of the electron, we
easily find the corresponding force ratio. From the application of the numerical values of the
formula, we see that the ratio 𝐹max 𝑒𝑙 𝐹𝑚𝑖𝑛𝑒𝑙
⁄ is 2,13. 1042
. The transition from the minimum
force to the maximum exposed force, referring to the universal law that expresses the force-
distance relationship, leads to the reduction of the physical or real radius of the object by the
fourth root of the numerical value of the force ratio. The work determines the real radius of the
object, starting from the point of rest where its real radius according to it is 𝑟𝑚𝑎𝑥 2
⁄ until we reach
the minimal radius. In this area, beyond the intersection, which the work considers outside the
limit of the applicability of the General Theory, the space-time parameters that express the ratio
r/t =c, are of quantum character but only virtual. Respecting the force-radius correlation and the
universal law that expresses it, we substitute the forces with their respective radii and find the real
radius.
𝑙𝑟𝑒𝑎𝑙𝑞 =
𝑟𝑚𝑎𝑥 2
⁄
√
𝑟𝑚𝑎𝑥 2
⁄
𝑟𝑚𝑖𝑛
(41) 𝑜𝑠𝑒 𝑙𝑟𝑒𝑎𝑙𝑒 =
𝑟𝑟𝑒𝑎𝑙 𝑞
√
𝐹𝑚𝑖𝑛
𝐹𝑚𝑎𝑥
(39)
With minimal arithmetic manipulation, we write the last formula as;
𝑙𝑟𝑒𝑎𝑙𝑒 = √
𝑟max. 𝑟𝑚𝑖𝑛
2
(40)
Placing the numerical values, we apply the last formula for the electron
𝑙𝑟𝑒𝑎𝑙 𝑒𝑙 =
√2,81.10−15.1.321.10−57
2
= 1,364 . 10−36
𝑚.
The formula is valid for all material objects from the electron to the universe. It characterizes the
final state of any object regardless of its mass. At the point where the Energy State has the
maximum value and the force has the same value. From this point, which corresponds to Planck's
Length, we can find the value of the force anywhere we want by utilizing the force-distance
relation. The conclusion thus reflects a new law of quantum gravitation, which shows in a
theoretical perspective the way of the existence of a material object. We emphasize here that the
conclusions reached do not need the concept of charge or the gravitational constant. This
expresses the unification of gravitation with electromagnetism.
Comparing the numerical values with Planck's Length, we see the analogy;
37

𝑙𝑟𝑒𝑎𝑙𝑒
𝑙𝑝𝑙𝑎𝑛𝑘
= √0,98. 𝑎 (41)
Planck does not place a in his table, as it is discovered later by Sommerfeld. The conclusion
emphasizes that in nature, we cannot find values smaller than that of the Real Radius, which
corresponds to Planck's Length. It is not difficult to get exactly the result of this length in the
value emphasized by Planck. The Classical Radius of the electron divided by the Sommerfeld
Constant gives what we call the Characteristic Length of the electron. It corresponds to the value
3.86. 10−13
𝑚. For the work, this value expresses the state of the electron at rest. Or expressed
differently, its hit by the photon enlarges the value of its wavelength to the value we see. But as
emphasized before, the electron presents a minimal energy state at rest expressed through the
Classical Radius. The conclusion emphasizes that the ratio of Planck's Constant to the
Sommerfeld Constant gives the ratio of the magnetic field to the electric field.
ℎ
𝑎ℎ
=
𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑓𝑜𝑟𝑐𝑒
𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐 𝑓𝑜𝑟𝑐𝑒
Placing a expands the limit of the applicability of our laws to the point called rest. It also solves
the dilemma that preoccupied Newton expressed with the "First Force" for a universe that initially
could have been at rest. Placing a makes it possible to correct this problem that appears in the
works of Bohr, De Broglie, or Schrödinger, which attribute an infinite wavelength to the electron
at rest and zero at point c. Placing a and the concept of the Energy State allows us to state that the
relation ah conceived here as the smallest quantum of rest energy, can replace that given by h.
