...There would be no time difference between the plane and a guy at the center of the Earth because there is no relative velocity between them....
Then realize you are claiming that everyone in that PSE article:
https://physics.stackexchange.com/q...of-light-in-uniform-circular-motion-of-source
, here's another one:
https://physics.stackexchange.com/q...-to-test-general-relativity?noredirect=1&lq=1
(which goes into an explicit derivation from SR first principles), ALL of them are wrong in your opinion!
What's more, that every experiment claiming unambiguous confirmation of Transverse Doppler shift age slowing for objects in steady circular motion is somehow wrong! Basically all the experimentalists there are frauds or at best really stupid!
No. Sorry to say it's your grasp of basic kinematics, we're not even talking SR here, that is woefully inadequate. In #313 I wrote:
"There is always relative velocity of
v =
ω × r between the orbiting twin B and stay at home twin A located anywhere on the orbit axis z. Whats more it's obvious that relative motion is always exactly normal to the radius line
r connecting B to A."
The expression for relative velocity
v there is correct, however I should have stipulated the
r in that vector expression is the radius line applying in the plane of rotation, and only coincides with the radius line joining A to B if A is also in the plane of rotation. At some distance h away the plane but still on the axis of rotation
z, the radius line
r' A to B will have length sqrt(r^2 + h^2), but that has no effect on relative velocity
v.
At this point I have about given up on you. One last reference to try and shake your above quoted ridiculous claim out of you:
https://en.wikipedia.org/wiki/Circular_motion
If you cannot grasp or refuse to accept the essentials laid out there, what's left to discuss?