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Trở về d_bb  ĐHKH

 

Trở về Trang Tác Giả

 

 

 

Giáo Sư Trần Cao Tần

ON THE FORMULA E=mc2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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THEORETICAL CONCEPTS
OF UNIVERSALITY

written in 2016

by Tan Tran, Ph. D.

This paper is in copyright. No reproduction of any part
may take place without the written permission of the author

 

 

 

       

This is the first essay on super-science in which we establish the basic equations of gravitation and electromagnetism for the universe composed of two material and spiritual worlds inseparably connected together. The equations are inspired from the equations of Maxwell in the theory of electromagnetism.

          We generalize the theory of electromagnetism to gravitation and karma, then explore the theory of life and death.

          We do not expect rigor in the proofs of the equations because we don't have for super-science any scientific experiment in laboratory so far. We can say these are “thought experiments” beyond the recent knowledge in the scientific world.

 

INTRODUCTION TO UNI-FORMS

        

          The basic tools used in mathematics, mechanics, physics are the real and complex numbers upon which are established equations and scientific theories. None of those theories can describe the spirits, senses, emotions and minds. To introduce a new theory concerning both matter and spirit, we need to create a new category of tools called THE UNI-FORMS.

          A uni-form is described as follows:

                                      (x|jξ)   or   (u|jv)

which are composed of two forms (x|j0) and (0|jξ), or of two forms (u|j0) and (0|jv) called    respectively the MATERIAL PART and the SPIRITUAL PART. The form can be regarded as a number (x|jξ) where x and ξ are real numbers, or as a vector (u|jv) where u and v are real vector.  The letter j used here is only a symbol indicating that jξ and jv belong to the category of spiritual, and it is not the imaginary number i. So the writing j2 is meaningless.      

          For scalar uni-function, we can write

                                      m = (mr|jms)

where mr is a scalar function of 3 real variables (x,y,z), and ms is a scalar function of 3 real variables (ξ,η,ζ).

          For a vector uni-function, we van write

                                      F = (Fr|jFs)

where Fr is a vector function of 3 real variables (x,y,z), and Fs  is a vector function of 3 real variables (ξ,η,ζ). We can also write for uni-vectors

                                      F = ((x,y,z)|j((ξ,η,ζ))

        With such representation, the uni-number (x|jξ) can be regarded also as a uni-vector (u|jv) where u(x) and v(ξ) are vector functions of a single variable.

          The uni-forms have the following operations

 

ADDITION OF UNI-FORMS

 

    (x|jξ )+(x'|jξ') = ((x+x')|j(ξ+ ξ')) = (x'|jξ')+(x|jξ) for numbers

     (u|jv)+(u'|jv') = ((u+u')|j(v+v')) = (u'|jv')+(u|jv) for vectors

     Addition is commutative. We can verify easily the associativity of the addition too.

          The zero uni-form (0|j0) is the additive unity.

 

MULTIPLICATION WITH REAL NUMBERS

 

                            α(x|jξ) = (αx|jαξ) = (x|jξ)α

                            α(u|jv) = (αu|v) = (u|jv)α.

where α is a real number.

           Multiplication is associative with real numbers.

           Note that we don't allow multiplication of uni-forms with imaginary numbers or with complex numbers.

 

INNER PRODUCT OF 2 UNI-FORMS

 

    We call INNER PRODUCT OF 2 UNI-FORMS the operation

                  (x|jξ) . (x'|jξ') = xx'- ξξ'= (x'|jξ') . (x|jξ)

                  (u|jv).(u'|jv') = u O u'- v O v'= (u'|jv').(u|jv)

where the dot “.” is the inner product, and the small circle “O” is the scalar product of 2 real vectors.       

          Recall the scalar product of 2 real vectors 

                             u O u' = xx'+yy'+zz

'                            v  O   v' = ξξ'+ηη'+ζζ'

                             (u|jv).(u'|jv') = (xx'+yy'+zz') - (ξξ'+ηη'+ζζ')

          The inner product of 2 uni-forms is a real number.

          The inner product can not be performed with 2 uni-forms of different categories, for example:

   a number (x|jξ) with a vector (u|jv) of several variables, or two vectors (u|jv) and (u'|jv') where u and u' have different variables, or v and v'have different variables.                                            

          Inner product is different from scalar product. Inner product applies to uni-forms in both cases of numbers and vectors. Scalar product applies only to real vectors.

 

ABSOLUTE VALUE AND NORM

          The inner square of a uni-form

                             (x|jξ)² = x²-ξ²

                             (u|jv)2 = u o u – v o v

can be positive, null, or negative. The absolute value of (x|jξ) is

                             ׀(x|jξ)׀ =  √(|x²-ξ²|) ≥ 0

          And the absolute value of (u|jv) is

                              |(u|jv)| = √(|u O u – v O v|) ≥ 0

          We call norm of a uni-form the expression

                             ||(x|jξ)|| =  √(|x²+ξ²|) ≥ 0

                             ||(u|jv)|| = √(|u O u + v O v|) ≥ 0

 The 2 vectors (1|j0) and (0|j1) are called the multiplicative unities.

          A uni-form is NULL if its absolute value is 0, that is x=ξ.

          The ZERO uni-form (0|j0) is a null uni-form.

 

ORTHOGONALITY

 

          The 2 unit uni-vectors (1|j0) and (0|j1) are orthogonal.

 

PARALLEL

 

      We call CROSS PRODUCT of 2 uni-vectors (x|jξ) and (x'|jξ') the following operation

                             (x|jξ) X (x'|jξ') = (0|j(xξ'-x'ξ))

          Two uni-vectors are said to be parallel if their cross product is the zero vector

                             (x|jξ) X (x'|jξ') = (0/j0)

that is, their components are proportional.

 

CROSS PRODUCT OF REAL VECTORS WITH UNI-VECTORS

 

                             w X (u|jv) = ((w X u)|j(w X v))

where wXu and wXv are the cross products of 2 real vectors of 3 components.

                             w X (u|jv) = - (u|jv) X w

 

OPERATIONS
 

  Let's call u, v, w...the uni-forms. We have the following formula.

                             u . v = v . u

                             u . (v + w) = u . v + u . w = (v + w) . u

                             u X v = -(v X u)

                             u X u = 0

                             u X (v + w) = u X v + u X w

                             au X bv =  ab(u X v)   a, b are real numbers

 

DIFFERENTIATION

 

          Its easy to verify the following formula

                             d(x|jξ) = (dx|jdξ)

                             d(u + v) = (du + dv)

                             d(u . v) = (du . v) + (u . dv)

                             d(u X v) = (du X v) + (u X dv)

 

UNI-VECTOR SPACE OF THE UNIVERSE

 

          We adopt here THE PRINCIPLE OF DUALITY OF THE UNIVERSE by which our universe is composed of TWO INSEPARABLE WORLDS: THE MATERIAL WORLD AND THE SPIRITUAL WORLD CONNECTED TOGETHER.

