In-depth analysis of the curvature of general relativity

——Metric transformation function(3)

1．For a particle, the light quantum system, it has:

(1）The velocity of light quantum from and its revolving spin speed . The energy they produce that determines the particle’s own light quantum point is the internal energy of the particle. Let’s call that inherent internal energy per unit volume of the system as. These internal energy is direct proportion to the density of light quantum system, .

When the particle is in isolation, the energy per unit volume which the particle has is expressed as. We’re talking about the macroscopic. According

 to Einstein’s low of mass-energy relation is: . is the density of light quantum measured by the curved metric. When the particle is in

 isolation, and is in equilibrium with the stable space around it, there should be.

(2）We’re talking about the macroscopic. In many cases，the energy of the local space around the particle is present. This energy is not constant. Such as there’s a heat source around the particle, and gravitational potential, electromagnetic potential energy in field. Their energy enters the particle by conduction. In addition to these, there are the kinetic energy and the potential energy of the total particle, and so on. Let’s call this energy as macro energy of the particle. The macro energy per unit volume is expressed as.

The following formula is often used to determine the macro energy：. is the temperature. is entropy，、are the

 generalized force and generalized coordinates respectively. The macro energy can also write it in the formula: ， .

 is the thermal energy of an object.  is the work to outside done by the system.

The above internal energy per unit volume of particle has been expressed as. The macro energy per unit volume is expressed as. The overall

 energy per unit volume of particle system should be the sum of internal energy and macro energy. The overall energy per unit volume of particle has

been expressed as. . When the particle is in equilibrium with the stable space around it, ,.

During the conduction process, the macro energy of the particle per unit volume changes as energy is transferred to the particle. is going to

 increase. As the rule , will be increased. But at this time, Einstein’s low of mass-energy relation still holds. The overall energy per

 unit volume of particleshould also go towards. , that is an important condition for the particle when it is in equilibrium with the

 stable space around it. This is an important hypothesis of Einstein, a large number of facts have been verified.

It’s going to be, according to this assumption. Now  by conduction, how does this formula be tenable? It only can be

 tenable when.

 Let’s . is the density of the light quantum of the particle in this case. So there will be . Only when

 this equation is true can the particle reach equilibrium with the surrounding space.

Let’s. The following equation is the same with equation.。

Let as the difference betweenand, .Then above equation becomes the equation. In order to keep

 balance with the whole stable space, it must be , so we are able to make ，particle can be keep in equilibrium with the

 whole stable space at that point.

Now during the conduction process said above, is going to increase by conduction. In order to keep balance with the whole stable space, it must

 be . This timeis increased，also has to increase in order to reach. But，if we increase,

 must decrease, and the density of light quantum of the particle must decrease, then get to reach , so the whole energy per unit

 volume is in equilibrium with the whole stable space.

It can be seen is a condition that determines the density of light quantum of the particle is in equilibrium with the

 whole surrounding stable space. is a factor that determines the density of light quantum of a particle to reach equilibrium with the surrounding

 stable space.is an important condition for determining the density of light quantum of a particle in the field too.

However, we have proved it above: The factor that is determined the density of light quantum of this particle is the metric transformation function

 at that point. ，And is a constant. In the metric transformation function,  is an initial condition of the

 differential equation. It should be one of an important condition that is determined the density of light quantum of this particle at that point. But as

 state above,  is an important condition that determines the density of light quantum of this particle at that point too.  For a particle,  and  are

 correspond to the density of light quantum of this particle at that point synchronously. There must be a functional relationship between them. Let

be a function of. We can write  as a function of. The metric transformation function can be expressed as.

(It should be noted here, the total curvature  in the metric transformation function is determined by the curvature equation. It are

 determined by the isospin quantum number and spin quantum number.  doesn’t have an explicit function of energy.)

In the article 《In-depth analysis of the curvature of general relativity——Metric transformation function(1) 》, we’ve got: When we use the flat metric

 to measure, the reading of distributing density of light quantum is . When we use the curved metric to measure, the volume density is

. There is the formula

 now，thus. To keep simple, we can also write this  as well.

In the field, if the overall energy per unit volume is equal to, the particle is in equilibrium with the stable space around it.  At this point set

. .

If the overall energy per unit volume is greater than,. This is going to be,.

If the overall energy per unit volume is less than,, This is going to be, . is a minus function.

When the particle is reached equilibrium with the surrounding space, the mass of particle is:

When the difference between the overall energy per unit volume of particleand is equal to 0. , at this point we’ve set . .

