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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





         This esay is an introduction to Meditation and Enlightenment via super-science.

         The first part is a continuation of the previous paper, Theoretical Concepts of Universality.




          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. The 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 of equations

                                   divB = 0

          In vector calculus, we know

                                   div(curlA) = 0

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

          The vector A is called in electromagnetism vector potential.

          We can express E directly in term of A

                                   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


          We 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


                                    curlE = - DtB

                                    curlB = εμDtE +μJ

                                    divE = ερ

                                    divB = 0


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.

          In vacuum, there is no mass, no electric charge, and no currents, the above system of equations becomes


                                     curlE = - DtB

                                     curlB = εμDtE

                                     divE = 0

                                     divB = 0


          With that system of equations, we study the propagation of the fields E and B in vacuum.




          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 of Universality.

          Let's take the derivative with respect to time of equation 2 of the system

                                     Dt(curlB) = εμDttE

                                    curl(DtB) = εμDttE         

          Substitute DtB from equation 1

                                     curl(-curlE) = εμDttE

          But we know

                                     X(▼X E ) = ▼(▼E ) - ▼2E

          From equation 3 in the system

                                     E = divE = 0

          So                       ▼2E = εμDttE





(1)                       DxxE+DyyE+DzzE = εμDttE

(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)

                          DxxEx+DyyEx+DzzEx = εμDttEx                    

                           DxxEy+DyyEy+DzzEy = εμDttEy

    DxxEz+DyyEz+DzzEz = εμDttEz   


          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 x only.

          Equation (1) becomes

(2)                                   DxxE = εμDttE

          Equation (2) is called wave equation, of which a solution has the form

(3)                                    E = E0 sin(x-qt)

          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

                                DxxE = - E0 sin(x-qt)

and twice with respect to t

                                DttE = - q2E0 sin(x-qt)

          Substitute in equation (2)

                               -E0 sin(x-qt) = -εμq2E0 sin(x-qt)

          Simplifying both sides yields with q2= |(v|jw)2| = |v2-w2|

                                εμq2 = 1

                                (εμ)-1/2 = q

          The speed of the wave propagation q equals (εμ)-1/2.

          Now we proceed with the vector B.

                                  Dt(curlE) = - DttB

                                  curl(DtE) = - DttB

                                  curl(curlB) = -εμDttB

                                  X(▼X B) = ▼(▼B) - ▼2B

But                            ▼B = divB = 0

(4)                              ▼2B = εμDttB

          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

(4)'                          DxxB = εμDttB

          Solution to equation (4)' has the form

(5)                           B = B0 sin(x-qt)

          Then take the second partial derivatives of B

                               DxxB = -B0 sin(x-qt)

                               DttB = -q2B0 sin(x-qt)

                  - B0 sin(x-qt) = -εμq2B0 sin(x-qt)


          After simplifying

(6)                                εμq2 = 1

(7)                                (εμ)-1/2 = q

          We get the same formula as before. We call (6) or (7) the rule of coefficients.

          We need also to determine the constants E0 and B0.

                Let's take the 2 equations

                               curlE = - DtB

                               curlB = εμDtE

          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 iz

                                curlE = E0 cos(x-qt) iz

          With the assumptions above we have

                                    DxE = E0 cos(x-qt)


                                    DxB = B0 cos(x-qt)

          Differentiate E and B with respect to t

                                    DtE = - q E0 cos(x-qt)

                                    DtB = - q B0 cos(x-qt)

          So                      E0 cos(x-qt) = q B0 cos(x-qt)

                                    B0 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

                                               εμq2 = 1

and                                          E0 = qB0

                 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.




          If we take the wave functions in the form

                                E = E0 sin(2π/λ)(x-qt)

                                B = B0 sin(2π/λ)(x-qt)

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 have

                                 q2 = v2 - w2

v and w are the material and spiritual speeds.

          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 waves.

          Today we have the precise values in classical notations


                       ε0 μ0)-1/2 = 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 - w2

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 karma system.




          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 the body/spirit.

          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

          The atomic polarizability α is a specific coefficient of the material element: different elements have different atomic polarizabilities.

          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

                                                εμq2 = 1

          Actually the three factors ε, μ, q appear together as a product (εμq2) which is called the self or ego of each individual.

          The 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.




           We 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 E

                                                2E = εμDttE

           Consider the propagation with speed q along the X-axis, and the field E assumed to be in the XY-plane, we have equation (2)

                                                DxxE = εμDttE      

           And a solution to (2) has the form

                                                E = E0 sin(x-qt).