 That principle of duality is our PRINCIPLE OF UNIVERSALITY.

          To represent the universe in mathematical mechanics, we consider 6 dimensions in a one-one correspondence:

                             LENGTH ------------ SENSE

                             DEPTH -------------- EMOTION

                             HEIGHT ------------ MIND

          The universe is represented by a UNI-VECTOR SPACE OF 6 DIMENSIONS x, y, z for length, depth, height, and jξ , jη , jζ for sense, emotion, mind.

          We consider the uni-vectors of 6 components in that UNI SPACE

                                      (x,y,z|jξ ,jη ,jζ)

The 3 components x, y, z are called MATERIAL COMPONENTS, and the 3 components jξ , jη , jζ  are called SPIRITUAL COMPONENTS.

                        Component                 x represents length

                                      y –----------  depth

                                      z ------------  height

                                      jξ -----------  sense

                                      jη ----------   emotion

                                      jζ –---------   mind

          Such  one-one correspondence once adopted can not be changed in the paper. That yields 3 two-components uni-forms (x/jξ), (y,jη), (z/jζ ).

          For convenience of writing, we can consider the 6-component uni-vector as a 2-component uni-vectors (u|jv) with the material part u=(x,y,z) and the spiritual part jv=j(ξ , η , ζ ).

          In that uni-vector space we take for inner product

      (x,y,z|jξ ,jη ,jζ) . (x',y',z'|jξ ',jη ',jζ') = xx'+yy'+zz'-ξξ̓'-ηη'-ζζ'

and we have similar operations and formula as for 2-uni-vectors in the above sections.

          The inner square of a 6-uni-vector is

                   (x,y,z|jξ ,jη ,jζ)² = x²+y²+z² -ξ²-η²- ζ²

which is positive, negative, or zero.

          In that uni space we consider a uni-system of reference of 6 axes Ox,y,z,jξ ,jη ,jζ.

    We have then a one-one correspondence of that uni-system of such axes with a REAL SYSTEM OF 6 REAL AXES  Ox,y,z,ξ,η ,ζ.

          By convention, if the real system of six axes is orthonormal, we say the uni- system of 6 axes is orthonormal. Such orthonormal systems are used in the rest of this paper.

          The unit vectors of the real system on the 6 axes are of length 1: e1, e2, e3, e4, e5, e6.

                                               e1=(1,0,0,0,0,0)

                                               e2=(0,1,0,0,0,0)

                                               e3=(0,0,1,0,0,0)

                                               e4=(0,0,0,1,0,0)  

                                               e5=(0,0,0,0,1,0)

                                               e6=(0,0,0,0,0,1)   

Those vectors are orthogonal to one another and form an orthonormal basis for the real space of 6 dimensions. And the one-one corresponding unit vectors of the 6 axes in the uni- system are by abuse of notations: e1, e2,e3, je4, je5, je6.

                                      e1=(1,0,0|j0,j0,j0)

                                      e2=(0,1,0|j0,j0,j0)

                                      e3=(0,0,1|j0,j0,j0)

                                      ie4=(0,0,0|j1,j0,j0)

                                      ie5=(0,0,0|j0,j1,j0)

                                      ie6 =(0,0,0|j0,j0,j1) 

          We verify that the inner product of any 2 of those 6 uni-vectors is zero. They form an orthonormal basis for the uni-space.

          An event is a point in the uni-space with 6 dimensions (x,y,z|jξ,jη,jζ), the three (x,y,z) representing the material components, the three (jξ,jη,jζ) the spiritual components of the event.

          If we consider the orthonormal subspace (x,y,z|j0,j0,j0), we call it the MATERIAL WORLD where all the theories of sciences mathematics, mechanics, physics, chemistry, cosmology...have been developed in the human history until today. In this material world, because we consider only x, y, z, we can identify the material event (x,y,z|j0,j0,j0) with the real event (x,y,z) as people have done. Specially, Einstein has added 1 more dimension 'ct' to the space-time in his theory of Relativity. We don't criticize scientists and theoreticians of materialism. Only we open the door to the new theory of universality. When performing operations in the material world separably, we will write x for (x|j0) by reason of simplicity.

          If we consider only the orthonormal subspace (0,0,0|jξ,jη,jζ), it is called the SPIRITUAL WORLD. We can identify the spiritual event (0,0,0|jξ,jη,jζ) with the event of only 3 components (jξ,jη,jζ) to simplify the writing in the mathematics and sciences theories of spiritual studies. Also when working with the spiritual world separately, we will write jζ for (0| jζ) for simplicity. That is what we will do later to show people the imperfect structure of spiritualism. But it is not the main purpose of this research in the theory of universality which we are developing.  We simply warn some people not to use the theory of universality to advocate for their spiritualistic doctrines or religions.

 

FUNDAMENTAL EQUATIONS OF

MASS AND ENERGY IN MOTION

 

     The object of this paragraph is to establish formula for mass and energy in motion.

          But first we study laws in the material world and next we extend the results to the spiritual world.

  In mechanics, on an axis when a force F displaces a distance du, it produces an energy de by the relation (here all the numbers are REAL)

                             de = Fdu  or  F = de/du

          By the principle of Newton, when the force F moves a mass m at speed q=du/dt, we have the momentum p=mq

                             F = dp/dt = d(mq)/dt           

          Therefor we have the equation

(1)                        de/du = d(mq)/dt

     Energy e and mass m are already proven to be related by the equation e = mc2 (See Tran, ON THE FORMULA e = mc2, 2002)

          Energy e and mass m are real-valued functions of one real variable u. The equation (1) is

                             d(mc2) = (dm.q+m.dq) du/dt

                             dm.c2   = dm.q.du/dt+m.dq.du/dt

                             (c2- qdu/dt)dm = m.dq.du/dt

                             (c2- q2)dm/m=q.dq

                             dm/m=q.dq/(c2-q2)

                             dm/m=(-1/2)d(c2-q2)/(c2-q2)

          Integrating we have

                             logm=log[1/√(c2-q2)]+C

Choosing properly the constant of integration we have the formula

                                 m=m0/√(1-q2/c2)

          But in the material world considered separately, we identify the material uni-form u=(x/j0) with the real number x, and the material speed du/dt with dx/dt=v                

          (2)               m=m0/√(1-v2/c2)

          Furthermore                           

                             e=mc2

          (3)               e=e0/√(1-v2/c2)

          The 2 formula (2) and (3) are the FUNDAMENTAL FORMULA FOR MASS AND ENERGY IN MOTION IN THE MATERIAL WORLD CONSIDERED SEPARATELY. Don't forget that the material world is inseparably connected to the spiritual world, and equations (2) and (3) are only PARTIAL in the sense that every complete equation must cover both material and spiritual worlds.

