相対性理論の継続

時計と原子の比較に戻ります。
Let r' be the rate of a clock in K' and r be its rate in K. Then r = r'(1+phi/c**2). In the previous discussion, phi was related to angular velocity and the radius of rotation. Apparently, the vibrations of light waves of an atom emitting light are analogous to the ticks of a clock. In this case, the potential difference is:
phi = -K*M/gamma
Here K is the gravitational constant, M is the mass of the star on which the atom is situated, and gamma is the distance of the atom from the center of the star. The potential difference phi decreases in magnitude as the radius gamma increases, as the gravitational force of attraction of the star is weaker. Note that the potential difference is inversely proportional to gamma and not gamma squared. This is probably because work is force times distance, so the force (proportional to gamma squared) is multiplied by the distance (gamma) to obtain the work required to move something from a distance of gamma to the center.
The equation for the frequency of light is:
r = r'-KM/((c**2)gamma)
Thus, the frequency decreases due to the gravitational field K'.
We could say that K is free space, but Einstein's text also treats the surface of the Earth as K. I assume this means that he can discount the gravitational field of the Earth as being relatively weak, as it is not a factor in comparing K and K'.
This reduction in frequency is known as a shift towards the red, as red is at the low-frequency end of the visible spectrum.
That this displacement towards the red occurs is essential evidence in support of general relativity (in particular that space and time perceptions differ based on the gravitational frame of reference).