相対性理論と原子のスペクトル

最近アインシュタインの相対性理論を再読しています。
Relativity basically involves the differences in our perception of temporal and spatial position depending on our frame of reference.
In an appendix to his relativity treatise, Einstein discusses the displacement of atomic spectral lines due to gravitational fields. He begins this discussion by revisiting the discussion of clocks sitting in a rotating frame of reference.
An object on a rotating disc has momentum mv in the direction tangent to the circular path traced by its motion at any instant.The force which keeps the object from moving off of the disc is centripetal,it seems. Imagine a ball on a string being spun over your head. Your hand exerts a torque on the string, and the string exerts a centripetal force on the ball to maintain its rotational path. So, it may be said that the ball feels a centrifugal force, which is countered by the pull of the string, i.e. a force pushing it out along the radius of the rotation. This is centrifugal force to someone at rest with respect to the rotating frame (who can see the rotation); but, to somebody in the rotating frame, it can be construed as a gravitational field (pulling the string taut). The closer you move to the center of rotation, the less pronounced such a force should be. At the center (length of string is zero), no centripetal or centrifugal force is present. The potential difference between an object at radius r and an object at the center is written as:
phi = -(omega**2)(gamma**2)/2
This is correct, as the potential at the center (like at the top of a hill) is greater than the potential closer to the edge (like at the bottom of a hill).
Einstein's thesis is that an atom absorbs or emits light at a frequency which is dependent on the potential of the gravitational field in which it is located. 　
This point is based on the notion that an atom in a gravitational field is analogous to a clock sitting on a rotating disc. The rate of the clock is affected by the rate of rotation. The disc is in a rotating frame of reference K' with x', y', z' positions of 0. The linear velocity of K' with respect to a rest frame K is omega*gamma, where gamma is the radius of K' from the center (is the center the origin in K?). The amount of time elapsed between two ticks of the clock in K' as perceived from K can be deduced from the Lorentz transformation. If in K' the first tick is at t=0 and the second tick is at t=1, we use the formula:
t' = (t-(v/c**2)x)/(radical(1-(v**2/c**2)))
Then substitute for x with x'(radical(1-(v**2/c**2))+vt
to obtain:
t = t'/(radical(1-v**2/c**2))
So first tick is 0, second is 1/radical(1-v**2/c**2). Thus, as the second tick is slightly greater than 1, the time has slowed down. If v0 is the rate of the clock in K', the rate of the clock as seen by K is v0(1-v**2/c**2). In other words, the rate of the clock is decreased.
This change in the perception of time is analogous to the change in the perception of length of a rod in a frame K' which is moving in the direction of the rod's length (say along the x-axis left to right). At t=0, the rod's left end is at x'=0 and x=0. The right end is at x'=1 (assuming length is 1), but the x coordinate is:
radical(l-v**2/c**2)
So the distance between two points diminishes as a rod moves in the direction of its length.
Both of notions -- the expansion of time and the contraction of distance are due to the Lorentz transform, but why does the Lorentz transform need to hold. It seems that these transforms are necessary to provide translations of space and time coordinates such that the speed of light (c) remains constant in all frames of reference. It seems necessary for c to be constant in order for tenets of electromagnetic theory (which apparently have been shown in experiments to be irrefutable) to hold. Basically, the transforms are derived by considering coordinates x,y,z,t in K and attempting to find x',y',z', and t' in K' such that the speed of light is the same in both frames of reference. i.e. x' = ct' implies c = x'/t'. c=x/t must produce the same result.
Back to the atom/clock case, we can express the clock rate in K in terms of the potential difference phi written above.