          When v=0, we have

                                       m=m0   and e=e0

                So m0 and e0 are the mass and energy at rest.

          Lorentz found the coefficient

                                      γ = (1-v2/c2)-1/2

in his research for a linear transformation of coordinates, which could explain the null results in Michelson-Morley experiment. In his time scientists did not know the theories of space-time of Minkowski and relativity of Einstein discovered after.

          We go now to the spiritual world. To have equations like (2) and (3) in the spiritual world, we simply replace x by jξ, and v=dx/dt by jw=jdξ/dt, and q2=(0|jw)2 = 0-w2

(4)                                  m=m0/√(1+w2/c2)

(5)                                  e=e0/√(1+w2/c2)

          In equations (4) and (5), m, m0 and e, e0 are spiritual masses and energies in the spiritual world. The equations (4) and (5) are related to the equations (2) and (3) in the connection of the spiritual part with the material part in the universe.        

          We have at this point 2 coefficients

(6)                                  γr = (1-v2/c2)-1/2

(7)                                  γs = (1+w2/c2)-1/2

          The subscripts r and s stand for material and spiritual.

         In the equations (4) and (5), the mass and energy in motion are decreasing functions of w, and w can increase to infinity. That is, a spirit can fly as fast as it can, even faster than light. The faster it flies, the lighter are its mass and its energy. When the spirit speed is infinity, its mass and energy tend to zero. Because v and w are related, we can expect that the material speed v can also be greater than the speed of light c, it is what we will find out next.  

 

TRANSFORMATION OF COORDINATES

 

          We look back at the technique used by Lorentz to prove his transformation of coordinates and the technique used by Minkowski and Einstein in their theories. We will use here similar technique to make a transformation of coordinates in the uni-space of 6 dimensions.

          To do that, we need a discussion on the concept of ABSOLUTE AND RELATIVE.

          By the principle of duality, the universe is composed of 2 inseparable material and spiritual worlds. The universe is THE UNIVERSE OF ENERGY AND MASS TRANSFORMING CONSTANTLY BETWEEN THE TWO STATES OF REST AND MOTION. ENERGY CHANGES TO MASS AND MASS CHANGES TO ENERGY CONSTANTLY. THE MUTUAL CHANGES OCCUR ON THE BACKGROUND OF THE STATE OF NO-REST-NO-MOTION, WHICH IS NONE-OF-REST-NONE-OF-MOTION. MATHEMATICALLY, MECHANICALLY, PHYSICALLY THAT BACKGROUND IS THE ABSOLUTE STATE OF THE UNIVERSE. ON THAT ABSOLUTE BACKGROUND EVERY THING IN THE UNIVERSE APPEARS AND CHANGES.

          Therefore an ABSOLUTE SYSTEM OF REFERENCE EXISTS FOR THE UNI-SPACE OF 6 DIMENSIONS.

          Any system of reference at rest in an absolute system is also absolute.

          A moving system is relative.

          If (O) is a relative system, and if another system (O') is moving in the system (O), the 2 systems are relative to each other, which is the case Einstein considers in his theory of relativity.

          We have to distinguish 2 different cases:

          1/ Two systems (O) and (O') are moving relatively to each other INSIDE AN ABSOLUTE SYSTEM

          2/ Two systems (O) and (O') are moving relatively to each other, DENYING the existence of absolute system. This case 2/ is of Einstein in his theory of relativity (The PRINCIPLE OF RELATIVITY.)

          In our theory of universality we take case 1/.

          Even in case 1/ we may ASSUME THAT THE TWO SYSTEMS (O) AND (O') HAVE THEIR OWN DIMENSIONS AND THEIR OWN TIMES t and t'. In an absolute system, consider 2 observers at O and O'. Assume that at time t=0, t'=0, O' coincides with O, and the plane O'x'ξ' moves at constant speed q=|(v|jw)|=|v2-w2| in a uniform linear motion on a line OX in the plane Oxξ; the other planes of the system (O') move and are still parallel to their corresponding planes of the system (O). The axes O'x',  O'ξ' are always parallel to the axes Ox,  Oξ in the translation motion.

Reserved:  
          The speed q has 2 components v and w, (q, v, w are constants). The 2 components v and w are on the axes Ox and Oξ. Call θ the angle of Ox and OX on the plane Oxξ. The direction of the line OX is determined by cosθ and sinθ. On the planes Oyη  and Ozζ consider the lines OY and OZ forming angle θ with the axes Oy and Oz, thus with directions  (cosθ, sinθ) in those planes.

          We can see easily that in the system of OXYZ, the 3 axes OX, OY, OZ are orthogonal to each other. We can find 3 unit vectors on those axes, and the system OXYZ is an orthonormal subspace of the real space of 6 dimensions (x,y,z,ξ,η,ζ). In the one-one correspondence between the real space of 6 dimensions and the uni-space of 6 dimensions, corresponding to the system OXYZ just defined above in the real space, we have a uni-system also called OXYZ by abuse of notations in the uni-space of 6 dimensions, which is an orthonormal subspace of the uni-space.

          Now we work on the uni-system OXYZ with 2 observers (O) and (O'). Observer (O') is attached to a uni-system of 3 axes O'X'Y'Z' which moves along the axis OX uniformly at speed q=|v2-w2| starting from point O, O'X' sliding on OX, O'Y' and O'Z' being sill always parallel to OY and OZ.

          Now assume at time t=0, t'=0, and O' at O, a light signal is emitted from point O=O' and propagates at speed c. At time t for O and t' for O', a point P on the wave front light has coordinates in the 2 systems

                                      (X,Y,Z) in system OXYZ

                                      (X',Y',Z') in system O'X'Y'Z'

                                       X'=X- qt

                                      Y'=Y

                                      Z'=Z

                                      OP=ct

                                      O'P=ct'

          The equations of the 2 distances OP and O'P are

                                      X2+Y2+Z2 = c2t2

                                   X'2+Y'2+Z'2 =  c2t'2

(8)            X2+Y2+Z2 - c2t2 = X'2+Y'2+Z'2- c2t'2= 0

          Equation (8) means that the form X2+Y2+Z2 – c2t2 is INVARIANT in the transformation.

                Because Y'=Y, Z'=Z, we have

(9)                                  X2-  c2t2 = X'2- c2t'2= 0

                Now we use the technique of Malcom Longair as follows.

