Written in 2017
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
essay is an introduction to Meditation and Enlightenment via
The first part is a continuation of
the previous paper,
Theoretical Concepts of Universality.
LAW OF CAUSE AND
In the Paper, Theoretical Concepts of Universality,
we have seen the three mental functions of a body/spirit:
sensitivity, emotion, and mind produced by electric charge
density ϭ on the skin, conduction current density ρbound,
and free current density ρfree.
natural process sensitivity-emotion-mind continues to two
more functions: word and action. Now we look at the issues
of those two last things.
The density of displacement
current DtE is the issue of WORD.
For ACTION we look at equation 4 of the system
divB = 0
In vector calculus, we know
for any vector A, which suggests that vector B
is the curl of some vector A. It is true that there
is a vector A such that
B = curlA
A is called in electromagnetism vector
We can express E directly in term of
curlE = - DtB
= - Dt(curlA)
curlE = - curl(DtA)
E = - DtA
In our study of body/spirit
activities, that vector A is the issue of
ACTION for the body/spirit.
The process of five steps
sensitivity-emotion-mind-word-action is the main generative
force that produces karma and makes change on
karma. The karma was produced by that
five-steps-process in the past, and in the present the
five-steps-process contributes to the change of karma, which
will continue effecting the future life of the body/spirit.
It is the law of cause and effect.
Since sensitivity, emotion,
mind, word and action of a body/spirit are due to the
spirit, the spirit is charged with the past karma in the
next incarnation into a new body for a new life, and the
karma during the whole new life will effect the death of the
body. It is the cycle of life and death. The spirit
carries the karma from the past to the future life. The next
incarnation is a consequence of the karma from the past.
WAVE ASPECT OF
GRAVITATION AND KARMA
have seen the two systems of equations for gravitation and
for karma. The two systems look analogous with different
interpretations of the coefficients ε and μ. Now we write
them in a unified form
= - DtB
= εμDtE +μJ
divE = ερ
where E, B represent the total fields
of gravitation or karma (electromagnetism) in both material
and spiritual worlds; J represents the total of bound
and free currents; ρ represents the total density of
mass-energy or of electric charge in both worlds; and ε and
μ represent the characteristic coefficients of gravitation
and mass-energy or of karma and consciousness.
vacuum, there is no mass, no electric charge, and no
currents, the above system of equations becomes
= - DtB
With that system of equations, we
study the propagation of the fields E and B in
WAVE FORM OF GRAVITATION PROPAGATION.
On 14 September, 2015
scientists at LIGO (Laser Interferometer Gravitational Wave
Observatory) in Louisiana and Washington have detected
gravitation waves between 2 enormous black holes from
billion years ago. Einstein has
predicted the wave form of gravitation 100 years before. Now
we can show the wave aspect of gravitation theoretically
with the system of equations for gravitation.
Consider the system of 4
equations for gravitation.
We work here in the uni-system of
coordinates OXY defined in the paper Theoretical Concepts
Let's take the derivative with
respect to time of equation 2 of the system
Substitute DtB from equation 1
But we know
) = ▼(▼E ) - ▼2E
From equation 3 in the system
divE = 0
(1) is a partial differential vector equation
of second order in E and it represents a set of
equations for the 3 components of E=(Ex,Ey,Ez)
To simplify the solution, we
consider the propagation of the wave plane along the
X-axis with velocity q, and the vector E is
supposed to be in the XY-plane, E being perpendicular
to q. See Fig 2
Then Ex=0 and
Ez=0; E=Ey is a function of t and
Equation (1) becomes
Equation (2) is called wave
equation, of which a solution has the form
(3) E = E0
Thus the propagation of E has a
sine form with amplitude E0 and speed of
propagation q. The universal speed is q=|(v|jw)|=|v2-w2)|
where v is the material speed and w the spiritual speed.
Differentiate solution (3) twice
with respect to x
= - E0 sin(x-qt)
and twice with respect to t
= - q2E0 sin(x-qt)
Substitute in equation (2)
sin(x-qt) = -εμq2E0 sin(x-qt)
Simplifying both sides yields
with q2= |(v|jw)2| = |v2-w2|
The speed of the wave
propagation q equals (εμ)-1/2.
Now we proceed with the vector
= - DttB
= - DttB
▼X(▼X B) = ▼(▼B) - ▼2B
But ▼B =
divB = 0
As we know the vector B is
perpendicular to both vectors E and q, so B
is in the XZ plane
Bx = By
= 0 and B = Bz is function of t and x only
Equation (4) becomes
DxxB = εμDttB
Solution to equation (4)' has the
(5) B = B0
Then take the second partial
derivatives of B
= -B0 sin(x-qt)
= -q2B0 sin(x-qt)
sin(x-qt) = -εμq2B0 sin(x-qt)
We get the same formula as
before. We call (6) or (7) the rule
need also to determine the constants E0 and B0.