Placing a gives a quantum explanation, or a different one, to Heisenberg's Uncertainty Relation.
Placing initially the two equations allows us to see the differences between them.
Heisenberg's Relation Work's Equation
𝑑𝑝 𝑥 𝑑𝑥 ≥ ℎ 𝑚𝑐𝑟 ≥ 𝑎ℎ
In Heisenberg's relation, energy expressed by the concept of speed v is considered a continuous
quantity. It also shows that we are talking about small energy values. The situation reminds us of
the analogy with Classical Mechanics. Heisenberg's Uncertainty Relation, which claims that in
the small, the energy expressed by the concept of speed v, can be considered a continuous quantity,
legitimizes the placement of arbitrary values of momentum or the parameter x. It is enough to
satisfy the condition set by the author. The work's equation shows why the values of momentum
x length cannot be smaller than the Energy State determined by ah.
6. CONCLUSIONS
One of the fundamental reasons that motivates the work to follow the consequences of the
Descartes-Leibniz debate comes from the Method that emphasizes the rule of constructing
fundamental theories, a rule that conceptually separates them from today's theoretical models.
The work attempted to prove the idea initially presented by Descartes with the Thesis "On the
constant quantity of motion" as well as Leibniz's suggestion for its realization through the process
of transformation. Despite the progress it brought to physics, it could not be realized. More than
the success of the Special Theory that proved that the classical kinetic energy 𝐸𝑘 = 𝑚𝑣2
2
⁄ is
valid for low speeds, the reasons for non-realization are of a different nature. The goal is not
achieved neither by the invariance relations, such as the invariance of the speed of light proposed
by Einstein in the Special Theory, nor by the different forms of energy as operated in Newton's
Classical Mechanics. The attempt to go from the laws of force to those of energy expresses the
38

first fundamental defect of the Relativistic Theory. Not having at hand the formula 𝐸 = 𝑚𝑐2
,
which is discovered after the construction of the Special Theory, Einstein goes to the idea that
with speed the energy of the object increases, which for the work is an incorrect conclusion. The
figure below emphasizes the idea why it is not possible to go from the laws of a lower form like
force or momentum to those of energy, but the opposite is possible.
Despite being imposed due to the initial process of understanding nature, this way of advancement
does not achieve the goal. The figure shows, according to the work, the impossibility of this effort.
Figure 6
We can go from Einstein's laws to those of Newton, but the opposite is impossible. Likewise, we
can go from the laws of Quantum Mechanics to those described by Einstein, but the opposite
seems impossible. As above, we say by analogy why it is not possible to go from the laws of force
and momentum to those of energy, but the opposite is feasible.
However, energy cannot be considered a continuous quantity because this consideration leads to
infinite quantities. Placing another inherent characteristic of the object, the Energy State, removes
them from the physics scene, enabling the realization of Descartes' Thesis. Referring to the central
idea of the work, the process of deriving laws from Quantum Mechanics to the theories described
takes the simplest form. The process appears in the formulation below.
Energy- momentum -force
𝑚𝑐2
− 𝑚𝑐 − 𝑓
The process shows the difficulty of transitioning from simpler forms of laws to higher ones
through integration. The difficulty is analogous to the attempt that seeks through the shadow,
which is a product of the leaves of a tree, to find the number of leaves that created this shadow.
Or expressed differently, to go from a straight line to a circle. Which figuratively seems to also
represent the fundamental law of energy conservation.
ACKNOWLEDGEMENTS
The author would like to thank Klaudio Peqini for technical help.
39

APPENDIX
1) Elimination of Newton's gravitational constant
Newton's gravitational constant is defined as the force between two objects with a mass of one
kilogram at a distance of 1 m. Here it originates from the object's field itself. We first find,
referring to formula (26), the minimal radius of the object from which the maximum force
originates.