          Let τ=it and  τ'=it', equation (9) becomes

(10)                                X2+ c2 τ2 = X'2+ c2 τ'2= 0

          Equations (10) are similar to the equations of a rotation on the plane. Because of that, we call our transformation an IMAGINARY ROTATION.

          The equations of a rotation of angle φ for (10) are

                                      X'= Xcos φ  + cτ sin φ

(11)                             cτ '= - Xsin φ  + cτ cos φ

          Then let φ=iψ, we have

                                      cos φ = cos(iψ) = cosh ψ

                                      sin φ  = sin(iψ) = i sinh ψ

          The 2 equations (11) become

                                      X'= Xcosh ψ + icτ sinh ψ

(12)                                cτ '= - iXsinh ψ + cτ cosh ψ

          Equations (12) with t and t' are

                                      X'= Xcosh ψ - ct sinh ψ

(13)                                ict'= -iXsinh ψ + ict cosh ψ

   At time t in (O), the coordinates of the point O' are X'=0 in (O') and X=qt in (O).

          Substituting in the first equation of (13), we have

                                      tanh ψ = X/ct =  qt/ct = q/c

          Since by the computation of hyperbolic functions we have

                                      cosh ψ = (1 – q2/c2)-1/2

                                      sinh ψ = (q/c)(1 – q2/c2)-1/2

the equations of the transformation become

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

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

                                      Y'= Y

(14)                                Z' = Z

          The above technique requires a uniform linear motion of the 2 systems relative to each other. So the 4 equations (14) are only a special case in which we find the coefficient

(15)                γ = (1 – q2/c2)-1/2= (1 – v 2/c2 + w 2/c2)-1/2

with q2 = v2- w2.

          Until today, people don't have a technique or a method to find similar formula to (14) with the coefficient γ (15) for the transformation of coordinates in a general motion.

          So when we use the transformation of coordinates (14) we must be very careful with the condition of uniform linear motion of the systems of reference.

          We have some more comments on the use of the PRINCIPLE OF INVARIANCE of Newton in the proof of the relative uniform linear motions of 2 different systems of reference. By that principle, distance and time have invariant forms in two systems in uniform motion relative to each other. In the theory of space-time of Minkowski and the theory of relativity of Einstein, they applied that principle of invariance and found what is called PROPER DISTANCE AND PROPER TIME WHICH EVERY OBSERVER AGREES: there are 3 different kinds of time, one for observer O, one for observer O', and the proper time which is the same for all observers. In computation, when differentiating functions with respect to time,  they take derivatives with respect to proper time. The concept of proper time in their theories is actually the concept of absolute time of Newton. We have discussed 2 cases of relative motions of 2 systems:

          1/ Two systems are moving in uniform linear motion with respect to each other IN AN ABSOLUTE SYSTEM

          2/ Two systems are moving in uniform linear motion with respect to each other WITHOUT ABSOLUTE SYSTEM.

          In our theory of universality, we take case 1/,  then our proper time and even proper distance are the absolute time and absolute distance in the absolute system.

          Minkowski and Einstein take case 2/, then they can not explain the concept of proper time and proper distance in the theories of space-time and relativity. It is only a remark, and we don't say it is a contradiction in those theories.

          In the first equation of (14), at an instant t of (O), 2 distant events A and B on a line parallel to the axis OX are determined by the formula

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

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

          Subtraction yields

                           X'a – X'b = (Xa - Xb)(1 - q2/c2)-1/2

(16)     ΔX' =  ΔX(1 - q2/c2)-1/2= ΔX(1 - v 2/c2 + w 2/c2)-1/2

                Equation (16) shows the change of the distance in relative motion depending on the 2 velocities v and w.

          In the second equation of (14), an observer fixed at X in (O) observes the times t and t' at 2 different instants

                                       t'2 = (t2 - qX/c2)(1 - q2/c2)-1/2

                                        t'1= (t1 - qX/c2)(1 - q2/c2)-1/2

          Subtraction yields

                                      t'2  - t'1 =  (t2 - t1)(1 - q2/c2)-1/2

(17)          Δt' =  Δt(1 - q2/c2)-1/2= Δt (1 - v 2/c2 + w 2/c2)-1/2

               Equation (17) shows the change of time in relative motion depending on the 2 velocities v and w.  

                The formula (16) and (17) can be written in the forms

 (18)            l = l0(1 – q2/c2)-1/2

(19)             t  = t0(1 – q2/c2)-1/2

                    γ = (1 – q2/c2)-1/2= (1 – v 2/c2 + w 2/c2)-1/2

               In the theory of Special Relativity, because people work only in the material world neglecting the spirit, w=0, q=v, the formula (18) and (19) are in the forms

                                     l = l0(1 – v2/c2)-1/2

                                     t = t0(1 – v2/c2)-1/2

and express A CONTRACTION OF LENGTH AND A DILATION OF TIME IN THE MOTION OF THE TWO SYSTEMS OF REFERENCE RELATIVE TO EACH OTHER. But yet in 100 years already,  no body can measure such contraction of length or dilation of time. The null results of the experiments for such measures can be explained now in the theory of Universality.

       The speed q in the coefficient γ depends on the 2 material and spiritual speeds v and w.

        If v=w, no change of length or time, even no change of mass or energy in motion.

        If v˃w, then length, time, mass, energy all increase in motion.

        If w˃v, then length, time, mass, energy all decrease in motion.

 

RELATION BETWEEN MATERIAL AND SPIRITUAL EVENTS

 

         When we studied mass and energy in each of the two separated material and spiritual spaces, we got 2 separate formula of transformation for mass and energy

                                          γr = (1-v2/c2)-1/2

                                          γs = (1+w2/c2)-1/2

        We wonder what relation is between the two material and spiritual world. In other words, what cements the two worlds together?

             In studying the transformation of coordinates in uni-space, we found the coefficient of transformation

                    γ = (1 – q2/c2)-1/2= (1 – v 2/c2 + w 2/c2)-1/2

which relate the 2 material and spiritual speeds with the coordinates of events.

        Because the two material and spiritual worlds are inseparably connected, we admit a fortiori the hypothesis that mass, energy, and coordinates have the same coefficient of transformation in any motion

                    γ = (1 – q2/c2)-1/2= (1 – v 2/c2 + w 2/c2)-1/2

              With that hypothesis, this coefficient γ = (1 – q2/c2)-1/2= (1 – v 2/c2 + w 2/c2)-1/2 is a universal coefficient of transformation.

