written in 2016
by Tan Tran, Ph. D.
This paper is in copyright. No reproduction
of any part
may take place without the written permission of the author
This is the first essay on super-science in which we establish
the basic equations of gravitation and electromagnetism for
the universe composed of two material and spiritual worlds
inseparably connected together. The equations are inspired
from the equations of Maxwell in the theory of
We generalize the theory of electromagnetism to
gravitation and karma, then explore the theory of life and
We do not expect rigor in the proofs of the
equations because we don't have for super-science any
scientific experiment in laboratory so far. We can say these
are “thought experiments” beyond the recent knowledge in the
INTRODUCTION TO UNI-FORMS
The basic tools used in mathematics, mechanics,
physics are the real and complex numbers upon which are
established equations and scientific theories. None of those
theories can describe the spirits, senses, emotions and
minds. To introduce a new theory concerning both matter and
spirit, we need to create a new category of tools called
A uni-form is described as follows:
(x|jξ) or (u|jv)
which are composed of two forms (x|j0) and (0|jξ), or of two
forms (u|j0) and (0|jv) called
respectively the MATERIAL PART and the SPIRITUAL
PART. The form can be regarded as a number (x|jξ) where
x and ξ are real numbers, or as a vector (u|jv)
where u and v are real vector. The letter
j used here is only a symbol indicating that jξ and jv
belong to the category of spiritual, and it is not the
imaginary number i. So the writing j2 is
For scalar uni-function, we can write
m = (mr|jms)
where mr is a scalar function of 3 real variables
(x,y,z), and ms is a scalar function of 3 real
For a vector uni-function, we van write
F = (Fr|jFs)
where Fr is a vector function of 3 real
variables (x,y,z), and Fs is a vector
function of 3 real variables (ξ,η,ζ). We can also write for
With such representation, the uni-number (x|jξ) can be
regarded also as a uni-vector (u|jv)
where u(x) and v(ξ) are vector functions of a
The uni-forms have the following operations
ADDITION OF UNI-FORMS
(x|jξ )+(x'|jξ') = ((x+x')|j(ξ+ ξ')) = (x'|jξ')+(x|jξ) for
(u|jv)+(u'|jv') = ((u+u')|j(v+v'))
= (u'|jv')+(u|jv) for
Addition is commutative. We can verify easily the
associativity of the addition too.
The zero uni-form (0|j0) is the additive
MULTIPLICATION WITH REAL NUMBERS
α(x|jξ) = (αx|jαξ) = (x|jξ)α
α(u|jv) = (αu|jαv)
where α is a real number.
Multiplication is associative with real
Note that we don't
allow multiplication of uni-forms with imaginary numbers or
with complex numbers.
PRODUCT OF 2 UNI-FORMS
We call INNER PRODUCT OF 2 UNI-FORMS the operation
(x|jξ) . (x'|jξ') = xx'- ξξ'= (x'|jξ') .
= u O u'- v O v'= (u'|jv').(u|jv)
the dot “.” is the inner product, and the small
circle “O” is the scalar product of 2 real vectors.
Recall the scalar product of 2 real vectors
u O u' =
' v O v' =
= (xx'+yy'+zz') - (ξξ'+ηη'+ζζ')
The inner product of 2 uni-forms is a real number.
The inner product can not be performed with 2
uni-forms of different categories, for example:
number (x|jξ) with a vector (u|jv) of several
variables, or two vectors (u|jv) and (u'|jv')
where u and u' have different variables,
or v and v'have different
Inner product is different from scalar product. Inner
product applies to uni-forms in both cases of numbers and
vectors. Scalar product applies only to real vectors.
ABSOLUTE VALUE AND NORM
The inner square of a uni-form
(x|jξ)² = x²-ξ²
= u o u – v o v
positive, null, or negative. The absolute value of
= √(|x²-ξ²|) ≥ 0
And the absolute value of (u|jv) is
|(u|jv)| = √(|u
O u – v O v|) ≥ 0
We call norm of a uni-form the expression
= √(|x²+ξ²|) ≥ 0
= √(|u O u + v O v|) ≥ 0
2 vectors (1|j0) and (0|j1) are called the multiplicative
A uni-form is NULL if its absolute value is 0, that
The ZERO uni-form (0|j0) is a null uni-form.
The 2 unit uni-vectors (1|j0) and (0|j1) are
call CROSS PRODUCT of 2 uni-vectors (x|jξ) and
(x'|jξ') the following operation
(x|jξ) X (x'|jξ') =
Two uni-vectors are said to be parallel if their cross
product is the zero vector
(x|jξ) X (x'|jξ') = (0/j0)
their components are proportional.
PRODUCT OF REAL VECTORS WITH UNI-VECTORS
= ((w X u)|j(w X v))
wXu and wXv are the cross products
of 2 real vectors of 3 components.
w X (u|jv)
= - (u|jv) X w
call u, v, w...the uni-forms. We have the following formula.
u . v = v . u
u . (v + w) = u . v + u . w =
(v + w) . u
u X v = -(v X u)
u X u = 0
u X (v + w) = u X v + u X w
au X bv = ab(u X v) a, b are
Its easy to verify the following formula
d(x|jξ) = (dx|jdξ)
d(u + v) = (du + dv)
d(u . v) = (du . v) + (u . dv)
d(u X v) = (du X v) + (u X dv)
UNI-VECTOR SPACE OF THE UNIVERSE
We adopt here THE PRINCIPLE OF DUALITY OF THE UNIVERSE
by which our universe is composed of TWO INSEPARABLE
WORLDS: THE MATERIAL WORLD AND THE SPIRITUAL WORLD CONNECTED
principle of duality is our PRINCIPLE OF UNIVERSALITY.