Let's take the 2 equations
= - DtB
Recall the definition of curl in vector calculus
curlE = (DzEy-DyEz)ix+(DxEz-DzEx)iy+(DxEy-DyEx)iz
But Ex=Ez=0, and E=Ey=function
of t and x only
curlE = DxE
curlE = E0 cos(x-qt)
With the assumptions above we
= E0 cos(x-qt)
= B0 cos(x-qt)
Differentiate E and B with
respect to t
- q E0 cos(x-qt)
- q B0 cos(x-qt)
cos(x-qt) = q B0 cos(x-qt)
cos(x-qt) = εμq E0 cos(x-qt)
Simplifying cos(x-qt), we have
E0 = q B0
and B0 = εμq E0
and E0 = εμq2
E0 and B0 = εμq2 B0
Consequently we get again the
rule of coefficients
In the theory of electromagnetism, people
assume q=c, then
The above calculations show that
the gravitation fields E and B
are in the wave form obeying the rule of coefficients.
Note that the gravimagnetic B is discovered in the
theory of universality but not yet detected even after the
detection of the gravitation wave in 2015.
The same argument shows that
electromagnetic fields – karma – also have wave form obeying
the rule of coefficients.
The rule of coefficients contains
3 factors ε, μ, q with product εμq2 equal to 1.
RULE OF COEFFICIENTS.
If we take the wave functions in
E = E0
B = B0
where λ is the wave length (period), after
the same calculations as above, we have the same rule of
coefficients εμq2 = 1.
In the theory of universality we
= v2 - w2
v and w are the material and spiritual
If we consider only the material
world, then q2=v2.
Working in the material world
(w=0 and q=v) Maxwell in 1856 found the formula (εμ)-1/2
= v for electromagnetic wave propagation by which he
calculated, at his time, the expression (εμ)-1/2
approximately equal to the speed of light c. Then he
identified light with electromagnetic
Today we have the precise values
in classical notations
= 299,792,458 meters/sec
μ0 = 4π
x 10-7 ohm-sec/m
ε0 = (4π
x 8,987551787 x 109)-1 sec/ohm-m
We are going to find essential properties of
the rule of coefficients.
The rule of coefficients depends on ε, μ and
the speed q. The speed q
q2 = v2
distinguishes our system of 4 equations from
that of Maxwell in electromagnetism and from that of the
theories in today physics . The presence of the spiritual
speed w is essential in studying the universe of dual
worlds. In the formula of the universal coefficient γ=(1-v2/c2+w2/c2)-1/2
we see that an event can move with speed greater than the
speed of light c.
Above is the study of the wave form of gravitation.
Let's have more comments on the universe
where we are living in.
In our universe, the coefficients
ε and μ have characteristic meanings of the gravitation and
mass-energy. We can adopt the precise values of ε0
and μ0 given above as the characteristics of our
universe. But the reader would be surprised if we give to ε
and μ other values. Most people believe that our universe is
unique in the sense that there are no other universes
different from ours. But if one practices meditation to a
high level, that person will see many universes other than
ours. It is not superstition, but real existence which
people can not see due to ignorance. We can envisage it as
follows. The different values of ε and μ are the
characteristics of other infinitely many universes that
meditation can reveal to us. To understand this, one has to
learn and practice super-religion that shows The Right Way
to Enlightenment. Each value of ε characterizes the
space-time of one universe and each value of μ
characterizes energy-mass in that universe. Those
characteristic values of different universes could be found
in some special circumstance later in the future.
Now we look at the
The system of 4 equations for
karma was derived from the
theoretical equations of electromagnetism in matter.
Actually we can write the equations for karma with 2
coefficients ε and μ in the same way as for gravitation. We
can assert it because our theory of
universality assumes the essential role of internal energy
of a body/spirit, and consequently the self-polarization in
Then with an argument similar to
that for gravitation, we also have the rule of
coefficients for karma (εμ)-1/2 = q or εμq2=1.
For karmic fields, ε and μ may
have different specific meanings
in the theory of karma.
We know that different species of
living beings have different methods of alimentary
nourishing and different structures of the body, which
provide different internal energies and different ways of
self-polarization in the body. For example, humans,
elephants, fish, birds, trees have different ways of living
and different forms of body.
We have seen in the paper
Theoretical Concepts of Universality the electric dipole
p in a dielectric polarized by an external
electric field E may be supposed to be
proportional to E
p = α E
atomic polarizability α is a specific coefficient of
the material element: different elements have different
In the context of
self-polarization inside a body/spirit, different species
have different coefficient ε. We say ε is the
karmic coefficient of the species. So humans,
elephants, fish, birds, trees have different karmic
coefficients. For a particular species, for example humans,
each individual has a different coefficient μ. So μ
is called the individualistic coefficient of the
individual in the species.
The karmic coefficient
ε and the individualistic coefficient
μ are related to the universal
speed q by the rule of coefficients
Actually the three factors
ε, μ, q appear together as a
product (εμq2) which is called the
self or ego
of each individual.
speed of propagation q of the karmic-consciousness field
varies with the coefficients ε, μ of each individual in a
species. Later on we will explore more about it.
INTERACTION BETWEEN TWO INDIVIDUALS
now study relations between two individuals like a man and a
woman, or a spirit and a body.