           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

                                                DxxB = εμDttB

and a solution of sine form

                                                B = B0 sin(x-qt)

 Now we apply those results to the interaction between a man and a woman.

 We set up the problem as follows.

 Suppose a man and a woman are at a distance d apart on the x-axis.

 The functions for the man are

                                                E = E0 sin(x-qt).

                                                B = B0 sin(x-qt)

 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' sin(x'+q't)

                                   B' = B0' sin(x'+q't)


                                     x-x' = d

                                     x' = x – d


(8)                          E' = E0' sin(x-d+q't)

(9)                          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' sin(x-d+q't)

                       B + B' = B0 sin(x-qt) + B0' sin(x-d+q't)


 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 another.

 Suppose now the 2 persons are under similar conditions of karmic and individualistic coefficients εμq2 such as q=q', E0=E0', B=B0'.

                           E + E' = E0 sin(x-qt) + E0 sin(x-d+qt)

                           B + B' = B0 sin(x-qt) + B0 sin(x-d+qt)


                            E + E' = E0 [sin(x-qt) + sin(x-d+qt)]

                            B + B' = B0 [sin(x-qt) + sin(x-d+qt)]


(10)                       E + E' = 2E0 sin(x-d/2) cos(qt-d/2)

(11)                       B + B' = 2B0 sin(x-d/2) cos(qt-d/2)


 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


                                                sin(x-d/2) = 0

                                                x-d/2 = kπ

                                                x = d/2 + kπ

 Those points are fixed on the x-axis. We say the waves of E+E' and B+B' are standing waves.


 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.

 We can see some particular cases.



 If d = 2nπ

 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 standing waves.


 If d = (2n+1)π

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 cosx sin(qt)

(15)             B + B' = -2B0 cosx sin(qt)

 The points fixed on the X-axis, where E + E' = 0 and B + B' = 0, are

                                     cosx = 0

                                     x = π/2 + kπ

 The interference waves are also standing.


 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

                                                εμq2 = 1


 A 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 community.


 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.



                           AND UNIVERSALITY


 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.

 By 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 quantum:

                                                λ = h/p

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 called photons.

 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 v is

                       (1/2)mv2 + (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

           mass (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 around.

 The electron mass me is

                               me = 9.109 389 7 x 10-31 Kg

 The electric charge of electron is

                               -e = -1.602 177 33 x 10-19 Coulomb




 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

 Vales of (n,l) Shell capacity cumulative total

 (1,0)                                                 2                2

 (2,0)+(2,1)                                        8                8

 (3,0)+(3,1)                                        8                10

 (3,2)+(4,0)+(4,1)                              18              36

 (4,2)+(5,0)+(5,1)                                        18               54

 (4,3)+(5,2)+(6,0)+(6,1)                              32               86


 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 nucleus.


                           NUCLEI AND BARYONS


 We have just seen that an atom is composed of a positively charged nucleus and electrons with negative charge orbiting around the nucleus on different shells.

 Now we look at the composition of the nucleus.




 Below 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

                                mp = 1.672 623 1 x 10-27Kg

 The proton-electron mass ration is

                                mp/me = 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.).


 In 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 transparent.


 In 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 interactions.


 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 q

 Quark u has anti-quark u

 Quark d has anti-quark d

 The pions have compositions:

 Pion π+ is ud

 Pion π- is ud

 Pion π0 is uu or dd

 In 1974, scientists discovered a new quark c (for charm)

 Quark c has electric charge +2e/3

 Mass of c = 1.5 mass of proton

 We have now 2 pairs of partners: u – d, and, c – s

 Then Lederman discovered the 5th quark b (for bottom)

 Quark b has electric charge -e/3

 Mass of b = 5 times mass of proton

 In 1989, scientist believed but not yet found a 6th quark t (for top)

 Quark t has electric mass +2e/3

 Mass of t = 100 times mass of proton.

 It is the 3rd pair of partners t-b.

 The 6 quarks u, d, c, s, b, t are called flavors.

 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 blue

                                similar for d, s, c, b, t

 But each 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 few MeV/c2

                   Family c-s, masses 1.5 protons - 100 MeV/c2

                  Family 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 positively charged.

                       Mass of muon = 207 times mass of electron.

 A tau-lepton is unstable with mass

                       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 mass zero.

 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.

