In his 1905 paper Einstein discovered that a clock moving with constant
velocity in a closed curve runs slow by a factor of 1/gamma or, by Taylor
approximation, of (1-v^2/2c^2), relative to a clock at rest. For the next
development of relativity that was an unreasonable discovery since 1/gamma
is obviously independent of any acceleration (gravitational field). Even
orthodox relativists (e.g. L. Marder in "Time and the space traveller")
protest against this independence but take comfort in the even sillier
argument that small accelerations can only have a small influence on the
clock's running.
I call it "discovery" since in fact it has nothing to do with special
relativity: the clock at rest undergoes time CONTRACTION with respect to the
moving clock and there is no such thing as "time contraction" in special
relativity. So the discovery would be a complete failure if it were not for
an extremely fortunate coincidence. Luckily (for Einstein), the quantity
v^2/2 is formally equivalent to a gravitational potential (phi) and
replacing v^2/2 with phi converts the approximation (but not the original
1/gamma !) into something that is formally identical to the redshift factor.
For the Juggler that was more than enough. Appendix 3 in his "Relativity"
should be carefully studied by anyone interested in scientific juggling.
Ironically, in the absence of juggling, the redshift factor DISPROVES the
postulate of the constancy of the speed of light (I will show this if there
is interest).
On the other hand, "time dilation/contraction independent of the
gravitational field but dependent on the gravitational potential" has become
one of the fundamental concepts in the relativity cult.