Gravitational Experiments and Space Time
Zhang Junhao
Shantou University, P.R.China
We point out that three classical relativistic gravitational experiments are advantageous to flat space-time and give a criterion to judge the nature of space-time in the gravity probe b experiment.
If a body
moves in the gravitational field due to the static sphere 
,
according to Newton gravitational theory, the variance of energy 
is
and the variance of angular momentum
is
This set of equation can’t explain the perihelion shift of the planet and the deflection of light. At least one of these equations must be wrong. According to the result of red shift experiment and the Einsten’s relation of photon
,
when a photon moves from the sun (
)
to the earth (
),
the variance of photon’s energy is
It means that (1) is correct, therefore only possibility is that (2) is wrong.
Now the problem focuses on that: (i) can we find out an expression of
,
that this expression and (1) may be use to explain the perihelion shift of the
planet and the deflection of light; (ii) what is the ‘source’ of
and ?
Equation (1) means that the relative variance
is equal to the variance of the field 
.
We may suppose that the relative variance 
has the analogous relation
where
are the constants. The quadratic term is too small, so we only consider the
first term. If we take
then (1) and (5) may be used to explain the perihelion shift of the planet and the deflection of light.
In 1990, we put forward the special relativistic gravitational theory basing on the flat space-time (Minkowski’s space-time). The first hypothesis of this theory is the equivalence of inertial mass and gravitational mass. The second hypothesis is that the equation of the gravitational tensor potential is
(6)
According to these hypotheses we obtain that, if a body
moves in the gravitational field due to a static sphere ,
the gravitational force acting on the body
is
where
is the 3- dimensional velocity of the body .
The first term is the Newton’s gravity, the second term is an additional
gravity deduced from the covariance of special relativistic theory. The
additional gravity is perpendicular to ,
so it does not contribute to do work, it only contributes to change the angular
momentum. According to (7), we can deduce equation (1) and (5).
General relativity obtains the other set of equation
People explain the perihelion shift of the planet and the deflection of light by using this set of equation. Then we have two ways to explain these two experiments, which way is the correct? The red shift experiment justifies that the set of equation (1) and (5) is correct. However the results of three classical relativistic gravitational experiments is advantageous to the flat space-time.
NASA and Stanford University are planning to proceed a new gravitational experiment, its title is “Test Einstein with Orbiting Gyroscopes—Gravity Probe B”, simply call GP-B experiment.
According to special relativistic gravitational theory, the orbit effect ‘s angular acceleration of the gyroscope is
According to general relativity, L.I.Schiff obtained (1960) that the geodetic (orbit) effect ‘s angular acceleration is
From (11), the GP-B group of Stanford University obtained that the geodetic precession rate is 6.6
.Then
the orbit effect precession rate predicted by special relativistic theory will
be 4.4.
According to special relativistic gravitational theory, the angular acceleration of the earth rotation effect is
According to general relativity, the angular acceleration of the frame-dragging (earth rotation) effect is
it is given by L.I. Shiff (1960). Form (13),
the GP-B group of Stanford University obtained that the predicted value of the
frame-dragging precession rate is 0.042.
Then the precession rate of earth’s rotation effect predicted by special
relativistic gravitational theory is 
,where
is the angle between the normal line of orbit plane and the direction of
projection of gyroscope’s axis in the equatorial plane.
These two sets of predicted values are the new criterion to judge whether the space-time is flat.
According to the results of three classical
relativistic gravitational experiments, we may find out all field components due
to a static sphere. Using the Lorentz’s transformation, we can further find
out all field components due to a moving sphere, and finally obtain the angular
acceleration of orbit effect. It is just (10). So it is extreme possible that
the experimental value of orbit effect precession rate will be 4.4 If this case
is really present. It means that the space-time is flat. And we can prove that,
the explanation of the perihelion shift of the planet and the deflection of
light given by general relativity is wrong. The next criterion to judge the
essence of space-time is whether the precession rate of earth’s rotation
effect is dependent to .
If we do not measure ,
then this experimental value can’t be used to illustrate the essence of
space-time and the nature of gravity. The best way is to set the rotation’s
axis of gyroscopes in two different ,
then we can determine whether the precession rate of earth’s rotation effect
is dependent to
from experiment.