RE: A Former Atheist
May 5, 2015 at 2:53 am
(This post was last modified: May 5, 2015 at 3:03 am by Hatshepsut.)
(May 4, 2015 at 5:29 pm)Alex K Wrote: ...use riemannian geometry even if it's just SR. Otherwise I wouldn't know how one would correctly take the new coordinates into account.
I dare not clog the forum. Callaghan considers a special case. The non-rotating frame is presumed inertial. The two observers coincide in space and have no linear motion relative to one another. The rotation is uniform about the x-axis. The only world line tracked belongs to a point that remains stationary in the rotating frame. In this case, Callaghan just applied the classical rotation matrix to change the two space coordinates and a separate equation, T(t) = t * sqrt(1 - w^2*r^2/c^2) to find the proper time T on the world line, which is a helix in the non-rotating frame. It was simple because the point's radial distance r, common to both observers, and the rotating frame's angular rate w are constant. I can see this won't work if the point begins moving about. But I admit I'm in pretty heavy seas with this kind of stuff.
![Tongue Tongue](https://atheistforums.org/images/smilies/tongue.gif)
Nonetheless, though the point is stationary in the rotating frame, it's clock is slower relative to both observers the greater r is. Callagan also noted that the rotating frame has a boundary: it only covers events inside the cylinder of radius c/w centered on the x-axis. I agree it's a non-interesting situation: all this to describe a stationary dot as seen by two people, one of whom is dizzy!