Explore " spin " deep going.
The
spin quantum number of particle exist, it is accepted early by all people. But
about its generated reason and some property are hardly researched. To explore
the spin of particle should begin from the spin of the light quantum system of
a particle, by which the particle is composed, then the generated reason of the
spin of a particle can be gotten. In this text, the
"spin" is discussed in detail. We set up a definition of the spin
movement for the light quantum system of a particle, discuss
spin vibration, and its causes, Established the spin wave equation. It
is proved that the spin quantum number 
is
a quantum number of the spin wave equation,
and the spin vibration is come into being looking at it in different spin
motion velocity coordinate systems. Beyond that we explore the strong interaction
action for 
meson
and 
meson,
they may be come into being by their spin vibrating energy.
1. The relativity of spin space.
The motion formulas
of a particle except translational motion, linear vibration or revolving to
wind to a fixed point ( or a fixed axle ) , should be included the spin or the spin
vibration to wind to a equiprobable vector axle( passing through the center of particle)
yet. So call the equiprobable vector axle, it is a vector axle, its direction
is changed in any instant and in every direction equiprobably. Take a small
part of a light
quantum system
of a particle in
a small volume
, 
. So-called
spin of particle just is this light quantum system in revolving
to wind to the equiprobable vector axle passing through the center of.
For the
equiprobable vector axle passing through a point, its direction is in arbitrary
change though, but according to the article: 《The
equiprobable vector and symmetry – broken》to state, the
positive direction of revolving axle is defined as the
direction of ray outward on distributing surface of the light
quantum systems. If when we take the mean of spin angular velocity, the range
of integral angle may be 
. How is it?
Only to take on this definition, thus can be corrected corresponding to spin
angular momentum, spin energy, spin symmetry equation, and so on. Please
see the articles 《The
equiprobable vector and symmetry – broken》and 《Vectorization
of symmetrical equiprobable vector》.
When define and observing
any
spin static point
from a same coordinate system, its spin
angular velocity and direction all are identical. When
observing a
same point from
two coordinate systems, we get the spin angular velocity and its
directions are different. The spin angular velocity of coordinate
system 
opposite to another
coordinate system 
is 
, which is we consider the spin
angular velocity of every spin static point in coordinate
system opposite
to another coordinate system all are .
The spin
angular velocity of a point opposite to coordinate system 
is 
, the spin
angular velocity of the same point opposite to coordinate system
is 
. Owing to the relative spin
angular
velocity between coordinate system and coordinate
system is existent, 
. In
the vacuum space, by appointing the spin angular velocity of
light quantum in any rotate coordinate
systems is permanent being 
all along, after
this appointing we may confirm for sure that the
metric transformation of the spin between relative coordinate systems is the
Lorentz transformation yet. This derivation process is alike with the
relativity about translational motion through simple calculating. But among
this 
，
. Among them 
is the relative spin
angular
velocity
between two coordinate systems. Please see the article《The equiprobable vector and symmetry – broken》.
According to the
Lorentz transformation, the transformation of the spin angular energy is: 
.
Among these is
the spin
angular velocity
between these two coordinate systems, 
,
are the spin
angular velocity of a light quantum point opposite
to the coordinate systems and
respectively. 
is
the spin inertia of a light quantum point. This above formula of the transformation
of the spin angular energy is:
.
For the mass
point of light
quantum:
,
,
thus the spin energy is
. So the transformation
of the spin angular energy is 
.
When observing
from the coordinate system, the spin kinetic
energy of a mass point is
.
When observing
from the coordinate system 
, the spin kinetic
energy of the mass point is 
；
When observing
from the coordinate system, the spin kinetic
energy of the
spin static mass point in coordinate system is 
.
After the spin
kinetic energy in coordinate system is transformulaed
to coordinate system, get its reading is 
. When observing
from the coordinate system, the spin
kinetic energy of the mass point of the light quantum in the coordinate systemis
.
