back              THE NATURE OF ELECTRIC CHARGE       back


                          ----"APPLE" MODEL


                         Guan Yiying


                     Harbin           China




      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] :




  KA+={正能             (t2≥t1)


                    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 )












      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




      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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