To represent the universe in mathematical mechanics, we
consider 6 dimensions in a one-one correspondence:
LENGTH ------------ SENSE
DEPTH -------------- EMOTION
HEIGHT ------------ MIND
The universe is represented by a UNI-VECTOR SPACE OF 6
DIMENSIONS x, y, z for length, depth, height, and jξ ,
jη , jζ for sense, emotion, mind.
We consider the uni-vectors of 6 components in that UNI
(x,y,z|jξ ,jη ,jζ)
components x, y, z are called MATERIAL COMPONENTS,
and the 3 components jξ , jη , jζ are called SPIRITUAL
Component x represents length
y –---------- depth
z ------------ height
jξ ----------- sense
jζ –--------- mind
Such one-one correspondence once adopted can not be changed
in the paper. That yields 3 two-components uni-forms (x/jξ),
(y,jη), (z/jζ ).
For convenience of writing, we can consider the 6-component
uni-vector as a 2-component uni-vectors (u|jv)
with the material part u=(x,y,z) and the spiritual
part jv=j(ξ , η , ζ ).
In that uni-vector space we take for inner product
(x,y,z|jξ ,jη ,jζ) . (x',y',z'|jξ ',jη ',jζ') =
have similar operations and formula as for 2-uni-vectors in
the above sections.
The inner square of a 6-uni-vector is
(x,y,z|jξ ,jη ,jζ)² = x²+y²+z² -ξ²-η²- ζ²
positive, negative, or zero.
In that uni space we consider a uni-system of reference of 6
axes Ox,y,z,jξ ,jη ,jζ.
have then a one-one correspondence of that uni-system of
such axes with a REAL SYSTEM OF 6 REAL AXES Ox,y,z,ξ,η
By convention, if the real system of six axes is
orthonormal, we say the uni- system of 6 axes is
orthonormal. Such orthonormal systems are used in the
rest of this paper.
The unit vectors of the real system on the 6 axes are of
length 1: e1, e2, e3, e4,
vectors are orthogonal to one another and form an
orthonormal basis for the real space of 6 dimensions. And
the one-one corresponding unit vectors of the 6 axes in the
uni- system are by abuse of notations: e1, e2,e3,
je4, je5, je6.
We verify that the inner product of any 2 of those 6
uni-vectors is zero. They form an orthonormal basis for the
An event is a point in the uni-space with 6 dimensions
(x,y,z|jξ,jη,jζ), the three (x,y,z) representing the
material components, the three (jξ,jη,jζ) the spiritual
components of the event.
If we consider the orthonormal subspace (x,y,z|j0,j0,j0), we
call it the MATERIAL WORLD where all the theories of
sciences mathematics, mechanics, physics, chemistry,
cosmology...have been developed in the human history until
today. In this material world, because we consider only x,
y, z, we can identify the material event (x,y,z|j0,j0,j0)
with the real event (x,y,z) as people have done. Specially,
Einstein has added 1 more dimension 'ct' to the space-time
in his theory of Relativity. We don't criticize scientists
and theoreticians of materialism. Only we open the door to
the new theory of universality. When performing operations
in the material world separably, we will write x for (x|j0)
by reason of simplicity.
If we consider only the orthonormal subspace
(0,0,0|jξ,jη,jζ), it is called the SPIRITUAL WORLD.
We can identify the spiritual event (0,0,0|jξ,jη,jζ) with
the event of only 3 components (jξ,jη,jζ) to simplify the
writing in the mathematics and sciences theories of
spiritual studies. Also when working with the spiritual
world separately, we will write jζ for (0| jζ) for
simplicity. That is what we will do later to show people the
imperfect structure of spiritualism. But it is not the main
purpose of this research in the theory of universality which
we are developing. We simply warn some people not to use
the theory of universality to advocate for their
spiritualistic doctrines or religions.
FUNDAMENTAL EQUATIONS OF
ENERGY IN MOTION
The object of this paragraph is to establish formula for
mass and energy in motion.
But first we study laws in the material world and next we
extend the results to the spiritual world.
mechanics, on an axis when a force F displaces a distance
du, it produces an energy de by the relation (here all the
numbers are REAL)
de = Fdu or F = de/du
By the principle of Newton, when the force F moves a mass m
at speed q=du/dt, we have the momentum p=mq
F = dp/dt = d(mq)/dt
Therefor we have the equation
(1) de/du = d(mq)/dt
Energy e and mass m are already proven to be related by the
equation e = mc2 (See Tran, ON THE FORMULA e =
Energy e and mass m are real-valued functions of one real
variable u. The equation (1) is
d(mc2) = (dm.q+m.dq)
(c2- qdu/dt)dm =
Integrating we have
properly the constant of integration we have the formula
But in the material world considered separately, we identify
the material uni-form u=(x/j0) with the real number x, and
the material speed du/dt with dx/dt=v
The 2 formula (2) and (3) are the FUNDAMENTAL FORMULA FOR
MASS AND ENERGY IN MOTION IN THE MATERIAL WORLD CONSIDERED
SEPARATELY. Don't forget that the material world is
inseparably connected to the spiritual world, and equations
(2) and (3) are only PARTIAL in the sense that every
complete equation must cover both material and spiritual
When v=0, we have
and e0 are the mass and energy at rest.
Lorentz found the coefficient
γ = (1-v2/c2)-1/2
research for a linear transformation of coordinates, which
could explain the null results in Michelson-Morley
experiment. In his time scientists did not know the theories
of space-time of Minkowski and relativity of Einstein
We go now to the spiritual world. To have equations like (2)
and (3) in the spiritual world, we simply replace x by jξ,
and v=dx/dt by jw=jdξ/dt, and q2=(0|jw)2
In equations (4) and (5), m, m0 and e, e0
are spiritual masses and energies in the spiritual world.
