.
CLASSICAL MECHANICS OF CHARGE, SPACE, TIME WITHOUT
MASS DIMENSION
CHAN RASJID KAH CHEW
10 April 2024
Abstract. This paper continues from the author’s earlier paper of Simple
Unified Theory (SUT).It extends the new electric classical mechanics based
on electric charge, space and time without mass as an independent physical
dimension. Mass is now a defined concept as magnitude of charge times
volume of charge. New definitions of an electric unified atomic unit and an
electric kilogram have been introduced. A complex Coulomb’s law is de-
veloped with a formal analytical extension of the electric charge as a com-
plex quantity; a charge Q of magnitude q is represented as z = Q + iqk
where the constant k is dependent on the system of units. The complex
Coulomb’s law for the forces between two charges z
1
, z
2
at distance r apart
is : F =
1
4πϵ
0
z
1
z
2
r
2
ˆ
r. The forces acting between two Hydrogen-1 atoms
would be shown to have a net attractive force; this explains how gravity is
the result of a slight excess of Coulomb attractions over repulsions.
1. Introduction
This paper continues from the author’s earlier paper on Coulomb electric
gravity and an aether simple unified theory (SUT) [6]. The paper proposes a
new classical mechanics without mass as an independent physical dimension
of the natural world. It may be called ‘Electric Mechanics’ as it is a new classical
mechanics without mass as an independent physical dimension of the natural
world. The fundamental physical dimensions of nature would be charge, space
and time instead of the traditional mass, space and time. Mass in electric me-
chanics is now a defined concept dependent on electric charge and space. The
electric mechanics is fundamentally the same mechanics of Newton’s ‘Principia’
[1]. Although this introduces no new principle in classical mechanics, it does
have great implications to physics if it is found to be the correct mechanics of
the physical world.
Currently, mainstream physics academia has accepted the relativistic me-
chanics of Einstein’s special relativity to be the correct mechanics of the physi-
cal world replacing Newtonian mechanics. It has to be noted that the relativis-
tic mechanics is founded on the postulates of special relativity together with
the hypothesis of mass-energy equivalence quantitatively represented by the
equation E = mc
2
. Newtonian mechanics, on the other hand, is founded on
Newton’sthree axioms of motion together with the concept of an invariant mass
Key words and phrases.
1
CLASSICAL MECHANICS OF CHARGE, SPACE, TIME WITHOUT MASS DIMENSION 2
as ‘quantity-of-matter’. The two mechanics are two completely independent me-
chanics that cannot be compared or brought into relationship in any manner.
The physical reality of nature may only be consistent with one mechanics, ei-
ther Newtonian mechanics or relativistic mechanics, but not both. The physics
community has to come to a conclusion as to which of the two mechanics truly
represents physical reality. It has to either accept Newton and dismisses Ein-
stein or it accepts Einstein and dismisses Newton; there is no compromise.
2. Postulates Of The Simple Unified Theory (SUT)
The mechanics of SUT is a new interpretation of Newtonian mechanics de-
veloped within the physical dimensions of space, time and electric charge. The
independent physical dimension of mass - as ‘quantity-of-matter’ - is no more
needed. Newton at his time could not have known that matter consists of atoms
with charged particles of protons and electrons. Today, we have the new knowl-
edge of the fundamental makeup of matter as atoms. It is this new knowledge
that allow us to reinterpret Newton’s ‘quantity-of-matter’. The new formal defini-
tion of mass can now be proposed solving one of the unsolved ‘greatest mystery’
of physics: ‘what is mass?’.
Mass is defined as the magnitude of charge times volume
For an amount of electric charge Q occupying a volume V, its mass is the mag-
nitude of QV.
There are eight (previously seven; added the mass postulate) basic postulates
of SUT:
(1) The electric charge - The material substance of the universe is the elec-
tric charge,positive and negative. The total amount of positive charge in
the universe is a constant equal to the total amount of negative charge.
(2) The aether - The aether is the substance of space. It is a superposition
of two uniform charge density +ρ
a
and −ρ
a
. It fills all space except
the volumes of discrete electric matter. An aether volume element is
electrically neutral, but may be polarized giving an electric dipole.
(3) Matter - Atoms of matter are formed from the fundamental subatomic
particles of the proton and the electron. The electron has an electron
charge of −e distributed uniformly within a sphere of constant vol-
ume V
e
. The proton has an equal electron charge of +e distributed uni-
formly within a sphere of constant volume V
p
.
(4) Matter creation and uncreation - Subatomic particles in pairs of equal
unlike charges, such as the proton and electron, are created from the
aether charge; they may be uncreated returning to the aether.
(5) Force - There is only a single universal force. It is the Coulomb electri-
cal forces of attraction and repulsion. The attraction of unlike charges
exceeds that of repulsion between like charges by a small fixed amount.
CLASSICAL MECHANICS OF CHARGE, SPACE, TIME WITHOUT MASS DIMENSION 3
(6) Energy - The source of all energy is electrical. It takes only three forms:
1) light energy as electric waves in the aether 2) electrical potential en-
ergy of matter 3) the kinetic energy of matter. Matter creation and un-
creation may involve transformation of energy.
(7) Universalgravitation - Gravity is the result of the small excess of Coulomb
attraction over repulsion. If the electric constant for Coulomb repul-
sion is k =
1
4πϵ
0
fo SI units, then the electric constant of attraction is
k(1+d) where d = Gm
2
h
/2ke
2
; G being the gravitational constant, m
h
the mass of hydrogen
1
H in kilogram, e the electron charge in coulomb.