𝑟𝑚𝑖𝑛 =
𝛼ℏ
𝑚𝑐
=
7.297×10−3
1.054×10−34
1.3×108 = 2.563 × 10−45
𝑚 (42)
The second step requires determining the force from this radius, which is of virtual character.
𝐹𝑚𝑎𝑥 =
𝑚𝑐2
𝑟𝑚𝑖𝑛
=
(1×3×108
)
2
2.562×10−45 = 3.513 × 1061
𝑘𝑔 𝑚/𝑠𝑒𝑐2
(43)
We find the value of this force at a distance of 1 m in the third step.
𝐹1 =
𝐹𝑚𝑎𝑥
[𝑟1 𝑙𝑚𝑖𝑛_𝑟𝑒𝑎𝑙
⁄ ]
2 =
3.513×1061
[1 1.364×10−36
⁄ ]2 = 6.54 × 10−11
(44)
The result obtained is 98% of the value given for Newton's gravitational constant.
2) Elimination of the fundamental constant of Coulomb
As in the previous cases, we find the minimal radius of the electron and then the maximum force.
𝑟𝑚𝑖𝑛 =
𝑎ℎ
1 𝑚𝑐
⁄
=
7,293.10−3
.6,62.10−34
1 9,1.10−31
𝑘𝑔.
⁄ 3.108
𝑚/𝑠
= 1,321.10−57
𝑚 (45)
The value corresponding to the Schwarzschild Radius is divided by 2 as emphasized in the work.
𝐹𝑚𝑎𝑥𝑒𝑙 =
𝑚𝑐2
𝑟𝑚𝑖𝑛 2
⁄
=
9.1.10−319.1016
1.321 .10−57 2
⁄
= 1.231.1044
𝑘𝑔 𝑚𝑠2
⁄ (46)
Now we find the value of this force at a distance of 1 m.
𝐹1 =
𝐹𝑚𝑎𝑥
[𝑟1 𝑙𝑚𝑖𝑛_𝑟𝑒𝑎𝑙
⁄ ]
2 =
1,231 .1044
[1 1.364×10−36
⁄ ]2 = 2,3 × 10−28
(47)
The value is the same as given by Coulomb's Law:
𝐹(𝑟) = 𝑘𝑒2
= (9)(109)(1.6 × 10−19)2
= 2.3 × 10−28
𝑘𝑔𝑚 𝑠𝑒𝑘2
⁄ (48)
3) Calculation of the values of nuclear forces
The work does not make any distinction between the types of forces in nature. It is known that
the forces called nuclear forces act at a distance of 10−14
𝑚. The problem solved is analogous to
the previous examples. The only specificity is that the force for objects with mass smaller than
Planck's Mass does not depend on mass. Therefore, in calculations, we use the mass of the electron
and not the proton.
40

𝐹𝑚𝑎𝑥 =
𝑚𝑐2
𝑟𝑚𝑖𝑛 2
⁄
=
9,1 .10−31
𝑘𝑔 𝑥9.1016
𝑚2/𝑠𝑒𝑐2
1,321 .10−57
2
⁄
= 1,22. 1044
𝑘𝑔𝑚/𝑠𝑒𝑐2
(49)
𝐹1 =
𝐹𝑚𝑎𝑥
[𝑟1 𝑙𝑟𝑒𝑎𝑙
⁄ ]2
=
1,22,×1044
[1𝑥10−14
1.364×10−36
⁄ ]
2 = 2.94 𝑘𝑔 𝑚/𝑠𝑒𝑐2
(50)
4) Calculation of the acceleration on the surface of the Earth
The problem is related to the demand to find out what is the force of the Earth with mass
5,974.1024
kg on its surface when the value of its radius is 6371. 106
𝑚. The first step requires
determining the minimal radius of it. Then the maximum force that originates from the real length
1.364 .10−36
𝑚:
𝑟𝑚𝑖𝑛 =
𝛼ℏ
𝑚𝑐
=
7.297×10−3 1.054×10−34
5,974 𝑥 3.108 = 4.291 × 10−70
𝑚 (51)
𝐹𝑚𝑎𝑥 =
5,974 𝑥1026 (1×3×108)
2
4,291×10−70 = 1.252 × 10111
(52)
Now, we find the value of this force on the surface:
𝐹1 =
𝐹𝑚𝑎𝑥
[𝑟1 𝑙𝑟𝑒𝑎𝑙
⁄ ]2
=
1,252×10111
[6,371𝑥106
1.364×10−36
⁄ ]
2 = 5. 74 × 1025
(53)
Knowing the mass of the Earth and the formula of mechanics for acceleration, we write:
𝑎𝐸 =
𝐹𝑟𝑒𝑎𝑙
𝑚𝐸
=
5,74 𝑥1025
5,974𝑥 1024 = 9,61 𝑚/𝑠𝑒𝑐2
(54)
The result is 98% of the value usually given for the acceleration of free fall.
