Analyses of the light quantum system for the electromagnetic field tensor.

In this article Einstein's electromagnetism tensor matrix has been establish only by use of the Newton’s law and the law of conservation of matter. It is proved that the electromagnetic phenomenon actually only just is a mechanics phenomenon in the light quantum system. The electric field intensity, the vector potential, the magnetic field intensity, the Einstein's electromagnetism tensor matrix, that real are all caused by the oscillations of the light quantum system.

(1) The light quantum system of a particle is distributed and moved on equipotential plans around the center of the particle. They form a continuous series of distribution surface. The light quantum is in motion and vibrating. For a particle (point charge) in a stationary state, or in a uniform motion state, the vibrating light quantum system are  acting on an external force by the surrounding space, these reactions form an electromagnetism field. Take a coordinate system at relative rest, with the center of particle  as the origin.

Let’s take a small region in the coordinate system. To regardless of the higher infinitesimal can get the system of equations:

(The law of conservation of matter),

  (Newton’s law ).

Among them is the density of the light quantum in the small region,  is the three-dimension vibration velocity of the light quantum in the small

 region. The vibration velocity of the light quantum should be four-dimension,  is corresponding to .  are the stress tensor in the small

region, are external force, that acted to the light quantum system in the small region.  are the outward action around the particle due to the

 vibration of light quantum system of the particle. There is no other field of force in the space around the particle.  just is the outward electric

 field of  the particle.

Take ，,  is rewritten as in order to keep the identity relation unchanged with formula of quantum mechanics.

 From the above two equations can get：

，.

Choose the principal stress axis as the coordinate,  It is symmetry and isotropy for the light quantum system of the particle ,   as  , as

，.

From these get:

，

， ————

 Multiply both sides of   on the left by,

gets:

,, .  is the volume of a small region in the coordinate system . Supposes the proportionality coefficient is ， That is

 in it, thus can get: .

 is the state function of  the particle,  andall are corresponding to the density of the light quantum of  the particle, , there are no other

 factors involved, after to substitutes forcan get： .

It has been found in the above article: << Symmetric equations of the light quantum systems.>> .

To compare the formula  with the formula , we can get:

, ， is the magnetic quantum number，it is the quantity of charge  too.

A free particle has a four dimensional energy tensor and a four dimensional state function, The energy tensor have the same vibration frequency and

 phase as the state function, so we can think .

We have substituted forabove, imitate to substitute  for , we can substituted for, and define .

 Back to the above, there are：

Multiply both side of this equation on the left by , can get

.

Define , mean  , ,.

That is：，.With plug in ，

then get：

。

Substitute for , then get:.

this expression is compare with ，can get：

………………（1）, . The same can be:

………………（2）,

………………（3）,

combined with formula :  ………………(4)

This is known as：.

The vector  is obtained from the matrix relation,

，We’ve defined:，

， ,

this is., , .

, get: ………………，

, get:………

From , above , get:

-+,

This is: .            

  In the same way：.    

Combined with equation :  .

These series of four equations  are called series of equation .

(    (2). Establishment of the energy-momentum tensor matrix..

The matrix relation  is established by referring to the series of equation:

This relationship is called the energy-momentum tensor matrix.

Suppose  , we can prove that the series of equations are equivalent with the matrix. The proof is as follows:

From the matrix relation, can get:

。

Multiply both side of the above matrix relation  on the left by, can get

,

namely .

Let’s use the formula   that have been hypothetical.

From this can get: , , .

The matrix relationis:

Multiply both side of the above formula  on the left by,

 .

That is ,

 namely , alike：,

,

another add ：

These four formulas (21)——（24） are the result from identical transformation of the matrix relation . These four formulas (21)——（24）and matrix relation  are equivalent. While the four formulas (21)——（24）and the above series of equations are all identical. The resulting is the energy-momentum tensor matrix and the series of equation are equivalent. The series of equation are derived from the mechanical principle of light quantum field, so it can be seen that the energy-momentum tensor matrix is derived from the mechanical principle of light quantum field theory.

((3)  Next we must explain what the matrix relation is ?

The fourth equation in system of equations  :  .

According to the law of conservation of matter, for the steady system

，

 It is a homogeneous equation according to the law of conservation of matter, but the other equations inare inhomogeneous. Just take the particular solution of the homogeneous, then matrix relation  is matrix relation.

，，are the external force acting on the light quantum system of particle  by the surrounding space at point.  are the force of

 the particle on outer space at point. For particles at rest or in motion, the force exerted on the outside caused by oscillation of the light

 quantum of the particle just is the force of electromagnetic field. just are the electric field of force. ，，are the magnetic force outside.

But in the tradition, so-called the field of a particle at a point, it is the force of the particle as a whole ( from the center to )on the

 external particle of the whole at point ( from the center to ) The charge density of particle  is concentrated at point . The charge

 density of external particle  is concentrated at point too.

The field strength of particle at point is, and the stress field strength of particle at point  is

. is the electric field strength of particle at point，

is the magnetic induction of  particle at point.

((4). Establishing the Einstein electromagnetic tensor matrix from the mechanics principle of the light quantum system.

Multiply the left-hand side of the matrix relation  by  and ,

and double integrate in the region  , the left-hand get:

，and .

 is the external electric field intensity of particle  at point ，is the magnetic induction intensity of particle  at point.

Multiply the right-hand side by and, double integrate in the region ：With  integrate:

 .

With  integrate: .

 Here the infinite integrate  is due to the density of external particle is  concentrated in.But the infinite integrate  is because the density of

 the action of particle on the external particle  is concentrated at point. The integrand is a spherical function ,  The integral can be done in

 spherical coordinate system.

According to the above definition, we can get:

.

To define  as vector potential，then get .

If the discussed point  just is the point, In this case  can be viewed as the velocity of the particle .  is the moving velocity of particle .

 Then the double integrate becomes unary integrate. Thus we can get  the matrix relation ：

.

This just is a meaning contained in Einstein’s electromagnetism tensor matrix.

To define the above quantum number  as charge number ，，，， are shown as the electric current

 density and the charge density at point  respectively. Thus the matrix differential equation  becomes:

.

The matrix differential equation  is exactly alike with the Einstein’s electromagnetism tensor matrix formula. As well as the series of equations is

 exactly identically with the Maxwell electromagnetic field equation.

It makes clearly from the above discussion, that the concept of the electric charge, and the vector potential, as well as the electromagnetism tensor all can be established by the vibration energy and momentum of the light quantum system. These are completely identical with the Maxwell electromagnetic field equation and the Einstein’s electromagnetism tensor matrix. The derivative and the establishment are without the Coulomb's law and the ampere ring road law etc. in the least, but have been established completely by the mechanics principle of light quantum system. These have been proved fully that the electromagnetism phenomenon is a mechanics phenomenon in the light quantum system.  Furthermore, it shows that the most basic composition of particle and matter field all are the light quantum system.

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