In the previous section, we
have seen the equation of propagation of a field
Consider the propagation with speed q along the X-axis, and
the field E assumed to be in the XY-plane, we have
And a solution to (2) has the
E = E0
The graph of that function is
a periodic sine-curve. E0 is the amplitude. The
period of that sine-curve is λ=2π on the x-axis.
For the vector B we have a similar
wave equation in the XZ-plane
and a solution of sine form
B = B0
Now we apply those results to
the interaction between a man and a woman.
We set up the problem as
Suppose a man and a woman are at
a distance d apart on the x-axis.
The functions for the man are
E = E0
B = B0
To set up the functions E' and B' for the
woman, See Fig 2
The man A is at the origin O,
the woman B on the x-axis, AB=d˃0. The waves E of man A
propagate with velocity q˃0, the waves E' of woman B
propagate in opposite direction at velocity -q'˂0. Consider
a point C, OC=x˃0 and BC=x'˂0. Note that the waves E' of
woman B are exactly the same as the waves E' starting from O
to the left at the same velocity -q'˂0. So the functions of
E' and B' are
E' = E0'
B' = B0'
x-x' = d
x' = x – d
(8) E' = E0'
B' = B0' sin(x-d+q't)
The waves E and E' interfere in the XY-plane,
and B and B' interfere in the XZ-plane.
E + E' = E0 sin(x-qt) + E0'
B + B' = B0 sin(x-qt) + B0'
The graphs sum up in a complicated shape (We don't draw a
figure in this general case) because of the differences
between E0 and E0', B and B0',
q and q', and because of the arbitrary distance d: that
shows the 2 persons have no particular influence on one
now the 2 persons are under similar
conditions of karmic and individualistic coefficients
εμq2 such as q=q', E0=E0',
+ E' = E0 sin(x-qt) + E0 sin(x-d+qt)
B + B' = B0 sin(x-qt) +
+ E' = E0
[sin(x-qt) + sin(x-d+qt)]
B + B' = B0
[sin(x-qt) + sin(x-d+qt)]
(10) E + E' = 2E0
(11) B + B' = 2B0
The graphs of E+E' and B+B'
have the factor sin(x-d/2) representing sine curves with
period 2π. The factor cos(qt-d/2) represents the
oscillations of the waves in wave planes perpendicular to
the x-axis at point x.
The points on the x-axis where
E+E'=0 and B+B'=0 are
x-d/2 = kπ
x = d/2 +
Those points are fixed on the
x-axis. We say the waves of E+E' and B+B' are
We interpret the above cases
as deep emotion between two persons in contact. They may be
in love or in dear friendship.
The cases of standing waves
also explain the incarnation of a spirit into a body to
make a living being.
can see some particular cases.
If d =
The additions of the functions
E and E', B and B' are
(12) E + E' = E0 sin(x-qt)+E0sin(x-2nπ+qt)
= 2E0 sinx cos(qt)
(13) B + B' = -B0 sin(x-qt)-B0
sin(x-2nπ+qt) = -2B0sinx cos(qt)
The graph of (12) is in the
XY-plane and the graph of (13) in the XZ-plane. The
waves of the man and the woman always continue propagating
in opposite directions along the X-axis, but the points
where E+E' and B+B' are always zero are
sinx = 0,
x = kπ
Those points x=kπ are always
fixed on the x-axis. The interference waves are
If d =
we have E + E' = E0
sin(x-qt) + E0 sin(x-(2n+1)π+qt)
B + B' = -B0
sin(x-qt) - B0 sin(x-(2n+1)π+qt)
So E + E' = E0
sin(x-qt) - E0 sin(x+qt)
(14) E + E' = -2E0
(15) B + B' = -2B0
The points fixed on the X-axis, where E + E'
= 0 and B + B' = 0, are
cosx = 0
x = π/2
The interference waves are also
The reader can envisage other
cases of interference of waves to interpret the relationship
between two individuals in a species.
Remark that each species of
living beings has a specific karmic coefficient ε which
characterizes that species. Within a species, each
individual has an individualistic coefficient μ which
characterizes special traits of that individual. Those
coefficients obey the rule of coefficient
community has a specific karmic coefficient, people in there
have similar thinking, similar wording, and similar acting.
The religious cults are examples of karmic coefficients
In society, some animals may
have their product εμq2 of karmic coefficients
close to that of persons, and their behavior is adorable to
people: such are the cases of pets like dogs, cats, birds...
which can live friendly with people.
Above we considered the simplest
case of sinusoidal functions. Actually the propagation of
waves is more complex than sine functions, but always
periodic. We know that a periodic functions can be
decomposed to a sum of sine functions each of which
represents a mental activity. We have five categories of
mental activities: sensitivity-emotion-mind-word-action
which form the 5-step process of life. Sensitivity is due to
the surface current on the skin, emotion due to the bound
current of electric dipoles, mind due to the free current of
free electrons, word due to the displacement current, and
action due to the vector potential. Each of those currents
produces a wave propagation. All the waves interfere and
superpose together with a complex graph. Each wave has a
different amplitude, wave length, and speed. In some short
period of time, one wave amplitude may be much greater than
the others, and the correspondent effect has the most
influence to the body/spirit, e.g. when one person is in the
cold, the cold sensitivity dominates the other things, or
when a person falls in love, the emotion is the most
important for that person.
