13   mass in the gravitational field

Annihilation experiments
    The first step: showed in figure 13.01-a. On the ground, we get 0.5Kg matter and 0.5m antimatter and combine them step by step. Now suppose that all of them are complete photon and be collected by the far photon receiver C. In the end, the photon receiver C gets a energy reading E1.

Fig. 13.01 Annihilation experiments of different heights

    The second step: we get the same matter again. This time, we will send the matter to the far space then contact them step by step, as Fig. 13.01-b. This time we get a energy reading E2.
    The question is that whether E1 is equal with E2?

    The first: According to Mass-energy Equation and the m and c in the two experiments are respectively the same, so, E1= E2 .
   If the energy received from the two experiments is equal, the energy from the external work would not explain where go. For example, if we send kf matter to space, it will be more than 60 million Joules energy. This amount of energy can't be ignored. So this answer is inconsistent with facts.
    The second: Some people consider: that the energy of the external work, which is consumed by the earth's gravity. That is to say the external work is changed into a part of the gravitational field. So, E1=E2.
     Let's make a Thought Experiment. We need just repeat a simple action by a long arm, which is taking definite object from the earth every time. We repeat this action until all the objects away. At last the gravitational field should gain much work. But, the gravitational field would be lost?
    According to The mass-energy conservation law, iIf the gravitational field absorbs the external work, the gravitational field itself should be strengthened. In this case, the objects' potential energy on the grouand would be increased. We can explain where the energy goes. however, the fact is reverse, the gravitational field itself becomes weaker after the objects is taken away from it.
   The third: Some people consider: that the proton must overcome the gravity to do work when it leave the gravitational field. So, E1<E2.
    This kind of parlance is also called "photon energy theory". This requires that the photon have the mass. If the photon have the mass, in principle, all the electromagnetic theory is incorrect and object with mass can't move at light velocity. On the other hand , if the energy of photon turns into the gravitational field, we should observe this accumulation effect especially the stars it is very notable which shine in a long time. But, people haven't observed that there is any abnormal in the gravitational field of the sun.
   The conclusion: Variety of explainer above are dissociable. The only accurate conclusion is that the external work has transfered the object which be raised and made the mass of the object increase At last. So: E2>E1
    The difference of the energy from the two experiments is:

   .............Equ.13.1
    Because:
    ................................Equ.13.2
    R - the radium of the earth, M the mass of the earth.
    To make the equation be a common form, we let the gravitational potential energy as U.
    ............................Equ.13.3

    This is the "mass-field equation" . The following facts can also deduct the "mass-field equation"
    1. The covariance requirements of different heights physical experiments
    2. The requirements of energy and momentum conservation laws
    3. Tthe requirements of the whole modern theoretical system self-consistency

The problems about the covariance in the gravitational field
    The relativistic covariance has been known by all, i.e. ruler, clock and mass in the time-space change in phase. Covariance assures that physical laws are fit to all the systems. For example, the cycle which observers get is still the same because the clock of the system slows down. The athletes can not gain any profit if  the venue change in a train with high speed. Although the clock becomes slow and the distance becomes shorter, however, the mass of the athletes' increase and response speed reduces. All these changes just assure the athletes gain the same grades with those on the ground. Absolutely true, we do not identify whether the syetem is at rest or moves uniformly forward in a straight line by any artifice.
    Whether does the gravitational field space meet the covariance regulation? The conclusion is that the experiments which haven't gravitational potential energy exchange meet the regulation. Such as the experiments in level. From the covariance in the level we can infer that when we measure the parameters of a level circular motion at different heights, such as centripetal force, cycle, radium will be complete the same. we can't know their heights from these parameters.
    The systems don't meet the relativistic covariance when it exchange energy with gravitational fields. Usually, the experiments which are not in the level don't meet the relativistic covariance. For example, the observer who are still relative to the gravitational field observer the parabola movement, they can infer the height of the system from the movement trajectory. So it doesn't meet the relativistic covariance.
    A typical important  example need explain, the observer can not fell the acceleration itself when he in a free-falling ystem. The potential energy of the system turns into kinetic energy step by step. So, the energy still stays in the system until it reach the ground. So, the free-falling system are equivalent with the inertial frame which absolutely meet the relativistic covariance. In the following, when we refer relativistic covariance in the gravitational field, we demonstrate the level experiments or the free-falling system.

Zhan, Li Kui 6/18/2007

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