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.

 

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