Spin and precession of particle

How can the light quantum traveling at 300,000 kilometers per second fuse into stable or relatively stable particles? This is mainly due to the Big Bang and other accidental reason, some of the light quantum clumps together. Due to precession, they form stable equipotential surfaces and form stable or relatively stable particle.

1. Spin and precession process about the light quantum system of particle.

Look at the fig 1. Suppose the coordinate system  is a static coordinate system. The center of particle  is point. is a point on a distribution

curved surface of the light quantum system. Curvature line is through point on a distribution

curved surface. Take a little volume unite round point. The moving direction of the light

quantum points in  are equiprobable vectors, Though their moving directions may be different, but

according to the theory about vectorization of symmetrical equiprobable vector, （Read the paper<< Equiprobabilityvector and symmetry- broken article>> carefully.） they may be regard as a set of the light quantum points to move at velocity, along with tangent direction of curvature line

and towardspoint from left to right. We define this set of the light quantum points as. Take a

coordinate system , its center is, Its axes is tangent direction of another curvature line

through point. .. Its ordinate is tangent direction of curvature line through

point.，.  The direction of  is normal direction of the curved surface. .  Point is revolving to wind point  at tangent velocity

along with curvature line,

Coordinate system may be regard as revolving to wind point  at tangent velocity along

with curvature line. The revolving angular velocity is,  is little less than.  ( is

a radius vector.), . ，，

The plane .、 are all through point,  The plane ,  is on the plane . ( The curvature line

doesn’t have to be in the plane , does not necessarily on the axis.)

The light quantum points in  all are spin with spin angular velocity. They are equiprobable vectors. But according to above mention: “The light

quantum points of particle spin along with a curvature line, their spin angular velocity are equiprobable vectors. Through Lorentz

transformation, these spin angular velocity may be regarded as a directional spin angular velocity vector, which direction is consistent with the

revolving angular velocity of the particle. This time may be resolved as two parts: tangential component and normal component.” 

The light quantum points in  may be regarded as a directional spin angular velocity vector, is consistent with the direction of.

Similarly, take  round point, the light quantum points in also can be regarded as moving at velocity, along with tangent direction of curvature lineand towards point from right to left. We defined this set of the light quantum points are.

andare in reverse direction，the positive collision between and  are happened. and are in reverse direction，and are in reverse direction too. The tangential acting force has been effected after the positive collision between and, its direction is downward.

 Due to the positive collision between and,  so that is subjected to a force opposite to the velocity. Then the moment of force  is formation from the center of curvature line to.

.，. is directed inward.  Owing to the spin angular velocity of the light quantum is existence

for, the center of rotation ofis the center of , the turning radius of is which is the radius of. forms a spin rotating moment of forceto the center of rotation. Look at the fig 3.

The procession is take place owing to the acting of. The angular velocity of precession is，its direction is determined by.

When the positive collision between and , there is a moment. At this moment the precession velocity of the light quantum in is

generated due to the precession angular velocity . , ，. ，，，， is parallel to

surely. ，the direction of  just is opposite direction of which is the velocity of the light quantum system in , therefor get . The direction of  just is vertical direction of curvature line.  The direction of just is the direction of another curvature line. From this we may know, because of the positive collision between and , caused precession, so that the moving direction from clockwise along with curvature line

are altered to become counter clockwise along with curvature line. ， ，and is parallel to， , namely . The resulting is，the direction of is the direction of ，.

Because of the positive collision between and, caused precession, so that the moving direction of from clockwise along with curvature line are altered to become counter clockwise along with curvature line.

After this precession, the anther positive collision between and another  are taken place at point  near point along with curvature line,  is another set of the light quantum system to moving along with curvature line. Therefor  is because the second precession occurs, turned moving along another curvature line. And so it goes on, take place positive collision and precession again and again as well as turns moving again and

again. These moving and precession all are taken place on the same distribution curved surface . From these one by one, it is formed a steady distribution curved surface of the light quantum system.

2. To calculate about spin and precession of the light quantum system in detail:

We discuss a steady or near steady particle. In the positive collision course, there are: .

The mean value .

Among them the transforming function from the flat metric to the curved metric is:

， ， , is a constant. Please see the paper << In-depth analysis of the curvature of general relativity ——Metric

transformation function(1) >>.

formed a moment of force which is relatively to the center of curvature line. ，, . The spin

angular moment of momentum of the light quantum system in  is. The spin rotational inertia of light quantum has been shown to be the paper

《Explore " spin " deep going.》：，，.，

Take  is spin angular velocity of the light quantum point, is radius of the light quantum point at,  is radius of the light quantum point when. . We have known the spin rotational inertia of a the light quantum point is .  Please see the paper: 《Explore " spin " deep going.》Therefore the spin angular moment of the light quantum point is

. .

Because of the precession under the action of . The angular velocity of precession is . As mentioned above: , according

to Lai Chai precession rule: .  is rotated about the center of the curvature line by precession.  The speed of light in a vacuum at infinity is constant ，For stable or relatively stable particles, the angular velocity of precession is the angular velocity of

rotation around the curvature line ，it should be . Thus, it must satisfy: , ，、are the radius

of curvature of the corresponding curvature line at point. This identity is：，，.