 

UNIVERSAL COEFFICIENT OF TRANSFORMATION

         In the universe of 6 dimensions, consider the uni-forms of mass m and energy e

                                      m = (mr|jms)  and  e = (er|jes)

the subscripts and  s standing for material and spiritual, then with the universal coefficient γ, we have the following fundamental equations                                                     

                                      m = m0(1-v2/c2+w2/c2)-1/2

                                      e = e0(1-v2/c2+w2/c2)-1/2

and

                                mr=mr0/(1-v2/c2+w2/c2)-1/2     

                                ms=ms0/(1-v2/c2+w2/c2)-1/2

                                   er= er0/(1-v2/c2+w2/c2)-1/2

                                  es= es0/(1-v2/c2+w2/c2)-1/2

          The material part and the spiritual part have similar formula in parallel.

          If we generalize those formula to uni-vectors of 6 dimensions, we have

                                      v2= x'2+y'2+z'2

                                       w2=ξ'2+η'2+ζ'2

the prime ' means derivatives with respect to absolute time t

                                      q2=v2-w2

then the above fundamental formula for mass and energy in motion are still valid.

          In the coefficient

                                        γ = (1-v2/c2+w2/c2)-1/2

when the spiritual speed w=0, we have

                                         γ = (1-v2/c2)-1/2

          This coefficient γ is essentially different from the coefficient γ which Lorentz, Minkowski and Einstein use in the Lorentz transformation and the space-time of relativity. In our proof for the fundamental formula of mass and energy in motion, we use differentiation and integration of analysis. But in setting up his formula for transformation of coordinates, Lorentz makes up an artificial tool to interpret the changes of length and time in Michelson-Morley experiment. Then Minkowski take Lorentz's coefficient γ as an evidence for his construction of space-time which Einstein uses in his theory of special relativity.

         Another essential remark is that the speed v of a material point or a solid can be greater than the speed of light c because of the presence of the speed w in the coefficient γ. This simply means the theory of relativity applies only to the material world where the spirit is neglected.

 

NULL SPACE

         The null uni-vectors, x= ξ

                                      (x|jx) = x(1|i1)

form a uni subspace called the NULL SPACE. In uni language, we can say that the null space is the space of events with the same degree of spirit as of matter.

         In the null space we have v=w, then

                                     m=m0,  e=e0, l=l0, t=t0

              That is a generalization of the theory of Newton in mechanics, in which the 4 basic quantities mass, energy, length, and time won't change in motion. So we may consider that the space of Newton is the null space of same degree for both spirit and matter in which the material and spiritual speeds are not necessarily zero, and the observers not necessarily at rest.

 

                  NULL SPACE AND NEWTON SPACE

 

               Remember that the universe of Newton is the null space where x=ξ and dx/dt=dξ/dt, i.e., v=w: the two material and spiritual worlds are superposed mechanically in the null space. That means the concepts of distance and time are similar for the 2 worlds. Thus the concepts of speed and acceleration are also similar. But the concepts of mass and energy are different for the 2 worlds.

          We have seen the relation between mass and energy

                                    e = mc2

for both material and spiritual worlds. But in each separated world, mass and energy in motion obey the fundamental equations with the universal coefficient

             γ = (1 – q2/c2)-1/2= (1 – v 2/c2 + w 2/c2)-1/2

                 In the null space, the coefficient γ=1, and mass and energy do not change with

speed and acceleration. All the theories already established in Newton space can be generalized to uni-space.

 

UNIVERSAL GRAVITATION

 

          Now we need to look at the concepts of mass and energy in the two worlds.

          The difference between matter and spirit is conventional (because its the most we can do at this time in mathematics and mechanics.) We postulate that

          MASS AND ENERGY ARE POSITIVE IN THE MATERIAL WORLD, and MASS AND ENERGY ARE NEGATIVE IN THE SPIRITUAL WORLD.

  Spiritual energy is negative, except kinetic energy of the spirit is positive

                      (1/2)(-m)q2 = (1/2)(-m)(-w2) = (1/2)mw2 > 0

          In the theory of light, light appears the same in the 2 worlds, and a photon is a combination of 2 opposite masses m and -m.

          Therefore the mass of a photon is

                                   m + (-m) = 0

and the kinetic energy of a photon is

                      (1/2)mc2 + (1/2)(-m)(-c2) = mc2= pc

p=mc is the momentum of photon. Those are the properties of light admitted in classical mechanics.

                  For the universal gravitation,

          *between 2 masses of same sign, there is an ATTRACTION,

          *between 2 masses of opposite signs, there is a REPULSION.

           Two masses in the material world, both positive attract one another.

           Two masses in the spiritual world, both negative attract one another.          

      A material mass and a spiritual mass repel one another, which explains why the attachment of a body and a spirit is unstable: the death of a living being can occur easily when the conditions of attachment vanish and then the spirit leaves the corps.

   Recall the PRINCIPLE OF GRAVITATION of Newton in the material world.

          The gravitation force in the material world is ATTRACTION

                                   F = Gmm'/r2

          In the system MKS, m and m' are in Kg, F in Newton, the distance r between m, m' in meters, G the universal coefficient of gravitation. The same law is true in the spiritual world with 2 negative masses.

          In the uni-space, we have

                                   (Fr,|jFs)=(Gr|jGs).(mr|jms)(m'r|jm's)/r2

                                        Fr = Gr(mrm'r-msm's)/r2

                                   Fs= Gs(mrm'r-msm's)/r2

        Above are the attractions between masses of the same sign.

         For 2 opposite masses (mr|j0) and (0|jms), there is a repulsion

                                   F' = - G'mrms/r2

                So a spirit can attach (incarnate) to a body only under a different kind of attractive force greater than the repulsive force F'. We call that attractive force the karmic force.

         We are going to show there are 2 different fields of force: the gravitational field and the karmic field. We will explore the Karma and the Karmic Field next.

         The gravitational field consists of attraction between masses of same sign, and repulsion between masses of opposite signs.

         By analogy, the karmic field also consists of attraction and repulsion depending on the karma, which will be seen.

         Now to explore the two fields, we have to review basic mathematics tools of vector calculus.

 

DIVERGENCE

 

          To simplify the writing in mathematics, since we have several kinds of products and sum, in the following we will use the dot “.” or even no dot to represent the all kinds of products if there is no confusion. For example

               u o v = u . v = uv for scalar product of 2 real vectors.

                                   (E|jE') = E + E'

                                   (m|jm') = m + m'

          For the definition of divergence:

          Let call Dx the partial derivative with respect to x, similarly for the variables y, z, and ix, iy, iz the unit vectors of the axes Ox, Oy, Oz. For a vector

                                     F = ixFx +iyFy +izFz

the divergence is

                                   divF = DxFx + DyFy + DzFz

                 Similarly for the vector F'(ξ͵η͵ζ).

         In the uni-space of six dimensions, we define the divergence of a uni-vector as follows.