The equations (4) and (5) are related to the equations (2)
and (3) in the connection of the spiritual part with the
material part in the universe.
We have at this point 2 coefficients
The subscripts r and s stand for
material and spiritual.
In the equations (4) and (5), the mass and energy in
motion are decreasing functions of w, and w can increase to
infinity. That is, a spirit can fly as fast as it can, even
faster than light. The faster it flies, the lighter are its
mass and its energy. When the spirit speed is infinity, its
mass and energy tend to zero. Because v and w are related,
we can expect that the material speed v can also be greater
than the speed of light c, it is what we will find out next.
TRANSFORMATION OF COORDINATES
We look back at the technique used by Lorentz to prove his
transformation of coordinates and the technique used by
Minkowski and Einstein in their theories. We will use here
similar technique to make a transformation of coordinates in
the uni-space of 6 dimensions.
To do that, we need a discussion on the concept of
ABSOLUTE AND RELATIVE.
By the principle of duality, the universe is composed of 2
inseparable material and spiritual worlds. The universe is
THE UNIVERSE OF ENERGY AND MASS TRANSFORMING CONSTANTLY
BETWEEN THE TWO STATES OF REST AND MOTION. ENERGY CHANGES TO
MASS AND MASS CHANGES TO ENERGY CONSTANTLY. THE MUTUAL
CHANGES OCCUR ON THE BACKGROUND OF THE STATE OF
NO-REST-NO-MOTION, WHICH IS NONE-OF-REST-NONE-OF-MOTION.
MATHEMATICALLY, MECHANICALLY, PHYSICALLY THAT BACKGROUND IS
THE ABSOLUTE STATE OF THE UNIVERSE. ON THAT ABSOLUTE
BACKGROUND EVERY THING IN THE UNIVERSE APPEARS AND CHANGES.
Therefore an ABSOLUTE SYSTEM OF REFERENCE EXISTS
FOR THE UNI-SPACE OF 6 DIMENSIONS.
Any system of reference at rest in an absolute system is
A moving system is relative.
If (O) is a relative system, and if another system (O') is
moving in the system (O), the 2 systems are relative to each
other, which is the case Einstein considers in his theory of
We have to distinguish 2 different cases:
1/ Two systems (O) and (O') are moving relatively to each
other INSIDE AN ABSOLUTE SYSTEM
2/ Two systems (O) and (O') are moving relatively to each
other, DENYING the existence of absolute system. This
case 2/ is of Einstein in his theory of relativity (The
PRINCIPLE OF RELATIVITY.)
In our theory of universality we take case 1/.
Even in case 1/ we may ASSUME THAT THE TWO SYSTEMS (O)
AND (O') HAVE THEIR OWN DIMENSIONS AND THEIR OWN TIMES t
and t'. In an absolute system, consider 2 observers at O and
O'. Assume that at time t=0, t'=0, O' coincides with O, and
the plane O'x'ξ' moves at constant speed q=|(v|jw)|=|v2-w2|
in a uniform linear motion on a line OX in the plane Oxξ;
the other planes of the system (O') move and are still
parallel to their corresponding planes of the system (O).
The axes O'x', O'ξ' are always parallel to the axes Ox, Oξ
in the translation motion.
The speed q has 2 components v and w, (q, v, w are
constants). The 2 components v and w are on the axes Ox and
Oξ. Call θ the angle of Ox and OX on the plane Oxξ. The
direction of the line OX is determined by cosθ and sinθ. On
the planes Oyη and Ozζ consider the lines OY and OZ forming
angle θ with the axes Oy and Oz, thus with directions
(cosθ, sinθ) in those planes.
We can see easily that in the system of OXYZ, the 3 axes OX,
OY, OZ are orthogonal to each other. We can find 3 unit
vectors on those axes, and the system OXYZ is an orthonormal
subspace of the real space of 6 dimensions (x,y,z,ξ,η,ζ). In
the one-one correspondence between the real space of 6
dimensions and the uni-space of 6 dimensions, corresponding
to the system OXYZ just defined above in the real space, we
have a uni-system also called OXYZ by abuse of notations in
the uni-space of 6 dimensions, which is an orthonormal
subspace of the uni-space.
Now we work on the uni-system OXYZ with 2 observers (O) and
(O'). Observer (O') is attached to a uni-system of 3 axes
O'X'Y'Z' which moves along the axis OX uniformly at speed
q=|v2-w2| starting from point O, O'X'
sliding on OX, O'Y' and O'Z' being sill always parallel to
OY and OZ.
Now assume at time t=0, t'=0, and O' at O, a light signal is
emitted from point O=O' and propagates at speed c. At time t
for O and t' for O', a point P on the wave front light has
coordinates in the 2 systems
(X,Y,Z) in system OXYZ
(X',Y',Z') in system
The equations of the 2 distances OP and O'P are
X2+Y2+Z2 - c2t2
= X'2+Y'2+Z'2- c2t'2=
Equation (8) means that the form X2+Y2+Z2
– c2t2 is INVARIANT in the
Y'=Y, Z'=Z, we have
(9) X2- c2t2
= X'2- c2t'2= 0
use the technique of Malcom Longair as follows.
