back              THE NATURE OF ELECTRIC CHARGE       back

 

                          ----"APPLE" MODEL

 

                         Guan Yiying

 

                     Harbin           China

 

                            ABSTRACT

 

      The electric charge is the reflection of the status of the  motion

 

of  particles.  The  difference  in time  of the  positive  and negative

 

particles is their time-forward motion and   time-backward  motion.  The

 

difference in  space depends on whether the acceleration of the particle

 

is greater than zero or less than zero  ( relative to the same reference

 

system ).

 

      Key Words : Positive and negative electrons, Positive and negative

 

energy states, Model G, Acceleration

 

      It is  known  that the negative energy state  appears  in the well

 

known Dirac Equation.  There  was a time when some people suggested that

 

the negative energy state  should be abandoned.  But later on, two basic

 

reasons  were  recognized against the abandonment of the negative energy

 

state. The first one is based on the theoretical physics. Dirac Equation

 

indicates that  the system in positive energy state at the beginning has

 

the possibility to  undergo  the  inductive  transition  to the negative

 

energy state.  So, contradictions may appear with the abandonment of the

 

negative energy state.  The second  reason is based on mathematics, i.e.

 

the abandonment of the negative energy state will result in an imperfect

 

set of wave functions, and  an arbitrary function will not be able to be

 

 

expressed as an expansion equation of an imperfect set of functions.[1]

 

      Therefore,  the  author  thinks  that the negative energy state is

 

neccesary. It is one of the basic states of the existence of matters,and

 

is an objective reality.

 

      Let's make an analysis on the classical equation of motion[1]:

   

    ( dZμ/ds is the velosity; e is the unit charge; m is the mass )

 

      If the direction of S, the intrinsic time, is reversed, the effect

 

is the same as the sign of the electric charge is reversed. According to

 

R. P. Feynman,  the state of  negative energy  stands for the electronic

 

state of time-backward motion.  The  electron  moving along the backward

 

time seems like a positive electron moving along the forward time.

 

      The  following  is  a  discussion  about  the  propagator  in  the

 

relativistic status moving from  time-space point 1 to 2.  In the static

 

field, if all  the states  of wave function Φn  in  the system have been

 

known, then Ka+  can be defined as [1] :

 

 

           ∑exp[-iEn(t2-t1)]φn(x2)φ~n(x1)

  KA+={正能             (t2≥t1)

            exp[-iEn(t2-t1)]φn(x2)φ~n(x1)

                    负能             (t2≤t1)

      It can be concluded that when the elaps of time is " forward "( t2≥t1

 

  ), there exists the electron, and only the positive energy state has

 

the  contribution.  When  the elaps of time is " backward " (t2≤t1),

 

 

there  appears  the  positive  electron,  and  only the negative  energy

 

has the contribution.

 

      Now, let's assume that the wave function at point x1  and  at time

 

t1    has been known, then the wave function [1] at point x2  and  at time

 

t2  can be written as :

 

 

      ( K is the propagator, and γt  is the factor of relativity. )

 

      It can be seen that the wave function at point x2   and at time t2

 

is composed of two terms. The first one comes from the  contribution  of

 

the earlier positive energy state, and the  second  one  comes  from the

 

contribution of the latter negative energy state.

 

      This indicates that  the  positive  and negative energy states are

 

interrelated closely.  They are the different  states  of  motion of the

 

same matter.

 

      Next,  let's  look at the  motion  of the charged particles in the

 

electromagnetic field.  In the extreme of non-relativity, i.e. V<<C, the

 

common equation [2] to describe the  motion  of the charged particles in

 

the electromagnetic field is :

 

      ma=e(E+VxB)        (4)

      ( E is the stength of the electric field; B is the strength of the

 

magnetic field; V is the velocity; a is the  acceleration;   e  is  the

 

 

 electric charge. )

 

      It  can  be seen that when E, B, and the initial direction  of the

 

particle are certain, the sign on the right side of equation (4) depends

 

only  on the charge e.  Since  e can be either positive or negative, the

 

left  side of the equation must also be either positive or negative,  so

 

the  equation  can  be  harmonic and natural. For this reason, it can be

 

regarded  that  the change of the sign of the acceleration is equivalent

 

to the  change of the sign  of the electric  charge, i.e. to reverse the

 

sign of  a  is  the same thing as to reverse the sign of e, the electric

 

charge. On the contrary,to reverse the sign of electric charge e is just

 

the same  as  to  reverse  the sign  of the acceleration. If we take the

 

acceleration that meets the   right-hand  screw  rule  as  positive, and

 

the acceleration that meets  the left-hand screw  rule  as negative, the

 

electron wil  follow the  left-hand  screw  rule.  The positive electron

 

will follow the right-hand screw rule. ( Fig. 1 )