In laboratory, scientists have
detected photons in the propagation of electric field
between 2 electric charges. That shows the propagation of
waves is quantized. A wave in motion is together with a
quantum in motion, and a quantum in motion is together with
a wave in motion. It is the
principle of complementarity in quantum mechanics.
that principle, the gravitation
has quantum called graviton, other waves are also quantized.
In 1924 L. de Broglie
postulated the formula for a wave and the corresponding
λ is the wave length, p=mv is the linear
momentum of the particle, and h is the Planck constant
h = 6.6
10-24 J sec
In 1900, Planck postulated
that the energy related to a light wave is
E = hc/λ
c is the speed of light.
The quanta corresponding to
light, electromagnetic, gravitation, karma waves...are
And a photon has no mass.
We have shown that a photon is
a combination of 2 opposite masses: a material mass +m and a
spiritual mass -m. The mass of a photon is therefore
(+m)+(-m) = 0
and the kinetic energy of a photon with speed
+ (1/2)(-m)(-v2) = mv2= pv
because the material speed square is v2
and the spiritual speed square is -v2. The
momentum of photon is then p=mv.
Since 1970 scientists have
discovered the existence of
anti-matter, e.g. electron has positron, a particle has
anti-particle...The concept of anti-matter is our concept of
spiritual-matter by the principle of universality
(m) of particle + mass (-m) of anti-particle = 0
In other words, a material mass
(m) has an opposite spiritual mass (-m). Furthermore, every
event in the material world has a correspondent event in the
spiritual world. If we use the “anti” language, we can say a
material event has anti-event (e.g. equation divE=ερ
has anti-equation divE'=ε'ρ'.)
At this point we have unified
the system of equations for gravitation with the system of
equations for karma.
In sciences physics, scientists
have 4 systems of forces: gravitational fores,
electromagnetic forces, strong forces, and weak forces which
many scientists expect to make a
grand unified system for the universe.
To see that, let's look at the
scientific researches and discoveries in physics so far.
ATOMS AND ELECTRONS
We have seen above the principle
of complementarity for particles and waves.
Now let's summarize briefly the
structure of atoms.
An atom has a positively
charged nucleus with negatively charged electrons orbiting
electron mass me is
9.109 389 7 x 10-31 Kg
electric charge of electron is
-e = -1.602 177 33 x
SHELLS IN ATOMS
The outline below is taken
from the article “Atoms” by A.P. French in Encyclopedia of
Physics, 2nd Edition, VHS.
The spatial states of an
individual electron could be determined by 3 quantum integer
numbers n, l, m. The value of n, called the principal
number, defines the electron energy just as in the Bohr
theory. But the identification of a state also requires
2 quantum numbers l, m that define the orbital angular
momentum of magnitude [l(l+1)]1/2h/2π of the
electron and the projection of magnitude mh/2π of this
orbital angular momentum along a specified axis. The quantum
analysis requires that 0 ≤ l ≤n-1 and -l ≤ m ≤ +l.
A partial table of the shell
structure up to Z=86 is the following.
Electron Shell Structure
(n,l) Shell capacity cumulative total
In 1924 Pauli, then in 1925
Uhlenbeck and Goudsmit assumed that the full quantum state
of an electron, in addition to 3 numbers n, l, m, depends on
one more number that is the intrinsic spin ±1/2 of the
electron in the atom corresponding to 2 quantized
projections ±h/4π of the spin angular momentum. This allows
a total of 2(2l+1) different quantum states for given values
of n, l.
And Pauli introduced the
exclusion principle (1924) according to which no two
electrons can have the same set of quantum numbers. This
principle is the fundamental key to the internal structure
of atoms. The electrons in an atom are forced to orbit on
shells of progressively increasing energy around the
We have just seen that an atom
is composed of a positively charged nucleus and electrons
with negative charge orbiting around the nucleus on
Now we look at the composition
of the nucleus.
is an outline from Adair's paper “Quarks” in Encyclopedia of
Physics, 2nd Edition, VHS.
Before 1950, a group named SU(2)
assummed that a nucleus contains 2 kinds of particles
called baryons that attract one another with
strong forces. The baryons are protons and
neutrons. The proton is positively charged and the neutron
is electrically neutral.
The mass of a proton is
1.672 623 1 x 10-27Kg
The proton-electron mass
= 1 836.152 701 x 10-3
The electric charge e+
of a proton is the opposite of the charge e- of
the electron. A proton has a
spin of ½.
A neutron has about the same mass as a
proton, and has a spin of ½.
Scientists discovered that
between 2 electric charges there is exchange of photons
with mass 0 and spin 1 in their electromagnetic
interactions. In Yukawa model for baryons, there is exchange
of mesons between 2 baryons in their strong interactions.
The mesons are of 3 kinds different only in their electric
charges: π+ is positively charged, π- is
negatively charged, and π0 is electrically
neutral. The mass of a meson is 270 times that of an
electron. A meson has spin 0. The baryons and mesons are
called together the hadrons. However, in spite of the
many similarities between electromagnetism and the strong
interactions, there are profound differences.