                                   div(Fr|jFs) = (divFr|jdivFs)

         The vectors Fr(x,y,z) and Fs(ξ͵η͵ζ) are real vectors of real variables.

 

GRADIENT OF A REAL-VALUED FUNCTION OF 3 VARIABLES

 

          Let E be a real-valued function of 3 variables x, y, z. Then by the definition of gradient:

                                   gradE = ixDxE  + iyDyE + izDzE

            Similarly for a function of 3 variables ξ͵η͵ζ.

            And for uni-vectors, the gradient is

                                   grad(Er|jEs) = (gradEr|jgradEs)

 

CURL OF A VECTOR FUNCTION OF 3 VARIABLES       

 

            Let A be a vector function of 3 variables x, y, z. The curl of vector A by definition is

     curlA = (DzAy-DyAz)ix+(DxAz-DzAx)iy+(DyAx-DxAy)iz

            Similarly for a vector function of 3 variables ξ͵η͵ζ.

            For uni-vectors, the curl is

                                   curl(Ar|jAs) = (curlAr|jcurlAs)

 

OPERATOR NAPLA

 

            In vector calculus, we use the operator ▼ defined symbolically as a vector

                                   ▼= ixDx+iyDy +izDz

            For real vector functions of 3 variables, we use the scalar product “o” of real vectors

                                   V(x,y,z) oV'(x',y',z') = xx'+yy'+zz'

           Then we have

  divA = ▼o = ▼A = (ixDx+iyDy+izDz) o (ixAx+iyAy+izAz)

                                            = DxAx +DyAy +DzAz

                      grad Φ = ▼Φ = (ixDx+iyDy+izDz

                                             = ixDxΦ +iyDyΦ +izDzΦ

            The curl of a vector A is the cross product of real vectors

      curlA = ▼X A = (ixDx+iyDy+izDz) X (ixAx+iyAy+izAz)

               = (DyAz-DzAy)ix-(DxAz-DzAx)iy+(DxAy-DyAx)iz

 

LAPLACIAN OPERATOR

 

             Here we use second partial derivatives Dxx, Dyy, Dzz  for the Laplacian of a scalar function Φ of 3 variables

                                   ▼2 Φ = Dxx Φ +Dyy  Φ+Dzz Φ

             For uni-functions, the Laplacian is

                                   ▼2 r|jΦs) = (▼2 Φr |j▼2 Φs)

 

DIVERGENCE THEOREM

 

                                   ∫S A o dS = ∫v divA dv

Surface S encloses volume V,  dS is the differential vector normal to an infinitesimal element of surface directed outside the volume, dv is an infinitesimal element of volume.

 

STOKES' THEOREM

 

                                   ∫c A o dl = curlA o dS

S is any surface bounded by the loop C,  dl is an infinitesimal element of the loop C, and dS is an infinitesimal element of S.

 

GREEN'S THEOREM

 

          Let f and g be 2 real-valued functions of 3 variables x, y, z

          First form         ∫v [f 2g+(▼f o▼g)]dv =  S f▼g o dS

          Second form  ∫v [ f 2g- g▼2f]dv = ∫S (f▼g – g▼f) o dS

 

MORE PROPERTIES

 

          We have the theorem:

   The 4 following propositions are equivalent for a vector field A

          1/ curlA = 0

          2/ A= - grad Φ

          3/ ∫C A o dl = 0 for any closed loop C

          4/ ∫ABA o dl is independent of the path from A to B

and the field A is called irrotational or conservative.

          Also we have some properties for curl, grad and divergence

                             div(curlA) = 0 for any vector A

                             curl(curlA) = grad(divA) - ▼2A

 

                      GRAVITATIONAL POTENTIAL
                           GRAVITATIONAL FIELD

 

         First we study the gravitational field in the material world separately, in which all masses and energies are positive, and between 2 masses there is a gravitational attraction

                                                F = Gmm'/r2

                 We define the gravitation field of an isolated point mass m in an absolute reference frame as the force field, at a point P

                                                f = Gmir/r2

where ir is the unit vector of the vector pointing from the point P to the point mass m.

         If a mass m' is placed at point P, the gravitation field of m acts on m' a force

                                                F = Gmm'ir/r2

                 Call O the origin of the reference frame. A mass m placed at O produces a gravitational field f. The work of the field f from a point A to a point B is the line integral

                                                Φ = - ∫AB f o dl     

independent of path from A to B.

          The scalar Φ is called the gravitational potential difference between 2 points A and B.  

          Along a radial segment AB, f and dl are parallel, then

                         Φ =  - ∫AB  Gmdr/r2 = Gm(1/rA – 1/rB)

          If B coincide with A, the path is a closed curve, and

                                                Φ = 0

          If the point B is at infinity, we have

                                   Φ =  - ∫ Gmdr/r2 =  Gm/rA

which is called the gravitational potential at point A due to the mass m.

          If we go radially from a point (x,y,z) to a point (x+dx,y+dy,z+dz) the change of Φ, going from A to B, is in first order approximation

                                    dΦ = DxΦdx + DyΦdy + DzΦdz = gradΦ o dl

          But from the definition of Φ above, we have

                                                 dΦ =  f o dl        

          Thus we can identify

                                                 f = gradΦ = ▼Φ

         If we have a system of masses, each mass produces an individual gravitational field and an individual gravitational potential. By the principle of superposition in physics, the resulting field is the vector sum of all the individual fields and the total potential at a point is the sum of all individual potentials. The total mass of the system is the sum of all masses, and the system is equivalent to a mass (= total mass) placed at the gravity center of the system. The resulting field is a force f

                                                f = ∑Gmir/r2

                  If we denote by ρ the mass density per volume       

                                                f = ʃGρirdv/r2

                 And the total potential is

                                                Φ = ∑ Φi

                                                f = grad Φ

               Furthermore the flux of the gravitational field f through a surface S enclosing a volume V is

                                            ʃS f o dS = ε ʃV ρdv

ε is a constant related to the gravitation.

          By the divergence theorem, we have

                                            ʃS f o dS = ʃV divFdv

          So

                                            divf = ερ

           

                            MAGNETIC-LIKE FIELD

                           GRAVIMAGNETIC FIELD

 

           In electromagnetism, we know that in an electric field E, an electric charge q moving with velocity v is acted by a force

                                                F = qE + qv X B

where B is the magnetic field.

           By analogy, in a gravitational field f, a mass m moving with velocity v is acted by a force F

                                                F = mf + mv X B

B is in the present case a magnetic-like gravitational field. It is not a magnetic field, but a field related to the gravitational field. In experiment, we can measure the gravitation f, then let a known mass m moving with velocity v, we can measure B. We call B the gravimagnetic field.