 

 

 

           Fig.1                         

 

 

 

                      Fig2

 

                      fig3

 

      So,  a model of  the electronic  motion  can be established, which

 

we call the Model of "APPLE" Cosmos ( or simply  "GuanYiying"  Model),    

 

               The region of AB-O-CD ( the double-horn region  inside

 

 the sphere ) is at the state of virtual space,  with  negative  energy

 

 and  negative curvature of time-space,  following  Robachev  Geometry.

 

 The region of AB-EF-CD ( the outer surface of the sphere )    is    at

 

 the  state  of real   sapce,     with  positive  energy  and  positive

 

 curvature of time-space, following Riemann Geometry. The  visual  ring

 

 consists of AB and CD.

 

      Now,  if  an  electron  is  moving  up in rotation along the outer

 

surface  of  the sphere,  when  it reaches AB,  the  electron enters the

 

virtual space  from  the  real  space,  and  both the  time and the hand

 

property are reversed.  When  the  electron moves  down in rotation in a

 

time-backward manner along  the  double-horn region on the inner surface

 

and reaches CD, it enters the real space with positive energy again, and

 

the time and the hand property  are reversed once again. According to R.

 

P. Feynman, an electron moving  in a time-backward manner in the virtual

 

space with negative energy is  equivalent  to a positive electron moving

 

in a time-forward manner along the inner side of the double-horn region.

 

Therefore, the above process  can be  regarded as  a pair   of electron-

 

positron produced in DC, moving  along forward time to AB, and resulting

 

in annihilation there. In addition, it can be expressed as follows: When

 

 

a particle moves from CD through EF to AB,  the  particle is negative in

 

charge in this section. When the particle  moves from AB through O to CD

 

in a time-backward manner, the particle is  in  positive  charge in this

 

section.

 

      If we cut off the model G along the central line, viewing one side

 

from the cross section  ( Fig. 2 ),  the  above  process is similar to a

 

particle doing a circular motion uniformly  in the space-time figure. If

 

the process is projected to the axis of space, the process turns  out to

 

be a simple periodic vibration. If we define that the direction from the

 

outer sphere surface to the inside of model G to be positive,viewing the

 

projection of the particle's motion on the axis of space, the force will

 

be negative and mainly attractive at the stage of D-F-B,  and the  force

 

will  be  positive  and  mainly  repulsive  at  the stage of  B-O-D. The

 

projection  of  the  particle's  speed  of  motion  on the axis of space

 

reaches  maximum  at  points  B and D, with opposite directions and zero

 

acceleration. As to the projection of the speed of motion on the axis of

 

space  at points  O and F,  the accelerations are in opposite signs, but 

 

have  the  maximum  absolute  value  with zero velocity.  Therefore, the

 

projection  of the matters moving along the visual ring CD and AB on the

 

axis of space forms the visual interface moving at a maximum speed.

 

 

      From the above,  it  can  be  seen  that  the  matters moving at a

 

constant velocity in the time-space figure will no longer  move  at  the

 

constant velocity if projected on the axis of space.  So, it can be said

 

that the force is the effect of projection of the moving  matters in the

 

time-space on the axis of space, and is the form  of  expression of time

 

which has effect on the space.

 

      Therefore, as to  the  differences  of  the  positive and negative

 

matters in the Model G,  from  the  view  of  time, one is moving in the

 

forward time,  and the  other is  moving in the backward time.  From the

 

view of space,  one is moving with a greater-than-zero acceleration, and

 

the other is moving with a less-than-zero acceleration.

 

 

      Up to now,  the  following conclusion can be deduced : In the same

 

fixed outer field, if the signs of the acceleration of the particles are

 

different,  the electric  properties must be different too.  This can be

 

used for the explanation of the distribution of the electric  charges in

 

the thouderclouds, and the origin of the electric charges in  the clouds

 

or in the falling rain.

 

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