We know that by calling the General Theory of Relativity, Einstein thought that his latter theory somehow encompassed the previous Special Theory of Relativity and the theory of gravitation. But is it really so?
Based on the very Special Theory of Relativity and the
curvature tensor and matter tensor, together with a thought experiment,
we can show that both special theory of relativity and general theory
of relativity have an intrinsic contradiction among themselves. And the
theories of relativity are to be explored further to tackle this
contradiction. In other words, the theories of relativity are not
“always right” such as the mass media often praises, when the
scientists find any new data confirming the theories.
Now let’s make it clearer.
The equation of General Theory of Relativity is as follows:
R(i,k) = k T(i,k) (1)
k is Einstein’s gravitational constant
R(i,k) is Riemann tensor of curvature
T(i,k) is the matter tensor.
Let’s
suppose we have a distribution of matter, being concentrated in a very
small area around a point O in space. Then we examine the curvature of
space time at a point P. The distance between O and P is 300 000 km + 2
meters.
Without regarding the wave nature (traveling
nature) of gravity, Einstein could have found and we could find that
the curvature of space time at the point P is a solution C(i) of the
equation (1). Just calculate the matter tensor and the curvature tensor.
Now
at the time t1 we start moving such matter distribution one meter away
from O to a point B, then stop moving this matter distribution at the
time t1+1 second while keeping the geometrical shape of this matter
distribution unchanged.
1) At the time t1+1, if General
Theory of Relativity is to be used as presence, we could have found a
new solution C(n) of space time curvature at the point P just by
applying again the equation (1) for the matter distribution at the
point B. This is the instant interaction that even Einstein had not
escaped its bound when he forwarded his General Theory of Relativity.
2)
By the very basics of Special Theory of Relativity, we can state that
if a light ray was switched on at O at the time t1, this light ray
would still be traveling from O to P and could not have reached the
point P at the time t1+1 second, then an observer at P at the time
(t1+1s) was no way possible to detect any change of the matter
distribution while we moved this matter distribution between O and B.
(No information about a physical system can be transmitted and received
at a speed that is higher than light speed in vacuum!)
Now the contradiction is very clear:
a) By argument 1), we could find the curvature change of space time at P at the time t1+ 1 second
b)
By argument 2) of the very Special Theory of Relativity, we should not
have detected (or more precisely, we could not detect) any change of
the curvature at P, caused by the change of matter distribution at the
time t1 +1 second.
By this very contradiction between the
“General Theory” of Relativity and the Special Theory of Relativity, is
the General Theory still “general” at all. And if the incorporation of
General Theory to Special Theory produces a contradiction among
themselves, can we have a right to revise carefully the theories of
relativity?