While the electromagnetic field is a vector
field described as 3 numbers that transform the components
of a vector, the strong interaction is described as only 1
number (like a pressure field): the strong field is scalar
field (a pseudo field.).
1960 many more hadrons and many more mesons were discovered
in strong interactions, some holding a new quality called
hyper-charge. Hyper-charge is a
quantum number relating to s quark.
Eugene Wigner formed a
technical group called SU(4) with a
description of protons of spins up and down, and of
neutrons of spins up and down. That pattern is less
1961, Murray Gell-Mann and Yuval Neemann found a group
labeled SU(3) which assumes the
fractional electric charges -e/3 and +2e/3. Those particles
are named the quarks u, d, s. All the quarks have spin-1/2
(called fermions in quantum mechanics) and have strong
Quark u (for up) has
electric charge 2e/3
Quark d (for down) has
electric charge -e/3
Quark s (for strange) has
electric charge -e/3
Mass of u = few MeV/c2,
a little greater than mass of d
Mass of s = 100 MeV/c2
A proton is uud
A neutron is udd
- Scientists also discovered
anti-matter, e.g. mass m has
anti-mass -m, quark q has anti-quark
Quark u has anti-quark
Quark d has
The pions have compositions:
Pion π+ is u
Pion π- is
Pion π0 is u
u or d d
In 1974, scientists discovered
a new quark c (for charm)
Quark c has electric charge +2e/3
Mass of c = 1.5 mass of
We have now 2 pairs of
partners: u – d, and, c – s
discovered the 5th quark b (for bottom)
Quark b has electric charge -e/3
Mass of b = 5 times mass of
scientist believed but not yet found a 6th quark
t (for top)
Quark t has electric mass
Mass of t = 100 times mass
It is the 3rd pair of partners t-b.
The 6 quarks
u, d, c, s, b, t are called
Each flavor has 3 colors:
red, yellow, blue (electric properties of flavors in strong
force.) In total there are 18 colors
u red, u yellow, u
similar for d, s, c,
quark has an anti-quark. So there
are 18 colors for 6 anti-quarks.
Now there are 3 quarks families
(different scales in electricity) forming 3 generations with
quite difference of mass scales.
Family u-d, masses
c-s, masses 1.5 protons - 100 MeV/c2
t-b, masses 100 protons - 5 protons
Scientists also found
leptons, particles with spin -1/2 (fermions) that are not
subject to strong force and that are believed to be truly
elementary and not composed of quarks or other subunits. The
leptons are electrons, muons, and tau-leptons.
A muon is similar in most
respect to the electron except that it is unstable and is
Mass of muon = 207
times mass of electron.
A tau-lepton is unstable with
Mass of tau = 3,500
times mass of electron.
Electron e has
electron-neutrino νe; muon μ has muon-neutrino νμ;
tau τ has tau-neutrino ντ. The neutrinos have
The leptons form 3 families
(different in scales of electricity) with 3 generations of
leptons and neutrinos that do not hold any color charges.
Therefore they do not take part in strong interactions. But
they play a role in weak interactions similar to that of
quarks in strong interactions. The 3 generations of leptons
have different scales of mass.
mass of electron 0.35 MeV/c2
mass of muon 105 MeV/c2
τ-ντ, mass of tau 1785 MeV/c2
We see that the 3 generations of quarks
(strong force) seem conjoining the 3 generations of leptons
(weak force). But how many generations of quarks are there
in the universe? We need to find the possible number of
generations of neutrinos to determine the number of
generations of quarks.
Neutrinos have anti-neutrinos. So how many
generations of neutrinos are there in the universe?
In any theories of the universe,
we must go back to the early times of the beginning of
Astrophysicists use their
understanding of cosmology and the knowledge of the relative
abundance of primordial hydrogen, deuterium, and helium to
guess the number of generations of neutrinos. In the early
universe, if we assume there are 3 generations of neutrinos
and anti-neutrinos, then the energy of 3 generations would
account for about 49% of the energy of the universe with the
photons taking 51%. If we assume 4 generations, the
neutrinos' energy would be 56% of the total energy leaving
44% to the photons. The assumption of 3 generations of
neutrinos and anti-neutrinos fit best the data. And we can
assert that there are certainly not more than 5 possible
The weak force and
the strong force have similarity as follows.
Between two leptons there is weak
force with the exchange of massless photons with spin 1.
Between two quarks there is
strong force with the exchange of massless gluons with spin
That may suggest a possible
unification of the weak and strong forces (?)
outline the article Quarkonium by
Elliot Bloom in the following.
A further study of the heavy
quarks c and b found the existence of 2 heavy mesons:
c ( c is anti c) and beautonium b b
( b is anti b.) Those heavy mesons are called
quarkoniums. Their binding energy is small compared to the
quark mass, and so the quarks move at a small fraction of
the speed of light. The use of charmonium as a bed for the
color force was initiated with the discovery of the J/ψ
meson in 1974, the first of a spectrum of charmonium c c
bound states, with a mass of 3095 MeV/c2. The
mass of the proton is about 30% of the mass of the J/ψ
mesons. The name J/ψ comes from simultaneous discoveries of
2 different groups, one led by Samuel Ting at the Brookhaven
National Laboratory naming the particle for J, the other
group led by Burton Richter at the Stanford Linear
Accelerator (SALC) naming it for ψ. Richter and Ting jointly
received 1976 Nobel price for the discovery.