(8) The mass postulate - The mass of an amount of electric charge Q occu-
pying a volume V is defined to be the magnitude of QV.The dimension
of mass is [Coulomb][Length]
3
. It is proposed that the charge of the
proton and the electron have volumes of V
p
, V
e
respectively; this ef-
fectively introduces two universal constants in physics. Their masses
would then be eV
p
, eV
e
, e being the electron charge.
3. New Definition Of Electric Unified Atomic Mass Unit And Electric
Kilogram
The author has papers [2, 3, 4, 5] which dismisses Einstein’s hypothesis of
mass-energy equivalence. Without mass-energy equivalence,the law of conser-
vation of mass would be restored. The notion of nuclear binding energy within
nuclii of atoms due to missing mass would be dismissed. As it is found that the
neutron disintegrates into a proton and an electron, its mass would be the same
as that of hydrogen
1
H; it may be taken to be another state of the hydrogen
1
H
atom. Within the nucleus of an atom, the neutron would be contributing an ex-
tra proton and a nuclear electron. This would mean that atoms have masses
which would be a whole number of units of the mass of
1
H. So the electric uni-
fied atomic mass unit may be defined as the mass of an atom of
1
H replacing the
definition based on Carbon-12; it is an invariant independent of the quantum
state of the atom.
The electric unified atomic mass unit (eu) is the mass of hydrogen
1
H
With our new definition of mass dependent on charge and volume, the mass of
hydrogen
1
H would be e(V
p
+ V
e
) eu.
With this new definition of the electric unified atomic mass unit eu,the macro-
scopic SI base unit of mass, the electric kilogram ekg, may be defined as 1000
N
A
eu, N
A
being the Avogadro’s number. If the universal constant N
A
is de-
fined to be an exact number, then we have a new electric kilogram definition
that is all based on defined universal constants without the need of the old kilo-
gram definition which requires keeping and maintaining a prototype sample of
the kilogram.
The SI electric kilogram is defined to be 1000 N
A
eu
CLASSICAL MECHANICS OF CHARGE, SPACE, TIME WITHOUT MASS DIMENSION 4
Although we have introduced electric versions of the unified atomic mass and
the kilogram with dimensions of [Coulomb][Length]
3
, for all practical purpose,
the traditional non-electric versions and their new electric versions may be used
interchangeably as they are defined to be consistent.
4. Complex Electric Charge And Complex Coulomb’s Law
Universal gravitation is now explained as being due to the slight excess of
Coulomb electric attractions over repulsions. Analytically, it may be formal-
ized by introducing complex versions of the electric charge and the complex
Coulomb’s law.
An electric charge Q with charge magnitude q has a complex charge
of z:z = Q + iqk
k being a constant to be determined dependent on the system of units.
The complex Coulomb’s law would now be defined between two complex
charges z
1
, z
2
at a distance of r apart. In SI units the Coulomb’s force would be:
F =
1
4πϵ
0
z
1
z
2
r
2
ˆ
r (1)
Based on equation (1), the forces between two Hydrogen-1 atoms may be de-
rived. The total repulsive forces,takingonly the real parts,would be:
1
4πϵ
0
r
2
(2e
2
−
2e
2
k
2
),ebeing the electron charge. The total attractive forces would be
1
4πϵ
0
r
2
(−2e
2
−
2e
2
k
2
). The net force acting would be the sum of the attractive and repulsive
forces: −
1
πϵ
0
r
2
e
2
k
2
. Since the sign of the net force is negative, it implies there
is a net attractive force between the two Hydrogen-1 atoms. To determine the
value of k for SI units,the known gravitational force is equated with −
1
πϵ
0
r
2
e
2
k
2
.
With G as the gravitational constant, m
h
the Hydrogen-1 mass in kilogram:
e
2
k
2
πϵ
0
= Gm
2
h
k =
m
h
e
p
πϵ
0
G
An electrically neutral body has a mass proportional to the number of Hydrogen-
1 atoms. Thus the gravitational forces between two neutral bodies would obey
the same Newton’s inverse square law of universal gravitation; only now, it is
founded on Coulomb’s law. With this Coulomb electric gravity, the ‘unsolved
mystery of gravity’ is now unraveled.
References
[1] The Mathematical Principles of Natural Philosophy, English translation by Andrew
Motte(1846).
https://en.wikisource.org/wiki/The_Mathematical_Principles_of_
Natural_Philosophy_(1846).
CLASSICAL MECHANICS OF CHARGE, SPACE, TIME WITHOUT MASS DIMENSION 5
[2] Chan Rasjid. The Relativistic Mechanics of E=mc2 Fails
https://vixra.org/1810.0005
[3] Chan Rasjid. Mass Energy Equivalence Not Experimentally Verified
https://vixra.org/abs/1810.0003
[4] Chan Rasjid. Nuclear Binding Energy Fails(Is Mass Spectrometry Accurate?)
https://vixra.org/abs/1809.0491
[5] Chan Rasjid. Chemical Analysis Of Plain Distilled Water May Refute Mass-Energy
Equivalence Of E=mc
2
https://vixra.org/1912.0378
[6] Chan Rasjid. Coulomb Electric Gravity And A Simple Unified Theory (SUT).
https://vixra.org/abs/1808.0211
Email address: chanrasjid@gmail.com
URL: http://www.emc2fails.com
Singapore
