14   ruler and clock in the gravitation field

    The clock in the gravitational field is slower than that out the gravitational field has been directly validated by experiments. And there is no any doubt.
   There are no clear conclusions and proof of experiment about the rule in the gravitational field. Some people think that the rule in the gravitational field is shorter than it out, others think that is longer.
    In the 11th chapter, we have explained the reason of radar echo delay which is the light velocity is less than c in the gravitational field. Why the general theory of relativity adopt changeless light velocity get the correct conclusion? In fact, the light velocity have never been used in the general theory of relativity. On the other hand, we should comprehend the historical background of the general theory of relativity. Dominant ideology accept just now the concept of changeless light velocity and it's causation is not entirely clear. It is unpractical that introduce the concept of "alien-measure". So, time is instead of distance in general theory of relativity.
   Time is instead of distance in general theory of relativity, which provide us with a direct method to deduce the relation of ruler in the gravitational field. It is truer that the that light velocity measured in the gravitational field is constant, also it is true that the time in the gravitational field is slow, apparently, the light can travel longer distance in a longer time. So, the ruler in the gravitational field is longer than it out. That is to say, the ruler is "stretched" rather than "shortened" in the gravitational field.
    The accepted relation of time in the gravitational field is:

    ......................Equ. 14.1
   T0 - the clock period which out of the gravitational field.
    Both sides of the equation multiply c .
    ......................Equ. 14.2
    This is the ruler in the gravitational field when we observe from far away. The denominator is obviously less than 1, which indicates that the ruler is stretched. We can also use the relativistic covariance to deduce the ruler relation.
Deducing the relation of ruler from the the relativistic covariance of the gravitational field
   After we do work of w on object of mass m, at last, the length of the object is.
    ........................Equ. 14.3
    Ls - length of start, Le - length of end.
   Now, we lift a same object in the gravitational field till it far away by the same work, At last, the speed of the object is zero. As discuss front, the embracer of work is the object Instead of the gravitational field, the mass of object will increase. According to the relativistic covariance of the gravitational field, So, the object is longer in the gravitational field at first.
      We are used to take L0 to express the free space length, and use L express the the gravitational field:
    ........................Equ. 14.4
    Because:
   
    We place the W into equation 14.4.
    .....................Equ. 14.5

summary of the equation about the gravitational field
    We observe the ruler, clock and mass in the gravitational field from far away.

    ......................Equ. 14.6
    ......................Equ. 14.7
    ................Equ. 14.8

    We can analyse the gravitational field from relativistic covariance. currently, the dominant ideology think:
    In the moving system :   " ruler shortens and clock slows" causes "mass increase".
    In the gravitational field:  "ruler shortens and clock slows" causes "mass constant".
    Does the gravitational field accord with the requirement of covariance? Apparently,it is obvious that the relation about the gravitational field is inconsistent. It is obvious self-contradictory. If we take into account many theories, many facts and many physical relations, we would find that is not avoidable about the mass change of the gravitational field. while it is self-consistent and harmonious of the change of mass.

  Fig. 14.0 the cartwheel in the gravitational field should be like this, but the one through measurement and observation is a circle.

Zhan, Li Kui 6/18/2007

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