At this time, when first increases by, . The mass of particle is .

In this case, the second time when is increased byagain. ，The mass per unit volume of particle is.

But look at it another way, if you increase by  at once, the difference between the overall energy and should be at this

 time. The mass per unit volume of particle should be .  The increase in the overall energy in both and  should

 be the same. The mass per unit volume of particle should be the same in both cases.

，

The resulting : ，.

，，

     While ，

， 。

，.      is a constant independent with , it doesn’t matter what kind of particle, what kind of,what form it is?

 is a minus function,   .  is a constant number. When the overall energy per unit volume of particle is equal to at that point,

 so that, and. The resulting is , . Under normal circumstances there is .

As stated above, the mass of a particle in full equilibrium with the surrounding space is. is the mass as . For a system

 composed of i particles, the mass of ith particle is.

To summarize what has been said: Let the mass of the object is. If the temperature of the particle is less than the surrounding space, before the

particle reaches equilibrium with the surrounding space, the overall energy per unit volume of particle is less than at that point, the particle

 absorbs light quantum from the surrounding space. So the internal energy of the particles increases, and the mass of particle increases too.

The added mass is: .

Before the particle reaches equilibrium with the surrounding space, when the overall energy per unit volume of particle is greater than at that point, the particle release light quantum to the surrounding space. So the internal energy of the particles decreases, and the mass of particle decreases too.

The reduced mass is:

Now let’s talk about how to luminescence when an object was heated. An object is in contact with a heat source. Think of the heat source as a part of

 the surrounding space. At this time, the overall energy per unit volume of massis less than the energy per unit volume of the part of surrounding

 space at that point. The heat source input energy into the object. Then make the macro energy per unit volume and the overall energy per unit

volumeincreased. . In an instant, in order to the tendency to balance with surrounding whole space,  , So the density

of light quantum of the particles and the mass will reduce. The light quantum of the particles will be emitted to surrounding whole space. This is the

process by which the object luminescence when heated. The so-called heat luminescence that is the object passes the light quantum of the heat source to

transmit to the surrounding space.

But after the mass of object is heated by a heat source, immediately it is away from the heat source. In a short time, it still contains the energy that the

heat source once provides it. So that make the overall energy per unit volume is temporarily larger than. The mass of object is now greater

than the original mass before heating. This phenomenon can be seen in the following article：“An experiment discovery about gravitational force

changes in materials due to temperature variation” in the journal “ENGINEERING SCIENCES” vol.8, NO.2, JUN 2010.”

The conclusions stated in that article should be consistent with the principles stated in our paper. It is said when the mass of object is heated and

immediately leaved the heat source, the mass of the object is temporarily greater than the mass before heating. That means: when the object where

heated, it absorbs the light quantum from the heat source. Of course over time it will come back to its original mass.

This experiment is also evidence that “ The most basic structure of matter is the light quantum.” Why do we say that any matter is made up of light

quantum? This is because: （1）The atomic structure of the material does not change before and after heating.（2）When the object is heated and

leaves the heat source immediately, the mass of the object is temporarily greater than the mass before heating.

From a view point of quantum mechanics, in the case of thermal radiation,  can be chosen and expressed in. It just is：.

 According to the above, the light quantum of the particles will be emitted to surrounding space when heated. The number of light quantum emitted

 should be: . It can also be written as. This formula seems to correspond to Planck’s formula for black-

body radiation. The distribution of black-body radiation is according to the frequency of energy when energy is in equilibrium with the surrounding

 object. The Planck’s formula for black-body radiation is . Take the vibration frequency of the light quantum in

 formula and formula  all as , and take  in formula  to be equal to  in formula . So this is just substitute  from formula

 for  from formula . So we get . Notice that in formula is the light quantum in units of emitted

 or absorbed into the surrounding space. The energy density of the emitted or absorbed light quantum also corresponds to  or an integer multiple

 of it. According to quantum mechanics and black-body radiation principle, must be corresponding to  or many times of. It can’t have an

 exponential factor on the right-hand side of the formula. There must be.  If the units of appropriate system is used, can lead to

.. is Boltzmann’s constant. is absolute scale temperature. is independent of. .

According to the above analysis, the metric transformation function is . Now we have gotten . The metric

 transformation function may be express into.

. However, under normal circumstances, especially when we’re talking about individual particle, the particle will be in equilibrium with

 surroundings. ，，, it is always true in this case.

Introduction and Contents 引言和目录