When observe
from the coordinate system, the spin
kinetic energy of the mass point of the light quantum is 
, but
when observe
from the
coordinate system at
the same time, the spin kinetic energy of the same mass point of
the light quantum in the coordinate system just is
. But
. When we observe from
the same coordinate system, the spin kinetic
energy of a same mass point of the light quantum
should be
identical.
Why now the gotten readings are different? That is shown: owing to the relative
spin angular movement exist
between the systemand the system,
through the
Lorentz transformation it is produced another part of spin angular vibration
energy of this light quantum in the system, when
observing from the coordinate system. 
We must extend the
transformation of spin angular coordinates, it is generalized to 
, and
make the mean vibrating value of spin angular displacement maybe equal to 0,
just
.
Then the
spin angular vibration of the mass point of the light quantum is generated when
observing
from the coordinate system, Take this
energy of spin
angular vibration is 
, thus 
. 
We
have gotten from foregoing paragraphs 
,
among
them
，
. 
Single mass
point of light
quantum system 
.
For a mass point of light
quantum if observing
from the coordinate system the
spin angular vibration energy 
has been
existent, then
there is
when
observing from the coordinate system,
If 
，then 
；
If 
，then 
.
2. The spin angular vibration.
The concepts of spin and spin angular vibration
have been explained above. Form foregoing paragraphs, if
there is a spin angular velocity
between two
coordinate systems, then there is a spin vibrating velocity
of
the mass point of the light quantum when observing from one of the coordinate
systems.
For every
particle there is a critical coordinate system
. Relatively
to the
critical coordinate system, the spin angular
velocity 
and
the spin angular vibration velocity
for the light
quantum system of a particle. If there is spin angular velocityfor
the coordinate
system
observing from the coordinate systems, then there are
spin angular vibrating velocity and spin angular
vibrating energy 
for light
quantum systems in the coordinate
system
observing from the coordinate systems. In
reverse if there is a spin angular vibrating velocity for the light
quantum systems of a particle relatively to the critical
coordinate system, then there are spin
angular velocitynecessary for the light
quantum systems of the particle. The and are
the equiprobable vector said above.
In the vacuum
space,
for the mass points of light, their spin angular
velocity is defined as
.
is a constant. When spin
angular velocity of mass points of the light quantum system is
, then the spin
angular velocity of the mass points is no longer to increase, all it
adds is its energy, the spin angular vibrating energyof the light
quantum system will be increased only.
A spin angular velocity is different to linear velocity, it isn’t distinguished between flat space and curved space. That is because for the spin angular velocity,
there is 
. Therefor for the
spin space there are not distinguished between flat space and curved space.
3. The spin wave equation.
Owing to the spin
angular vibrating energy are existent, the particle are with a spin angular
velocityopposite to the
spin static coordinate system. The spin
angular vibrating energy is.
, 
.
It has been explained on the preceding part of the text, any spin angular velocity isn’t distinguished between flat space and curved space, it don’t change along
with space position. In a same coordinate system, 
. How does
we define to the spin rotational inertia of a mass point of light quantum
system 
?
For
single mass point of light quantum system 
.
Let us first
review the linear vibrations of individual light quantum, there are 
. This is similar to the
spin vibration of a single mass point of light quantum. For away from the
particle, in a vacuum, the vibrational energy all are the velocity of light is multiplied
by momentum of light quantum. The velocity
of light in spin vibration is
equivalent to 
. and
momentum or angular momentum is equal to 
. (
is the radius of the light quantum when 
,
is the radius of the particle.).
Firstly
let a single mass point of light quantum system to lock upon as a very small
sphere，
is the mass of a mass point of
the light quantum.
Refer
to traditional calculation method for . At a distance from the particle, in a vacuum equals the velocity
of light, 
equals
the
momentum of a light quantum, 
should be equal to
. But closer to the center of the
particle, 
，
. But the angular
velocity and still
have no change for coordinate system. 