          Also by analogy with electromagnetism, we have the 4 equations for the gravitation in the material world analogous to the 4 Maxwell equations

                                                curlf = - DtB

                                                curlB = με Dtf + μJ

                                                divf = ερ

                                                divB = 0

                Now in the spiritual world, we have equations similar to those in the material world.

                                              curlf' = - DtB'

                                                curlB' = μ'ε' Dtf'+μ'J'

                                                divf' =  ε'ρ'

                                                divB' =  0

               In that system of 4 equations of the spiritual world, mass and energy are negative, and the gravitation force is repulsive.

         At this point we have seen the fields' equations separately for each world. To have the equations for the universe, we apply the principle of superposition:

                                                curl(f+f') = - Dt(B+B')

                                  curl(B+B') = μεDtfJ+μ'ε'Dtf'+μ'J'

                                                div(f+f') = ερ+ε'ρ'

                                                div(B+B') = 0     

J and J' are conduction current densities per volume; ε and ε' are related to the universal gravitation in the 2 worlds; μ and μ' are coefficients related to mass-energy in the 2 worlds.

 

INTERPRETATION OF THE 4 BASIC EQUATIONS

 

           The 4 basic equations above govern the phenomena concerning matter and spirit in the universe.

          Equation 3

                                       div(f+f') = ερ+ε'ρ'

shows the intimate relation between mass (material and spiritual) and gravitation (attractive and repulsive). Where there is mass, there is gravitation. Mass is positive in the material world and negative in the spiritual world. Gravitation is attractive in the material world and repulsive in the spiritual world. In the universe, the 2 worlds are superposed: in matter there is spirit. Because matter and spirit repel one another, the attachment (incarnation) of spirit to matter requires an essential condition of KARMA. What is karma? We will explore it in the next paragraph.

         The actual gravitation that affects life constantly is the superposition of 2 opposite gravitational forces: living beings are affected at the same time by the attractive material force and the repulsive spiritual force.

         Equation 2

                             curl(B+B') = μεDtfJ+μ'ε'Dtf'+μ'J'

means that the gravimagnetic field B+B' occurs constantly in the universe due to the change of the gravitation field f+f'and the motion of J+J'of matter/spirit. The term μεDtf+μ'ε'Dtf' is called the displacement current of matter/spirit. The term μJ+μ'J' is called the conduction current of matter/spirit. The earth around the sun, the moon around the earth are examples of displacement currents. People's action, trees growing are conduction currents of matter/spirit. Matter/spirit always changes, which implies that the gravitation field always changes. Because every mass/spirit changes and moves constantly, the gravimagnetic force is always present in all activities.

          Then equation 1

                                     curl(f+f') = - Dt(B+B'

shows that the change of B+B' affects the gravitation f+f'.  Thus gravitation field and gravimagnetic field mutually affect one another. When changing, the gravitation produces the currents of matter which make change in the gravimagnetic field, and the gravimagnetic field in its turn affects the gravitation.

           Equation 4

                                           div(B+B') = 0

means that there is NO gravimagnetic charge, that is, the gravimagnetic field is produced by the displacement current and the conduction current. Masses produce gravitation, but we can not find anything “like mass” to produce gravimagnetic force.

 

                                 POLARIZED FIELD

                                 AND KARMIC FIELD

 

          We study now the concept of electric polarization inside the body of a living being.

          We call body the total of a material corps with an incarnated spirit of a living being.

          Our stand point here is only on the electromagnetic state of the body in the simplest description of polarization of the cells.

          The body moves and acts itself by internal energy without aid of an exterior electric or magnetic field. We know each person has his/her own power to sense, to emotion, to  think,  to speak, and to action. The body/spirit is self-powering and is self-relating to the environment.

      So we admit that the body/spirit has an internal potential energy Φ.

          Then there is an electrical field E generated by Φ

                                                E = - grad Φ

          We assume that all the cells in the body are polarized by the field E, and each cell is an electric dipole p. Those dipoles are arranged in accordance with the functions of different organs. The simplest case we can assume is a uniform polarization of water in the body since water is 90% of the body. Such case may be of a person in deep meditation. 

           The dipole p of a cell and the electric field E are supposed to be proportional

                                                p = αE

α is called the coefficient of polarization of the body/spirit and has the dimension of volume. That polarization is a zooming image of the polarization of atoms distorted by electric fields.

           Following are the measures of atomic polarization for some elements in Units of cm3 under the effect of an external electric field:

 

Elements        H         He        Li        Be        C        Ne        Na        A        K

Atomic α        0.66    0.21      12        9.3       1.5      0.4        27       1.6      34

 

 μ         A further research would have the measures of the polarization coefficients of the cells in a body due to the self polarization.

          A polarized body is a dielectric and has a permittivity coefficient ε and a permeability coefficient   μ that effect the fields E and B.  That is the use of the vocabulary in electromagnetism, but when we use the equations for karma,  ε will be called the karmic coefficient, and μ will be called the individualistic coefficient of a living being.

           In a uniform polarization, the density of polarization is P and plays a role analogous to that of electric field inside the body. The dipoles p plays the role of electric charge, called bound charges. Let ρbound be the density of bound charge

                                                divP = - ρbound

           The current of bound charge has intensity

                                                Jbound =  DtP         

           There are also free ions in the body with density ρfree which produce a current of free charge of intensity Jfree.          

           The change of the electric field E produces a displacement current of density

                                                Jd = DtE

           The electric field E is discontinuous at the boundary of the medium which is the skin of the body in the present study case. At the skin there is a thin layer of electric charge with surface density ϭ. Let's write at a point of the skin 3 vectors with their components normal and tangent to the skin


                                P = Pnormal  + Ptangent

 Ei = Einormal + Eitangent

                             Eo = Eonormal + Eotangent      

                The relations between those vectors concerning discontinuity and continuity are

                      Eonormal  Einormal Pnormal       

                                                                                         Eotangent  = Eitangent  

         the superscripts “i” and “o stand for inside and outside of the body. In the theory of electric field at the  boundary of a medium, we know the tangent component of E is continuous, but the normal component of E has a discontinuity equal to the surface density of charge

                                      ϭ = Pnormal.

                 We can mimic the equations of Maxwell by writing the 4 equations for a self-polarizing body as follows

                                   curlE = -  DtB

                                    curlB = με DtE+μDtPJfree

                                    divE = ερbound +ερfree

                                     divB = 0

          DtE is the displacement current in the body. DtP is the conduction current. Jfree is the free current of free electrons in the body.

          Above is the illustration of electrical and mechanical study of the body in the material world.