                    Family e-νe, mass of electron 0.35 MeV/c2

                    Family μ-νμ, mass of muon 105 MeV/c2

                    Family 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 everything.

 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 generations.

 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 1.

 That may suggest a possible unification of the weak and strong forces (?)




 Then we 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: charmonium cc (c is anti c) and beautonium bb (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 cc 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 bb states named Y with mass 9460 MeV/c2, about 10 times the mass of the proton.

 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 Derrick.

          Mesons consist of quark-antiquark pair qq 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(cd), 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.

          We 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.


                   A HYPOTHETICAL ANALYSIS



          The 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 ε- η η-

                                                ε ε- η η-

                Those sub-particles can stand single, or combined in 2 called bios, or combined in 3 called trios. For example

                                          εε εε- εη ε-η …

                                          εηη- εεη- 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 absolute space.

          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 time.

 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.

          Now 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

                                   X' = (X-qt)(1-q2/c2)-1/2

                                   t' = (t-(q/c2)X)(1-q2/c2)-1/2

                                           Y' = Y

                                           Z' = Z

          The inverse system of equations is

                                X = (X'+qt')(1-q2/c2)-1/2

                                t = (t'+(q/c2)X')(1-q2/c2)-1/2

                                             Y = Y'

                                             Z = Z'

          In the 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 relative frames.




          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 = 0


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

dX/dt = (dX'+qdt')/[dt'+(q/c2)dX']

                        dX/dt =(dX'/dt'+q)/[1+(q/c2)dX'/dt']


          And the relative velocity of the same event in O'X'Y'Z' is

                        dX'/dt' = (dX/dt-q)/[1-(q/c2)dX/dt]

                         dX/dt dX'/dt'

          Since Y=Y', Z=Z', but dt≠dt', then

                                    dY/dt ≠ dY'/dt'

                                    dZ/dt ≠ dZ'/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 = 0

                               t' = (t-qX/c2)(1-q2/c2)-1/2

                                        Y' = 0

                                        Z' = 0

 So from the equation of X', we have

                                       X = qt

 That is, observer (O) sees (O') moving with relative velocity

                                       dX/dt =q

 We can proceed with the inverse coordinates of the pointO'

                     X = (X'+qt')(1-q2/c2)-1/2 =qt'(1-q2/c2)-1/2

                    t = (t'+qX'/c2)(1-q2/c2)-1/2 =t'(1-q2/c2)-1/2

                                        Y = 0

                                        Z = 0


                                                X/t = 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

                                                dX'/dt' = -q

 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 write

                                                dX/dt + 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 absolute observer.




 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.

 The 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.




 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 constant

                                                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/( Δx/λ±1)

 Solving for λ yields

                                                 λ = λ± λ2/ Δx

 The uncertainty is

                                                 Δλ = λ2/ Δx

(18)                                          (Δλ/λ2) /Δx = 1

 From de Broglie equation, differentiating p with respect to λ gives

                                                | Δλ/λ2| = | Δp/h|

and therefore

(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




 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 photon.

 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

                                                (Δλ/λ2) /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.

 Then                                       c(Δλ/λ2) /(Δx/c) = 1        

Δx/c is the time it takes for the decay, since Δx/Δt=c.

 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 time.

 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.




 So the determinations of mass, energy, space and time all have uncertainty.

 If we take the product of the 2 inequalities (20) and (21) above, we have

                                 Δp ΔE Δx Δt ≥ h2 

(22)                          [Δ(mv) ΔE] [Δx Δt] ≥ h2

 In virtue of the equation E=mc2, we see that the first bracket [Δ(mv) ΔE] concerns mass and energy

                                [Δ(Ev/c2) ΔE] = (ΔE)2v/c2 +E ΔE Δ(v/c2)

 We can assume v< c2, and Δv< c2.


                      (ΔE)2v/c2 +E ΔE Δ(v/c2) < (ΔE)2+E ΔE

                                                             < (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


 That means 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 energy.

 But 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

(24)                                  Δx 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 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 precision.

 Every event 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 substance.

 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 No-space-time.

 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 Universe appeared.

 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-religion.

 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 Universe.

 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.




 The 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 universe.

 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 the Truth.

 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.





* Reference books listed in the paper THEORETICAL CONCEPTS OF UNIVERSALITY







GS Trần Cao Tần
Tiến Sĩ Toán học

Giáo sư Toán Đại học Loras tại Iowa, Hoa Kỳ