。in the medium should be equal to
。
。
Define 
。 
，
。
If the density
of the light quantum is 
in the small volume element
, the
vibration energy is
,
then from the 
system，the vibrational energy of a
single light
quantum is: 
.
Firstly, we look back the case of mass of a particle. From classical point of view：The mass of a particle is centralized at the center of the particle.
. From the viewpoint of
general theory of relativity and the light quantum analytical mechanics：
，
To
unify the classical point of view with the light quantum analytical mechanics
as well as the viewpoint of general theory of relativity，
can
substitute
for
in 
.
Secondly,
the spin angular velocity direction of the particle is distributed on the
sphere. The direction of spin angular velocity of the light quantum are
distributed on the sphere, the radius of the sphere is
. The integral
element is 
. Near the
center of the particle, the light quantum is densely distributed. The integral element
should
be change to
.
，
.So the integral
has shrunk
，but it’s enlarged
by the
integrand.
We were
summing in terms of 
to
get 
,
the summation has to be done by integrating in spherical coordinates.
For
and 
, the values of definite
integrals
should be the same in infinite space.
.
，
The
key question is, why does this term 
appear in the
spin vibrational energy? We’re all
integration in spherical space, the integral element is
.
Due to spin angular vibrating momentum
and energy exists and spread, take form a set of spin angular vibrating wave. So
that there is a spin angular vibrating wave function. The spread
factor is friction and bump. In a unit volume the
state function of spin angular vibration is：
.
is said for the
four-dimensional component, the subscript 
corresponds to . 
。Here
we use the " curved metric"，
is the mass point of light quantum
starting from 
to
point , at this
time, the spin of point has been rotated. The subscript 
or 
indicates the reading
measured by the curved metric. The subscript
or 
indicates the reading measured by the
flat metric. 
is
the spin angular velocity of the light quantum. 
represent the angle by which a single light
quantum has been rotated in the curved space.
According to the principle of path integrals, the state functions of the particle is:
. Among
，
。
says the spin
rotational inertia of the particle, 
is the spin
angle of the particle.
The resulting: 
It
can be obtained from equation 
：
，
.
In spherical coordinates,
is the third
compound of spin angular momentum, 
。
.
In
the article << Symmetric equations of the light quantum systems>>,
there are 
, Where 
is the projection of the
angular momentum in the Z-axis direction, corresponding to the charge of the
particle.
In
this paper, 
is the
projection of spin angular momentum in the Z-axis direction, which corresponds
to a quantum number, but does not corresponding to the charge of the particle.
The difference between equation 
and equation 
is that the
equation has
an extra factor 
on
the right-hand side. They can both be viewed
as symmetric wave equations. and 
both correspond
to the energy in the spin vibration or the line vibration, but the two
homogeneous terms have different. The curved surface of the distribution of
spin vibration wave is a sphere, while the curved surface of distribution of
line vibration is a plane surface. We have to integrate in two different
coordinate systems.
The center of the state function of
equation is
the center of the particle, the range of the wave is the whole space, while the
center of state function of equation is also the center of the particle, but
the obvious region of broken part of the wave is in the area adjacent to the
center of the particle.
The reason for the difference is that
the homogeneous term coefficient of equation has an extra factor 
. In the region farther
from the particle
center 
, 
, 
, 
is just the radius of the mass point
of the light quantum, 
，
，
.
Only the region near
the center of the particle, 
, 
, 
. The region where the symmetrical part
of the spin wave function exists is the whole space, but the region where the broken
part of the spin wave function obviously exists is only the region adjacent to
the particle center.
Therefore, we believe that the region where the spin vibration wave of the particle obviously acts on the outer space is the region very close to the particle center, and the external interaction caused by it is the strong interaction.
These ideas seem to be a conjecture at present and need further investigation in the next section.
Introduction and Contents 引言和目录