Let τ=it and τ'=it', equation (9) becomes
(10) X2+ c2
τ2 = X'2+ c2 τ'2=
Equations (10) are similar to the equations of a rotation on
the plane. Because of that, we call our transformation an
The equations of a rotation of angle φ for (10) are
X'= Xcos φ + cτ sin φ
cτ '= - Xsin φ + cτ cos φ
Then let φ=iψ, we have
cos φ = cos(iψ) = cosh
sin φ = sin(iψ) = i
The 2 equations (11) become
X'= Xcosh ψ + icτ sinh
(12) cτ '= - iXsinh ψ + cτ
Equations (12) with t and t' are
X'= Xcosh ψ - ct sinh
(13) ict'= -iXsinh ψ + ict
time t in (O), the coordinates of the point O' are X'=0 in
(O') and X=qt in (O).
Substituting in the first equation of (13), we have
tanh ψ = X/ct = qt/ct
Since by the computation of hyperbolic functions we have
cosh ψ = (1 – q2/c2)-1/2
ψ = (q/c)(1 – q2/c2)-1/2
equations of the transformation become
X'= (X -
qt)(1 - q2/c2)-1/2
= (t - qX/c2)(1 - q2/c2)-1/2
(14) Z' = Z
The above technique requires a uniform linear motion of the
2 systems relative to each other. So the 4 equations (14)
are only a special case in which we find the coefficient
(15) γ = (1 – q2/c2)-1/2=
(1 – v 2/c2 + w 2/c2)-1/2
= v2- w2.
Until today, people don't have a technique or a method to
find similar formula to (14) with the coefficient γ (15)
for the transformation of coordinates in a general motion.
So when we use the transformation of coordinates (14) we
must be very careful with the condition of uniform linear
motion of the systems of reference.
We have some more comments on the use of the PRINCIPLE OF
INVARIANCE of Newton in the proof of the relative
uniform linear motions of 2 different systems of reference.
By that principle, distance and time have invariant forms in
two systems in uniform motion relative to each other. In the
theory of space-time of Minkowski and the theory of
relativity of Einstein, they applied that principle of
invariance and found what is called PROPER DISTANCE AND
PROPER TIME WHICH EVERY OBSERVER AGREES: there are 3
different kinds of time, one for observer O, one for
observer O', and the proper time which is the same for all
observers. In computation, when differentiating functions
with respect to time, they take derivatives with respect to
proper time. The concept of proper time in their theories is
actually the concept of absolute time of Newton. We have
discussed 2 cases of relative motions of 2 systems:
1/ Two systems are moving in uniform linear motion with
respect to each other IN AN ABSOLUTE SYSTEM
2/ Two systems are moving in uniform linear motion with
respect to each other WITHOUT ABSOLUTE SYSTEM.
In our theory of universality, we take case 1/, then our
proper time and even proper distance are the absolute time
and absolute distance in the absolute system.
Minkowski and Einstein take case 2/, then they can not
explain the concept of proper time and proper distance in
the theories of space-time and relativity. It is only a
remark, and we don't say it is a contradiction in those
In the first equation of (14), at an instant t of (O), 2
distant events A and B on a line parallel to the axis OX are
determined by the formula
X'a= (Xa -
qt)(1 - q2/c2)-1/2
(Xb- qt)(1 - q2/c2)-1/2
X'a – X'b =
(Xa - Xb)(1 - q2/c2)-1/2
ΔX' = ΔX(1 - q2/c2)-1/2=
ΔX(1 - v 2/c2 + w 2/c2)-1/2
(16) shows the change of the distance in relative motion
depending on the 2 velocities v and w.
In the second equation of (14), an observer fixed at X in
(O) observes the times t and t' at 2 different instants
t'2 = (t2
- qX/c2)(1 - q2/c2)-1/2
(t1 - qX/c2)(1 - q2/c2)-1/2
t'2 - t'1
= (t2 - t1)(1 - q2/c2)-1/2
(17) Δt' = Δt(1 - q2/c2)-1/2=
Δt (1 - v 2/c2 + w 2/c2)-1/2
(17) shows the change of time in relative motion depending
on the 2 velocities v and w.
formula (16) and (17) can be written in the forms
= l0(1 – q2/c2)-1/2
= t0(1 – q2/c2)-1/2
γ = (1 –
q2/c2)-1/2= (1 – v 2/c2
+ w 2/c2)-1/2
theory of Special Relativity, because people work only in
the material world neglecting the spirit, w=0, q=v, the
formula (18) and (19) are in the forms
l = l0(1 – v2/c2)-1/2
t = t0(1 – v2/c2)-1/2
express A CONTRACTION OF LENGTH AND A DILATION OF TIME IN
THE MOTION OF THE TWO SYSTEMS OF REFERENCE RELATIVE TO EACH
OTHER. But yet in 100 years already, no body can
measure such contraction of length or dilation of time. The
null results of the experiments for such measures can be
explained now in the theory of Universality.
The speed q in the coefficient γ depends on the 2 material
and spiritual speeds v and w.
If v=w, no change of length or time, even no change of mass
or energy in motion.
If v˃w, then length, time, mass, energy all increase in
If w˃v, then length, time, mass, energy all decrease in
RELATION BETWEEN MATERIAL AND SPIRITUAL EVENTS
When we studied mass and energy in each of the two
separated material and spiritual spaces, we got 2
separate formula of transformation for mass and energy
We wonder what relation is between the two material and
spiritual world. In other words, what cements the two worlds
studying the transformation of coordinates in uni-space, we
found the coefficient of transformation
γ = (1 – q2/c2)-1/2=
(1 – v 2/c2 + w 2/c2)-1/2
relate the 2 material and spiritual speeds with the
coordinates of events.