During the collision, ,is from, Take the average. All relevant figures are substituted to obtain: ..

During the positive collision between  and,  is subjected to the external moment of force  due to the action of’s tangential spin angular momentum on .

。

In the process of positive collision, since the edge of is affected by the external moment of force , the force is generated by the external moment of force.

.

is the coefficient of elasticity of distortion. is going down in the direction.

Because of on the distribution curved surface of adjacent levels their curvature radius are different,  On the distribution curved surface up and down, So that their transform function from the flat metric to the curved metric  are different.  Here the difference of pressure force is made for the light quantum points. The difference of pressure force is . is a slight distance from the adjacent levels of distribution curved surface. . The difference of pressure force is:

. is the elasticity coefficient.

For, the difference in compression force  should be little than or equal to the action force,  is produced by the external angular moment of momentum, this is namely . 

For, when the difference in compression force  is equal to the action force, then the distribution curved surface of the light quantum of the

particle will be reach balance state: , ,

,

， , ,

，。

， 。

All like： ，.

，

according to the foregoing paragraphs, can be known a constant.

Know take ，

。

，

。

Namely . This equation is suitable for the Helmholz equations.

We call this equation is curvature equation.   The particle is

spherically symmetry, we take the total curvature is:

， its equation can be resolved into two part:

Association Legendre equation

, and

Spherical harmonics Bessel’equation, or imaginary factor Bessel’equation.

。

.  According to the foregoing paragraphs,  can be known a constant. is a quantum number of association Legendre equation.

To equation, The particle can be regard as spherically symmetry. Take the polar axis of spherical coordinate system as a symmetry axis, 

take,

then ,

Takeagain，then .

If the polar axis of spherical coordinate system is a symmetry axis, then is independent of ，then， the solutions

 of this equation are Legendre polynomials：， ，，

，

.

If the polar axis of spherical coordinate isn’t a symmetry axis, thenis related with. The solutions of this equation are Association Legendre polynomials:

.

Now discuss the imaginary factor Bessel’equation ,

.For the particle, when  then , This case，The equation is order imaginary factor

Bessel function.

When , its radial is accord with the imaginary factor Bessel equation. The specific form of the total curvature is determined by the value of quantum number. is the quantum number of association Legendre equation.

, if ， ，, 。

When ，for the total curvature ,

the curvature equation becomes ，Its surrounding direction is still the Associative Legendre equation：

. But its radial becomes the Euler’s equation. Take. .

Next we discuss the density of mass of a particle: We discuss the stable or close to the stable particles yet. ， .

.

,   alike：，

.

, near the area of the center of particle, ，,

，

We call this equation as mass equation.

For the mass equation, it is corresponding to motionless state, . Relative to the state of motion, it needs to add a term.  This equation may rewrite:

.

 The mass equation under wave state should add a wave term，it should become an state wave equation, but it is an inhomogeneous wave state equation (1):

.

Among the equation (1), .

Take a modulus to show association Legendre function:

，

。

The equation is derived from the curvature equation.

But when the particle is at linear vibrate relative to the static coordinate, following the linear wave question should be existence always, the linear wave question is （2）:

.

The question  with  all are the wave state question, they are corresponding with the state function of mass density respectively.

If they can be consistent, it is shown as the particle can steady exist, the particle has a long life. But now the equation ：

is a inhomogeneous

differential equation, the with  can’t be consistent, The particle can’ t exist steady so, the particle has not a long life, or it is oscillated state. Only when, the particle can exist steady, and has a long life.

Firstly we discuss the quark. Take the quark  for example. For quark , the isotopic、spin quantum number 、 all are , ,  is radius of

the light quantum point. Take  as minimum radius of particle , ，, ,  .

At this state, equation  should be close to a homogeneous equation, quark  can exist steady, and has a long life. Alike same way we may derive other quarks can exist steady all.

Next we discuss particle. Take proton for example：For the proton the isotopic –spin quantum number 、 all are , ，.

，this equation should be close to a homogeneous equation too.  Proton can exist steady, and

has a long life.

But for meson ，，，when increases， this formula is not possible.

The term  can’t be existence.

So the term can’t be existence.

For the particle ， isotopic –spin quantum number ，spin ，

The term  can’t be existence，

so the term  can’t be existence . For ，  can’t be existence steady all.

For , meson K，because they all are belong to singular meson，in the strong interaction they are produced, in the weak interaction they are sharp. In the changed process，its energy and momentum are changed very complex. The curvature equation is not existence.  For ,,, because of the strangeness number has appeared, the curvature equation are not always existence, these particle can’t steady.

All in all，If the particle can be existent steady, 、 must be selected，it must be choose as ，，let the curvature

 equation（1）are very close to a homogeneous equation，let the question  with  all are close to the homogeneous wave question, let matter question with wave question of particle can be consistent，such as quark, electron, proton, neutron, etc.         　　　　　　　

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