----"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.

-----------------------------------

Tel. (0451)3621792

e-mail:gyy63@yeah.net or gyy63@0451.com

－－－－－－－－－－－－－－－－－－