Because the two material and spiritual worlds are
inseparably connected, we admit a fortiori the
hypothesis that mass, energy, and coordinates have the
same coefficient of transformation in any motion
γ = (1 – q2/c2)-1/2=
(1 – v 2/c2 + w 2/c2)-1/2
hypothesis, this coefficient γ = (1 – q2/c2)-1/2=
(1 – v 2/c2 + w 2/c2)-1/2
is a universal coefficient of transformation.
UNIVERSAL COEFFICIENT OF TRANSFORMATION
In the universe of 6 dimensions, consider the uni-forms of
mass m and energy e
m = (mr|jms)
and e = (er|jes)
subscripts r and s standing for
material and spiritual, then with the universal coefficient
γ, we have the following fundamental
m = m0(1-v2/c2+w2/c2)-1/2
e = e0(1-v2/c2+w2/c2)-1/2
The material part and the spiritual part have similar
formula in parallel.
If we generalize those formula to uni-vectors of 6
dimensions, we have
' means derivatives with respect to absolute time t
above fundamental formula for mass and energy in motion are
In the coefficient
γ = (1-v2/c2+w2/c2)-1/2
spiritual speed w=0, we have
γ = (1-v2/c2)-1/2
This coefficient γ is essentially different from the
coefficient γ which Lorentz, Minkowski and Einstein use in
the Lorentz transformation and the space-time of relativity.
In our proof for the fundamental formula of mass and energy
in motion, we use differentiation and integration of
analysis. But in setting up his formula for transformation
of coordinates, Lorentz makes up an artificial tool to
interpret the changes of length and time in Michelson-Morley
experiment. Then Minkowski take Lorentz's coefficient γ as
an evidence for his construction of space-time which
Einstein uses in his theory of special relativity.
Another essential remark is that the speed v of a
material point or a solid can be greater than the speed of
light c because of the presence of the speed w in the
coefficient γ. This simply means the theory of
relativity applies only to the material world where the
spirit is neglected.
The null uni-vectors, x= ξ
(x|jx) = x(1|i1)
uni subspace called the NULL SPACE. In uni language,
we can say that the null space is the space of events with
the same degree of spirit as of matter.
In the null space we have v=w, then
That is a
generalization of the theory of Newton in mechanics, in
which the 4 basic quantities mass, energy, length, and time
won't change in motion. So we may consider that the space of
Newton is the null space of same degree for both spirit and
matter in which the material and spiritual speeds are not
necessarily zero, and the observers not necessarily at rest.
NULL SPACE AND
that the universe of Newton is the null space where x=ξ and
dx/dt=dξ/dt, i.e., v=w: the two material and spiritual
worlds are superposed mechanically in the null space. That
means the concepts of distance and time are similar for the
2 worlds. Thus the concepts of speed and acceleration are
also similar. But the concepts of mass and energy are
different for the 2 worlds.
We have seen the relation between mass and energy
e = mc2
material and spiritual worlds. But in each separated world,
mass and energy in motion obey the fundamental equations
with the universal coefficient
= (1 – q2/c2)-1/2= (1 – v
2/c2 + w 2/c2)-1/2
null space, the coefficient γ=1, and mass and energy do not
acceleration. All the theories already established in Newton
space can be generalized to uni-space.
Now we need to look at the concepts of mass and energy in
the two worlds.
The difference between matter and spirit is conventional
(because its the most we can do at this time in mathematics
and mechanics.) We postulate that
MASS AND ENERGY ARE POSITIVE IN THE MATERIAL WORLD, and
MASS AND ENERGY ARE NEGATIVE IN THE SPIRITUAL WORLD.
Spiritual energy is negative, except kinetic energy of
the spirit is positive
(1/2)(-m)q2 = (1/2)(-m)(-w2)
= (1/2)mw2 > 0
In the theory of light, light appears the same in the 2
worlds, and a photon is a combination of 2 opposite masses m
Therefore the mass of a photon is
m + (-m) = 0
the kinetic energy of a photon is
(1/2)mc2 + (1/2)(-m)(-c2)
= mc2= pc
is the momentum of photon.
Those are the properties of light admitted in classical
*between 2 masses of same sign, there is an ATTRACTION,
*between 2 masses of opposite signs, there is a
Two masses in the material world, both
positive attract one another.
Two masses in the spiritual world, both
negative attract one another.
material mass and a spiritual mass repel one another,
which explains why the attachment of a body and a spirit is
unstable: the death of a living being can occur easily when
the conditions of attachment vanish and then the spirit
leaves the corps.
the PRINCIPLE OF GRAVITATION of Newton in the
The gravitation force in the material world is ATTRACTION
F = Gmm'/r2
In the system MKS, m and m' are in Kg, F in Newton, the
distance r between m, m' in meters, G the universal
coefficient of gravitation. The same law is true in the
spiritual world with 2 negative masses.
In the uni-space, we have
are the attractions between masses of the same sign.
For 2 opposite masses (mr|j0) and (0|jms),
there is a repulsion
F' = - G'mrms/r2
spirit can attach (incarnate) to a body only under a
different kind of attractive force greater than the
repulsive force F'. We call that attractive force the
going to show there are 2 different fields of force: the
gravitational field and the karmic field. We will
explore the Karma and the Karmic Field next.
The gravitational field consists of attraction
between masses of same sign, and repulsion between masses of
By analogy, the karmic field also consists of
attraction and repulsion depending on the karma, which will
explore the two fields, we have to review basic mathematics
tools of vector calculus.
simplify the writing in mathematics, since we have several
kinds of products and sum, in the following we will use the
dot “.” or even no dot to represent the all kinds of
products if there is no confusion. For example
u o v = u . v = uv
for scalar product of 2 real vectors.