          In the spiritual world, by analogy we have similar concepts and equations

                                 curlE' = -  DtB'

                                 curlB' =  μ'ε'DtE'+μ'DtP'+μ'J'free

                                  divE' = ε'ρ'bound +ε'ρ'free

                                                divB '= 0

          The superposition of the 2 worlds in the universe gives the 4 complete equations of self- polarization and karma.

                                      curl(E+E') = - Dt(B+B')

  curl(B+B') = μεDtE+ μDt P+ μJfree +μ'ε'DtE'+  μ'DtP'+μ'J'free

            div(E+E') = ερbound + ερfree+ ε'ρ'bound +ε'ρ'free

                                                div(B+B') = 0

          Now we interpret those equations.

          First we need to clarify the difference in nature of the two concepts material and spiritual.  

          For mass and energy, we see clearly the difference between 'material mass' and 'spiritual mass', also the difference between 'material energy' and 'spiritual energy'. The material mass and energy is said to be 'positive', and the spiritual mass and energy is 'negative'.

          But for electric and magnetic, we say 'positive or negative material electric' to distinguish with 'positive or negative spiritual electric'. Similarly 'positive or negative material magnetic', and 'positive or negative spiritual magnetic'.

          In the universe, the total (material and spiritual) electric and karmic potential Φ+Φ' is the KARMA of the living being. The electric field E+E' is its KARMIC FIELD. We give a new name to the “magnetic” field B+B': the CONSCIOUSNESS FIELD. Karma and consciousness always go together, a change of one affects the other.

          The surface density

                               ϭ+ϭ'  = Pnormal + P'normal

is the sensitivity density. The electric bound charge density ρbound +ρ'bound is the emotion density. The electric free charge density ρfree+ρ'free is the mind density.          

          As we know, after the death, the dead body does not have any more sense, emotion, mind, word, action, so all those things are due to the spirit. It is the spirit that directs every thing of the living body in life by superposition with the body.

          We can now answer the question, HOW DOES A SPIRIT INCARNATE IN A MATERIAL BODY TO CREATE A LIVING BEING? HOW DOES A SPIRIT LEAVE A LIVING BODY TO MAKE IT A DEAD CORPSE?

          For a living matter/spirit body, we have seen the charges in the body are the electric charges.

          In the material world, two material electric charges of same sign repel one another; two material electric charges of opposite signs attract one another.

          In the spiritual world, two spiritual electric charges of same sign repel one another; two spiritual electric charges of opposite signs attract one another.

          Between the two worlds, a material electric charge and a spiritual electric charge of the same sign attract one another; a material electric charge and a spiritual electric charge of opposite signs repel one another.

          The attractive karma forces and the attractive consciousness forces make the incarnation of the spirit in the body if both spirit and body have the same sensitivity, and similar karmic and conscious conditions. During life, sensitivity, emotion, mind, word, action change with time until the karmic conditions are ameliorated and the karmic and conscious forces become weaker than the repulsive forces, the spirit must leave the body. The death ossurs.

          That is the LAW OF LIFE AND DEATH.

 The sensitivity field is the cement to attach a spirit and a body.

          After the death, the corps has no more sensitivity.

 

STRUCTURE OF THE UNIVERSE

 

       The motion of an event is caused by the forces of karma and conscience acting on it. Those forces produce accelerations in the motion. For an event (x|jξ) in motion, the material and spiritual speeds are

                                    v=dx/dt and w=dξ/dt

           The accelerations are

                                    v'=d2x/dt2 and w'=d2ξ/dt

           If ξ˃x, the uni-forms (x|jξ) are in the SUBSPACE OF SPIRIT-LIKE EVENTS.  

                   If x˃ ξ, the uni-forms are in the SUBSPACE OF MATTER-LIKE EVENTS.

          Now we explore the structure of the universe with the spirit-like subspace and the matter-like subspace.

           Let's call ACTION an event in motion.  An action of a spirit-like event or a material-like event depends on the forces (accelerations) that act on it.

          There are 3 different realms in the spiritual-like subspace:

          1/ REALM ONE WHERE ξ˃x WITH SPIRITUAL ACCELERATION GREATER THAN MATERIAL ACCELERATION w'˃v'. In this realm, we say that an action has higher MERIT, or greater spirit than matter. We call it the HEAVEN OR HEAVENLY REALM.

          2/ REALM TWO WHERE ξ˃x WITH w'=v'. In this realm, an action has the same degree of MERIT spiritually as materially. It is the HUMAN REALM.

          3/ REALM THREE WHERE  ξ˃x WITH w'<v'. In this realm, an action has less MERIT in spirit than in matter. It is the ATULA REALM OR SPIRITUAL REALM.

         In the matter-like subspace, there are also 3 different realms.

         4/ REALM FOUR WHERE ξ WITH w'˃v'. In this realm, an action has LOWER MERIT OR LOWER CONCIOUSNESS. It is the ANIMAL REALM.

         5/ REALM FIVE WHERE x˃ ξ with w'=v'. In this realm, an action has the same degree of SIN materially as spiritually OR NO CONCIOUSNESS. It is the DEMON REALM.

         6/ REALM SIX WHERE x˃ ξ WITH w'<v'. In this realm, an action is of mostly MATERIAL or MATTER WITHOUT SPIRIT. It is the HELL.

         The analysis shows the existence of six realms in the universe with different degrees of merit and sin in the two spirit-like and matter-like subspaces.

         Dynamically, a body/spirit can move from one of the six realms to another, depending on the spiritual and material actions forces and accelerations acting on it. A more precise study on forces and accelerations can show how such a move occurs. If a body/spirit has to move from the matter-like subspace ξ to the spirit-like subspace ξ˃x or conversely, it must pass through the null space with x=ξ.

 

SUMMARY

 

          By the principle of universality, the universe is composed of two worlds, material and spiritual, inseparably connected together. On the stand point of super-sciences, there are in the universe two compensate fields: the gravitation and the karma.

          The gravitation has two different forms, gravitational field and gravimagnetic field of mass/spirit. The karma has two different forms, self-polarization and self-magnetism of body/spirit. Those fields are attraction or repulsion. The surface electric charge density on the skin of a body/spirit is the sensitivity density of the body/spirit, which is the source of sense, emotion, mind, word, action. Those things together affect the karma.

When a spirit has similar karmic conditions with a body, the spirit is incarnated-attached to the body by the karmic attractive forces due to the sensitivity-cement. When the karmic attachment ameliorates and vanishes, the spirit leaves the body by the repulsive forces of the fields and the sensitivity-cement is gone on the corps.

          This essay is written after many years of meditation, and after several months of consultation from books.

 

                                REFERENCES

 

*THE PRINCIPLE OF RELATIVITY, A. Einstein, Lorentz, Weyl, Minkowski, Dover Publication

*THE