In 1977 Leon Lederman at the
Fermi National Accelerator Laboratory (Fermilab) discovered
a larger spectrum of beautonium b
b states named Y
with mass 9460 MeV/c2, about 10 times the mass of
So far particle scientists
can not isolate a free quark, because the strong force
between 2 colors is inversely proportional to the distance
square, but at distance less than 10-13
centimeters, the force has a constant value about 16 tons
independent of the distance. They conclude that a free quark
does not exist.
Also we outline some
information of the article “Mesons” by Malcolm
Mesons consist of
quark-antiquark pair q
q bound together by strong
force, which is mediated by the gluons. The quantum numbers
of the mesons are specified by the intrinsic properties of
the quarks and the spectroscopic state of the spin or
orbital angular momentum. The mesons can also carry flavor
property of s, c, and b. Most mesons decay strongly with
lifetime 10-24 sec. High-mass mesons involving u
and d quarks decay by giving π mesons. Mesons with s, c, b
decay to a K( sd), D(c d), B( bd) meson
plus π mesons. These lowest-lying states mesons decay weakly
with lifetimes in the range 10-8 -10-10
sec. In strong-interaction theory, the gluons also interact
strongly and should be composed to form new particles called
glueballs. But so far, no glueballs have yet been seen.
The lowest mass meson, called
the π meson, predicted by Yukawa 40 years ago are not
completely understood today.
can summarize the description above as follows.
Sciences have been developed in
two parallel routes: the discovery of anti-matter as
opposite to matter, and the decomposition of particles to
the scales of quarks, flavors and colors. The two routes of
sciences concur in super-science
that explores the two material and spiritual worlds and
reaches the frontier of the universe.
concept of fractional electric charge -e/3 and +2e/3
suggests that there are sub-particles with electric charges
ε=e/3 and η=2e/3 and anti-charges
ε and η
which are positive or negative
ε- η η-
Those sub-particles can stand single, or
combined in 2 called bios, or combined in 3 called trios.
εε- εη ε-η …
εη- ε-ηη εε-η
Beside those sub-particles and
anti sub-particles, there are neutrinos.
Those sub-particles can be
combined with neutrinos. Thus there is a great number of
combinations of sub-particles and sub-neutrinos, which
scientists will take time to discover and detect in the
future. Some dozens of those sub-particles and sub-neutrinos
were already discovered and detected by scientists and were
given different names along their separate experiments as we
have just seen above.
Furthermore, in the future we can
go on decomposing the sub-particles and sub-neutrinos into
smaller particles, then smaller and smaller, and so on…
While the particles still have
material mass and anti-mass, or charge and anti-charge, we
can decompose them again and over again.
Finally we will reach the final state of
particle-no-particle that is the state of no-rest-no-motion
of energy. Particle-no-particle is non-decomposable. The
state of no-rest-no-motion of energy with
particle-no-particle is the absolute state of the universe.
In the absolute state of the universe, we can
define an absolute frame of reference. And in an absolute
frame of reference we can define 2 relative systems in
relative motion with one another.
Yet we have defined the
The next step is the absolute
time. How do we define the absolute time?
Time is defined by motion.
In the universe, consider all motions of all the masses and
energies in both material and spiritual worlds. The
resultant velocity of all those motions is a vector
called vector of the universe, which may vary or is
constant beyond our human knowledge. So mathematically,
mechanically and physically we assume that the vector of the
universe is constant. That constant resultant of velocity
defines the absolute motion of the universe which
manifests the absolute
With two relative frames of
reference in motion relatively to one another, for an event
we have 2 different systems of relative coordinates and two
different relative times. So when studying a relative motion
of an event with respect to the two relative systems, we
must distinguish the absolute coordinates from the relative
coordinates, and distinguish the absolute time from the two
relative times in the two systems of reference.
we look back at the equations of transformation of
coordinates in the Paper,
Theoretical Concepts of Universality, to see clearly the
distinction of absolute coordinates and time from the
relative coordinates and times in 2 relative systems OXYZ
and O'X'Y'Z'. Remember that in the thought experiment we
assume that the system (O') moves along the axis OX
uniformly with velocity q. Thus with respect to the
system (O'), (O) moves on the axis O'X' uniformly in
opposite direction with velocity -q. And we have
established the 4 equations
Z' = Z
The inverse system of equations
X = (X'+qt')(1-q2/c2)-1/2
Z = Z'
2 above systems of equations, X,Y,Z,t and X',Y',Z',t'
represent the coordinates and time of the same event in 2
Let's examine the assumption in
the above thought experiment of 2 systems moving in uniform
motion relatively to one another.
There are 3 observers (not 2):
one observer in the absolute system with absolute time τ,
two observers in the relative systems (O) and (O') with
relative times t and t'.