E + E'
(m|jm') = m + m'
For the definition of divergence:
Let call Dx the partial derivative with respect
to x, similarly for the variables y, z, and ix,
iy, iz the unit vectors
of the axes Ox, Oy, Oz. For a vector
F = ixFx
the divergence is
DxFx + DyFy + DzFz
for the vector F'(ξ͵η͵ζ).
In the uni-space of six dimensions, we define the divergence
of a uni-vector as follows.
vectors Fr(x,y,z) and Fs(ξ͵η͵ζ)
are real vectors of real variables.
GRADIENT OF A REAL-VALUED FUNCTION OF 3 VARIABLES
Let E be a real-valued function of 3 variables x, y, z. Then
by the definition of gradient:
gradE = ixDxE
+ iyDyE + izDzE
Similarly for a function of 3 variables ξ͵η͵ζ.
And for uni-vectors, the gradient is
OF A VECTOR FUNCTION OF 3 VARIABLES
Let A be a vector function of 3 variables
x, y, z. The curl of vector A by definition is
Similarly for a vector function of 3 variables
For uni-vectors, the curl is
In vector calculus, we use the operator ▼
defined symbolically as a vector
For real vector functions of 3 variables, we use
the scalar product “o” of real vectors
Then we have
= ▼o A = ▼A = (ixDx+iyDy+izDz)
Φ = ▼Φ = (ixDx+iyDy+izDz)Φ
The curl of a vector A is the cross
product of real vectors
curlA = ▼X A = (ixDx+iyDy+izDz)
Here we use second partial derivatives Dxx,
Dyy, Dzz for the Laplacian of a
scalar function Φ of 3 variables
▼2 Φ = Dxx
Φ +Dyy Φ+Dzz Φ
For uni-functions, the Laplacian is
= (▼2 Φr |j▼2 Φs)
∫S A o
dS = ∫v divA dv
encloses volume V, dS is the differential vector
normal to an infinitesimal element of surface directed
outside the volume, dv is an infinitesimal element of
∫c A o
dl = ∫S curlA o dS
S is any
surface bounded by the loop C, dl is an
infinitesimal element of the loop C, and dS is an
infinitesimal element of S.
Let f and g be 2 real-valued functions of 3 variables x, y,
First form ∫v [f ▼2g+(▼f
o▼g)]dv = ∫S f▼g o dS
Second form ∫v [ f ▼2g- g▼2f]dv
(f▼g – g▼f) o dS
We have the theorem:
following propositions are equivalent for a vector field
1/ curlA = 0
2/ A= - grad Φ
3/ ∫C A o dl = 0 for any
closed loop C
4/ ∫ABA o dl is
independent of the path from A to B
field A is called irrotational or conservative.
have some properties for curl, grad and divergence
div(curlA) = 0
for any vector A
= grad(divA) - ▼2A
First we study the gravitational field in the material
world separately, in which all masses and energies are
positive, and between 2 masses there is a gravitational
the gravitation field of an isolated point mass m in an
absolute reference frame as the force field, at a point P
ir is the unit vector of the vector pointing
from the point P to the point mass m.
If a mass m' is placed at point P, the gravitation field of
m acts on m' a force
the origin of the reference frame. A mass m placed at O
produces a gravitational field f. The work of the
field f from a point A to a point B is the line
Φ = - ∫AB
f o dl
independent of path from A to B.
called the gravitational potential difference between 2
points A and B.
radial segment AB, f and dl are parallel, then
Φ = - ∫AB
Gmdr/r2 = Gm(1/rA – 1/rB)
If B coincide with A, the path is a closed curve, and
Φ = 0
If the point B is at infinity, we have
Φ = - ∫ Gmdr/r2
called the gravitational potential at point A due to the
If we go radially from a point (x,y,z) to a point
(x+dx,y+dy,z+dz) the change of Φ, going from A to B, is in
first order approximation
dΦ = DxΦdx +
DyΦdy + DzΦdz = gradΦ o dl
But from the definition of Φ above, we have
dΦ = f
Thus we can identify
gradΦ = ▼Φ
If we have a system of masses, each mass produces an
individual gravitational field and an individual
gravitational potential. By the principle of
superposition in physics, the resulting field is the
vector sum of all the individual fields and the total
potential at a point is the sum of all individual
potentials. The total mass of the system is the sum of all
masses, and the system is equivalent to a mass (= total
mass) placed at the gravity center of the system. The
resulting field is a force f
denote by ρ the mass density per volume
total potential is
Φ = ∑ Φi
= grad Φ
Furthermore the flux of the gravitational field f
through a surface S enclosing a volume V is
f o dS = ε ʃV ρdv
ε is a
constant related to the gravitation.
By the divergence theorem, we have
f o dS = ʃV divFdv
divf = ερ
In electromagnetism, we know that in an
electric field E, an electric charge q
moving with velocity v is acted by a force
F = qE
+ qv X B
B is the magnetic field.
By analogy, in a gravitational field f,
a mass m moving with velocity v is
acted by a force F
+ mv X B
is in the
present case a magnetic-like gravitational field. It
is not a magnetic field, but a field related to the
gravitational field. In experiment, we can measure
the gravitation f, then let a known mass m moving
with velocity v, we can measure B. We call
B the gravimagnetic field.
analogy with electromagnetism, we have the 4 equations for
the gravitation in the material world analogous to
the 4 Maxwell equations
= - DtB
= με Dtf + μJ
the spiritual world, we have equations similar
to those in the material world.
= - DtB'
= μ'ε' Dtf'+μ'J'
system of 4 equations of the spiritual world, mass and
energy are negative, and the gravitation force is
At this point we have seen the fields' equations separately
for each world. To have the equations for the universe,
we apply the principle of superposition:
= - Dt(B+B')
are conduction current densities per volume; ε and ε' are
related to the universal gravitation in the 2 worlds; μ and
μ' are coefficients related to mass-energy in the 2 worlds.