REFERENCES
[1] Lee, S.hyun. & Kim Mi Na, (2008) “This is my paper”, ABC Transactions on ECE, Vol. 10, No.
5, pp120-122.
[2] Gizem, Aksahya & Ayese, Ozcan (2009) Coomunications & Networks, Network Books, ABC
Publishers.
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[2] Leibniz, G.W. (1686). Letter to Henry Justel, June 9, 1686.
[3] Kirchhoff, G. (1870). Annalen der Physik, 141, 480.
[4] Einstein, A. (1967). Evolution of Physics. In Selected Works (Vol. 4, p. 394). Moscow: Nauka
Publishing House.
[5] Maxwell, J.C. (1865). A dynamical theory of the electromagnetic field. Philosophical Transactions
of the Royal Society of London, 155, 459-512.
[6] Einstein, A. (1967). Evolution of Physics. In Selected Works (Vol. 4, p. 510-511). Moscow: Nauka
Publishing House.
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[7] Galilei, G. (1632). Dialogo sopra I due massimi sistemi del mondo.
[8] Einstein, A. (1948, August 19). Letter to Lincoln Barnett. Archive of the Albert Einstein.
[9] Misner, C.W., Thorne, K.S., & Wheeler, J.A. (1973). Gravitation. W.H. Freeman and Company,
pp. 400-450.
[10] Dirac, P.A.M. (1928). The quantum theory of the electron. Proceedings of the Royal Society of
London, Series A, Containing Papers of a Mathematical and Physical Character, 117(778), 610–
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[11] Feynman, R.P., Leighton, R.B., & Sands, M. (1964). The Feynman Lectures on Physics, Vol 1.
Addison–Wesley, Chapter 16.
[12] Amelino-Camelia, G. (2000). Relativity in space-times with short-distance structure governed by
an observer-independent (Planckian) length scale. International Journal of Modern Physics D,
11(01), 35-60.
[13] Fischer, E.P. (2000). *Niels Bohr*. Siedler, p.91.
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Author
-Birth Date:August 18, 1959
- Education: Technical School of Fier (1974-1978); Goethe Institute, Mannheim, Germany (1992-
1993)
- Occupation: Political analyst, publisher of several periodicals such as "Dita Informacion" (1993-
1998), "ABC" (2005-2009), and "Konica" (2017-2024) under Nazarko Publishing.
Professional Activities:
- Journalist
- Advisor to the President of the Republic (1991-1992)
- Advisor to the Prime Minister of Albania (1998-2001)
Conference Participation and Presentations:
- International Conference on Physics, Crete, Greece (2015)
42

- Rome, Italy 2022 Marcel Grossmann meeting
- La Sapienza, University of Rome (2016, 2017)
- Moscow (2018)
- Armenia, 5th
Zeldovich meeting (2023)
Additional Achievements:
- FIDE Master in chess
43

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