For the absolute observer, the
thought experiment can be described as follows. Two points O
and O' move on the same axis in opposite directions with
relative velocities -q and q. Suppose at time τ=0, the 2
points start at a point Ω on the line Ωu which is the same
as the lines OX and O'X'. The point Ω is the fixed origin of
the absolute reference. The point O' left the point O at a
relative velocity q but left the point Ω (midpoint of OO')
at the absolute velocity q/2. Similarly, O left Ω at the
absolute velocity -q/2. At time τ, we have ΩO=u= -qτ/2 and
ΩO'=u'=qτ/2. The absolute velocity of O' is du'/dτ=q/2, and
the absolute velocity of O is du/dτ=-q/2. Thus for the
absolute observer we can write
du/dτ + du'/dτ
which satisfies the assumption of uniform
linear motion of (O) and (O') relative to one another.
The absolute observer sees the 2
simultaneous events (O) and (O')moving in opposite
directions with opposite velocities. That is the concept
of simultaneity in our theory of uni-relativity.
Remark that in the sense of
uni-relativity (2 relative frames within an absolute frame)
for an event with coordinates X, Y, Z, and time t in the
system OXYZ, and with coordinates X',Y' Z' and time t' in
the system O'X'Y'Z', the relative
velocity of the event in OXYZ is
relative velocity of the same event in O'X'Y'Z' is
dX/dt ≠ dX'/dt'
Since Y=Y', Z=Z', but dt≠dt',
So in the relativistic sense,
the relative velocities of the same
event in the 2 relative systems are different in 3
directions (not in the only direction of the motion.)
The assumption that the 2
relative systems (O) and (O') move with opposite uniform
linear motions relatively to one another is meaningful
for the view of the absolute observer. The 2 relative
observers see the relative velocities of the same event
completely different in three directions.
We can find out how each of the 2
observers sees the velocity of the other.
The point O' in the system O'X'Y'Z' has
relative coordinates and time
X' = (X-qt)(1-q2/c2)-1/2
t' = (t-qX/c2)(1-q2/c2)-1/2
Y' = 0
Z' = 0
So from the equation of X', we
X = qt
That is, observer (O) sees (O')
moving with relative velocity
We can proceed with the inverse
coordinates of the pointO'
X = (X'+qt')(1-q2/c2)-1/2
t = (t'+qX'/c2)(1-q2/c2)-1/2
Z = 0
qt'/t' = q
X = qt
dX/dt = q
It is the same result: (O) sees (O')
moving with relative velocity dX/dt=q.
Similarly observer (O') sees (O)
moving with relative velocity
We have just computed the 2 relative
velocities dX/dt=q and dX'/dt'=-q for 2 different
events, so we
can not add them and we can not
dX'/dt' = 0
which is meaningless.
That is the 2 relative observers
can not see the simultaneity in their relative motion.
Even if we suppose that the 2 relative observers have 2
synchronized clocks when they start moving, we can not
figure out simultaneity of the 2 systems if there is NO
THE PRINCIPLE OF UNCERTAINTY
Should the reader need to know some basic of the
principle of uncertainty in physics of Heisenberg, we
outline the mathematical proof of it from the article “Quantum
Mechanics” by Ernest Seglie and Susan Fox in Encyclopedia of
Physics, 2nd Edition, VHS.
problem is that in doing research with particles, many
experiments can be understood with only particle aspect,
while others only with wave aspect. To explain the dual
aspect wave-particle, Heisenberg introduced the principle of
UNCERTAINTY ON MOMENTUM AND SPACE
In 1900 while studying the
black box in thermodynamics, Planck assumed the equation
(16) E = hc/λ
E is the energy of light quantum, c is the
speed of light, λ is the wave length, and h is the Planck
h = 6.626 075 5
10-34 J sec
In 1924 L. de Broglie assumed
that the wave length λ is associated with the momentum p=mv
of a particle by the equation
(17) λ = h/p
Consider a particle supposed to
be within a region Δx (assume 1 dimension x.) Let N be the
number of waves in Δx, but we don't know precisely where the
waves begin and terminate in Δx, then
N = Δx/λ±1 (minimum error
assumed to be 1)
λ = Δx/(
Solving for λ yields
λ = λ± λ2/
Δλ = λ2/
/Δx = 1
From de Broglie equation, differentiating
p with respect to λ gives
= | Δp/h|
(19) Δp Δx ~ h
Since the error on N is greater
than or equal to 1, we have the
uncertainty on the momentum and the position
(20) Δp Δx ≥ h
UNCERTAINTY ON ENERGY AND TIME
We also have uncertainty on
energy and time by computing typically the
uncertainty on the lifetime Δt of an excited state
and the energy E of the state of a
That energy is measured by the wave
length λ of the photon emitted by the de-excitation process.
For photons, an analysis similar to above
gives equation (18) again
/Δx = 1
where Δx measures the maximum photon wave
length which can not be longer than c Δt, and Δt is
the time from excitation to de-excitation.
