1.3.6
Relationship between the two models
Once the necessary steps to transform the two
dimensional curved spacetime model for gravity, into the
stretched three dimensional model have been illustrated,
the next reasonable step is to find any relationship
between the two.
Relating to the three dimensional model, as it was
mentioned in the previous paragraph, and as illustrated
in Figure 1.8, the small squares of the lattice, get more
and more stretched as they approach the mass. In fact,
there should be the maximum stretch somewhere near the
surface of the mass, and the minimum at infinity, with a
decrement equal to the inverse square law until the
relaxed distance between two nodes of the lattice is
restored. In the same way, the curvature of spacetime in
the original model, is proportional to the gravitational
pull that would affect another mass in the vicinity.
Therefore, as for the three dimensional model, the slope
of the curvature should decrease with inverse square law
as it leaves the mass. By consequence of both obeying the
same law, the degree of stretching in the three
dimensional model, is proportional the slope of the
curvature in the two dimensional model without any
mathematical change.
The experiments carried out to test the gravitational
redshift, launch a high frequency signal vertically to
measure its frequency at a certain altitude. From the
spacetime point of view, from Figure 1.8, the two
measurements are taken at different positions along the
stretching, therefore, located in different squares with
different degree of stretching. Consequently, the
difference in the frequency measured at the two ends of
the launched signal, tells us how steeply the degree of
stretching changes at that point, or, for the two
dimensional model, they would tell us about the slope of
the curve at that point.