INTERPRETATION OF THE 4 BASIC EQUATIONS
The 4 basic equations above govern the phenomena
concerning matter and spirit in the universe.
intimate relation between mass (material and spiritual) and
gravitation (attractive and repulsive). Where there is
mass, there is gravitation. Mass is positive in the
material world and negative in the spiritual world.
Gravitation is attractive in the material world and
repulsive in the spiritual world. In the universe, the 2
worlds are superposed: in matter there is spirit. Because
matter and spirit repel one another, the attachment
(incarnation) of spirit to matter requires an essential
condition of KARMA. What is karma? We
will explore it in the next paragraph.
The actual gravitation that affects life constantly is the
superposition of 2 opposite gravitational forces:
living beings are affected at the same time by the
attractive material force and the repulsive spiritual force.
that the gravimagnetic field B+B' occurs constantly
in the universe due to the change of the gravitation field
f+f'and the motion of J+J'of
matter/spirit. The term μεDtf+μ'ε'Dtf'
is called the displacement current of matter/spirit.
The term μJ+μ'J' is called the
conduction current of matter/spirit. The earth around
the sun, the moon around the earth are examples of
displacement currents. People's action, trees growing are
conduction currents of matter/spirit. Matter/spirit always
changes, which implies that the gravitation field always
changes. Because every mass/spirit changes and moves
constantly, the gravimagnetic force is always present in all
Then equation 1
curl(f+f') = - Dt(B+B')
that the change of B+B' affects the gravitation
f+f'. Thus gravitation field and gravimagnetic field
mutually affect one another. When changing, the gravitation
produces the currents of matter which make change in the
gravimagnetic field, and the gravimagnetic field in its turn
affects the gravitation.
that there is NO gravimagnetic charge, that is, the
gravimagnetic field is produced by the displacement current
and the conduction current. Masses produce gravitation, but
we can not find anything “like mass” to produce
AND KARMIC FIELD
We study now the concept of electric polarization inside the
body of a living being.
We call body the total of a material corps with an
incarnated spirit of a living being.
Our stand point here is only on the electromagnetic state of
the body in the simplest description of polarization of the
The body moves and acts itself by internal energy without
aid of an exterior electric or magnetic field. We know each
person has his/her own power to sense, to emotion, to
think, to speak, and to action. The body/spirit is
self-powering and is self-relating to the environment.
So we admit that the body/spirit has an internal
potential energy Φ.
Then there is an electrical field E generated by Φ
E = -
We assume that all the cells in the body are polarized by
the field E, and each cell is an electric dipole p.
Those dipoles are arranged in accordance with the functions
of different organs. The simplest case we can assume is a
uniform polarization of water in the body since water is 90%
of the body. Such case may be of a person in deep
The dipole p of a cell and the electric
field E are supposed to be proportional
p = αE
called the coefficient of polarization of the body/spirit
and has the dimension of volume. That polarization is a
zooming image of the polarization of atoms distorted by
Following are the measures of atomic polarization
for some elements in Units of cm3 under the
effect of an external electric field:
He Li Be C Ne Na
Atomic α 0.66
0.21 12 9.3 1.5 0.4 27
μ A further research would have the measures of the
polarization coefficients of the cells in a body due to the
A polarized body is a dielectric and has a
permittivity coefficient ε and a permeability
coefficient μ that effect the fields E and
B. That is the use of the vocabulary in
electromagnetism, but when we use the equations for karma,
ε will be called the karmic coefficient, and μ will be
called the individualistic coefficient of a living being.
uniform polarization, the density of polarization is
P and plays a role analogous to that of electric
field inside the body. The dipoles p plays the role
of electric charge, called bound charges. Let ρbound
be the density of bound charge
divP = -
The current of bound charge has intensity
There are also free ions in the body with
density ρfree which produce a current of free
charge of intensity Jfree.
The change of the electric field E
produces a displacement current of density
The electric field E is discontinuous at the
boundary of the medium which is the skin of the body in the
present study case. At the skin there is a thin layer of
electric charge with surface density ϭ. Let's write at a
point of the skin 3 vectors with their components normal and
tangent to the skin
P = Pnormal
relations between those vectors concerning discontinuity and
- Einormal = Pnormal
superscripts “i” and “o”
stand for inside and outside of the body. In the
theory of electric field at the boundary of a medium, we
know the tangent component of E is continuous, but
the normal component of E has a discontinuity equal
to the surface density of charge
ϭ = Pnormal.
mimic the equations of Maxwell by writing the 4 equations
for a self-polarizing body as follows
curlE = - DtB
= με DtE+μDtP+μJfree
divE = ερbound
divB = 0
DtE is the displacement current in the
body. DtP is the conduction
current. Jfree is the free current
of free electrons in the body.
the illustration of electrical and mechanical study of
the body in the material world.
spiritual world, by analogy we have
similar concepts and equations
curlE' = - DtB'
divE' = ε'ρ'bound
The superposition of the 2 worlds in the universe gives the
4 complete equations of self- polarization and karma.
= - Dt(B+B')
= μεDtE+ μDt P+
div(E+E') = ερbound +
ερfree+ ε'ρ'bound +ε'ρ'free
Now we interpret those equations.
First we need to clarify the difference in nature of the
two concepts material and spiritual.
For mass and energy, we see clearly the difference
between 'material mass' and 'spiritual mass', also the
difference between 'material energy' and 'spiritual energy'.