/(Δx/c) = 1
Δx/c is the time it takes for the decay,
By differentiating E with respect
to λ in the Planck equation (17) we have
ΔE = |(hc/λ2)Δλ|
(21) ΔE Δt ≥ h
which is the uncertainty on energy and
The uncertainty on momentum and
position (20) is the uncertainty on mass and space
and the uncertainty (21) is the
uncertainty on energy and time.
UNCERTAINTY ON SPACE AND TIME
So the determinations of mass,
energy, space and time all have uncertainty.
take the product of the 2 inequalities (20) and (21) above,
ΔE Δx Δt ≥ h2
ΔE] [Δx Δt] ≥ h2
In virtue of the equation E=mc2,
we see that the first bracket [Δ(mv) ΔE] concerns mass and
= (ΔE)2v/c2 +E ΔE Δ(v/c2)
We can assume v< c2, and
(ΔE)2v/c2 +E ΔE Δ(v/c2) <
< (ΔE+E) ΔE
In the determination of space and
time, let's assume (ΔE+E) ΔE < k, then from (22) we have
(23) Δx Δt ≥ h2/k
there is uncertainty on the determination of
space and time. So we can not determine space and time
precisely as we expect when we assume certain precision on
in the condition (ΔE+E) ΔE < k we can always take k as large
as we want, even we can assume that k is infinity. So
in the uncertainty condition of space and time Δx Δt ≥ h2/k,
the 2nd member h2/k can be made very
small even equal to zero
Δt ≥ 0.
Thus we can take
the limit case
Δx = 0 and
Δt = 0
which means the determinations of both space
and time are precise. In general, there is some uncertainty
on space and time, but by a proper method of
super-science-religion (meditation) we can have precision on
both space and time together.
THE PRINCIPLE OF IGNORANCE
uncertainty on particle and wave in some sense is that when
we know the particle aspect in an event, we don't know its
wave aspect, and conversely. By saying “We don't know”, we
mean ignorance. It is
the principle of ignorance. We can say that
the principle of uncertainty is a
manifestation of the principle of ignorance.
For space and time of energy, if we
determine the form (space) of an event with certain
precision, we can't in general determine its time (duration)
with precision, and conversely. But if we practice
meditation, we can perceive both space and time with
in the universe contains energy in some form within in space
and time. Space and time of energy are like the two faces of
a coin. If a coin is, for example, made of nickel, when the
two faces disappear, the coin is transformed back to nickel
material (the coin won't subsists any more.) The coin with 2
faces is a phenomenal form, and the nickel material is its
The Universe (Energy with
Space-Time) is the Greatest Phenomenal Form whose substance
is the Supreme Energy or Transcendental Power. If we
clear Space and Time from Energy by meditation,
Energy-Space-Time will transform itself back to the
Transcendental Power which is the Sacred Substance with
At the Beginning of the
Universe, Ignorance created Space and Time that covered the
Transcendental Power, and the sacred Transcendental Power
with No-space-time becomes Energy with space-time: The
To abolish Ignorance we can not
use our minds and thoughts. It requires ENLIGHTENMENT. The
key to Enlightenment is Meditation. Meditation is the method
and enlightenment is the purpose of Super-religion.
The fundamental problem of
super-science is the search of the origin of the universe,
and the solution to that problem is super-religion.
Super-science and super-religion combine together in
Super-science studies phenomenal
laws in the universe of two material and spiritual worlds.
Super-religion reveals the
transcendental substance of the Universe, and shows the
Right Way to Enlightenment through out the Origin of the
With super-science we discover
the duality of the spiritual world and the material world,
then reach the origin of the universe by the decomposition
of particles to the limit of particle-no-particle.
With super-religion we learn and
practice the Right Way of Meditation to Enlightenment to
transcend beyond the universe.
IGNORANCE AND ENLIGHTENMENT
researches and discoveries in super-science help us know the
Natural Laws of energy and matter in both material and
spiritual worlds. Among the laws, there is the principle of
ignorance which means we can not with our minds and thoughts
Truly Understand the Transcendental Power beyond the
At this point we make clear how
we can understand the Transcendental Power. There are
3 levels of understanding.
1/ Understand the normal meaning
of the words “Transcendental Power” like any other words in
the conversation or in a dictionary.
2/ But the words “Transcendental
Power” indicate a secret meaning beyond human perception. So
Meditation is the Right Method of
Enlightening, that is “understanding” the sacred object
beyond normal knowledge.
3/ The 3rd level of
“understanding” is Experiencing
oneself the Transcendental Power.
Enlightening is revealing the
Truth. Experiencing is itself The Truth, that is living with
A Right Belief is a Sacred
Understanding of the Transcendental Power. A belief with no
understanding is superstitious.
We end this paper here and suggest the reader
to continue reading the papers on Meditation and
Enlightenment already written 10 years ago in Vietnamese
which we did not have time to translate into English. We
hope to rewrite them in English in the near future. Those
papers are not in copyright and are available to be
translated by anybody interested in the sacred subject.
* ENCYCLOPEDIA OF PHYSICS, 2nd
* Reference books listed in the paper
THEORETICAL CONCEPTS OF UNIVERSALITY
Tiến Sĩ Toán học
Giáo sư Toán Đại học Loras
tại Iowa, Hoa Kỳ