The material mass and energy is said to be 'positive', and
the spiritual mass and energy is 'negative'.
But for electric and magnetic, we say 'positive or
negative material electric' to distinguish with
'positive or negative spiritual electric'. Similarly
'positive or negative material magnetic', and
'positive or negative spiritual magnetic'.
In the universe, the total (material and
spiritual) electric and karmic potential Φ+Φ' is the
KARMA of the living being. The electric field E+E'
is its KARMIC FIELD. We give a new name to the
“magnetic” field B+B': the CONSCIOUSNESS FIELD.
Karma and consciousness always go together, a change
of one affects the other.
ϭ+ϭ' = Pnormal
sensitivity density. The electric
bound charge density ρbound +ρ'bound
is the emotion density. The electric
free charge density ρfree+ρ'free is
the mind density.
As we know, after the death, the dead body does
not have any more sense, emotion, mind, word, action, so all
those things are due to the spirit. It is the spirit that
directs every thing of the living body in life by
superposition with the body.
We can now answer the question, HOW DOES A SPIRIT
INCARNATE IN A MATERIAL BODY TO CREATE A LIVING BEING? HOW
DOES A SPIRIT LEAVE A LIVING BODY TO MAKE IT A DEAD CORPSE?
living matter/spirit body, we have seen the charges in the
body are the electric charges.
In the material world, two material electric charges of
same sign repel one another; two material electric charges
of opposite signs attract one another.
In the spiritual world, two spiritual electric
charges of same sign repel one another; two spiritual
electric charges of opposite signs attract one another.
Between the two worlds, a material electric charge
and a spiritual electric charge of the same sign attract one
another; a material electric charge and a spiritual electric
charge of opposite signs repel one another.
The attractive karma forces and the attractive
consciousness forces make the incarnation of the
spirit in the body if both spirit and body have the same
sensitivity, and similar karmic and conscious conditions.
During life, sensitivity, emotion, mind, word, action change
with time until the karmic conditions are ameliorated and
the karmic and conscious forces become weaker than the
repulsive forces, the spirit must leave the body. The death
That is the LAW OF LIFE AND DEATH.
sensitivity field is the cement to attach a spirit and a
After the death, the corps has no more
STRUCTURE OF THE UNIVERSE
The motion of an event is caused by the forces of karma and
conscience acting on it. Those forces produce accelerations
in the motion. For an event (x|jξ) in motion, the material
and spiritual speeds are
v=dx/dt and w=dξ/dt
The accelerations are
If ξ˃x, the uni-forms (x|jξ) are in the SUBSPACE
OF SPIRIT-LIKE EVENTS.
ξ, the uni-forms are in the SUBSPACE OF MATTER-LIKE
Now we explore the structure of the universe with the
spirit-like subspace and the matter-like subspace.
Let's call ACTION an event in motion. An action
of a spirit-like event or a material-like event depends on
the forces (accelerations) that act on it.
There are 3 different realms in the spiritual-like
1/ REALM ONE WHERE ξ˃x WITH SPIRITUAL
ACCELERATION GREATER THAN MATERIAL ACCELERATION w'˃v'. In
this realm, we say that an action has higher MERIT, or
greater spirit than matter. We call it the HEAVEN OR
2/ REALM TWO WHERE ξ˃x WITH w'=v'. In this
realm, an action has the same degree of MERIT spiritually as
materially. It is the HUMAN REALM.
3/ REALM THREE WHERE ξ˃x WITH w'<v'. In
this realm, an action has less MERIT in spirit than in
matter. It is the ATULA REALM OR SPIRITUAL REALM.
In the matter-like subspace, there are also 3
4/ REALM FOUR
ξ WITH w'˃v'. In this realm, an action has LOWER MERIT
OR LOWER CONCIOUSNESS. It is the ANIMAL REALM.
5/ REALM FIVE WHERE x˃ ξ with
w'=v'. In this realm, an action has the same degree of SIN
materially as spiritually OR NO CONCIOUSNESS. It is the
6/ REALM SIX WHERE x˃ ξ WITH
w'<v'. In this realm, an action is of mostly MATERIAL or
MATTER WITHOUT SPIRIT. It is the HELL.
The analysis shows the existence of six realms in the
universe with different degrees of merit and sin in the two
spirit-like and matter-like subspaces.
Dynamically, a body/spirit can move from one of the six
realms to another, depending on the spiritual and material
actions forces and accelerations acting on it. A more
precise study on forces and accelerations can show how such
a move occurs. If a body/spirit has to move from the
matter-like subspace x˃ ξ to the
spirit-like subspace ξ˃x or conversely, it must pass
through the null space with x=ξ.
By the principle of universality, the universe is
composed of two worlds, material and spiritual, inseparably
connected together. On the stand point of super-sciences,
there are in the universe two compensate fields: the
gravitation and the karma.
The gravitation has two different forms,
gravitational field and gravimagnetic field of mass/spirit.
The karma has two different forms, self-polarization and
self-magnetism of body/spirit. Those fields are attraction
or repulsion. The surface electric charge density on the
skin of a body/spirit is the sensitivity density of the
body/spirit, which is the source of sense, emotion, mind,
word, action. Those things together affect the karma.
spirit has similar karmic conditions with a body, the spirit
is incarnated-attached to the body by the karmic attractive
forces due to the sensitivity-cement. When the karmic
attachment ameliorates and vanishes, the spirit leaves the
body by the repulsive forces of the fields and the
sensitivity-cement is gone on the corps.
This essay is written after many years of
meditation, and after several months of consultation from
PRINCIPLE OF RELATIVITY, A. Einstein, Lorentz, Weyl,
Minkowski, Dover Publication