Rotating frames desynchronization

[FactChecker]

term 2 represents "the relativity of simultaneity" and is responsible for the issue under discussion

Given the numerical approach above, you basically apply the result from the Einstein train thought experiment around a closed loop of "trains", summing together the second term around the loop.

Ha! I like that.

 

[JVNY]

The simplest simultaneity convention that makes use of light signals along the rim to and fro observers is Einstein simultaneity and as you know this will not give rise to a valid global time coordinate for the family of observers on the rim. On the other hand if you use the Einstein time of the inertial frame fixed to the symmetry axis as the global time coordinate for the family of observers on the rim then you will get a consistent global simultaneity convention and it will just be given by the simultaneity surfaces of the observer at the center of the disk. The observers on the disk will agree on simultaneity of events anywhere and everywhere as per this convention-it's trivially transitive because it's just the synchronous time of an inertial frame. Keep in mind this simultaneity convention only works because of axial symmetry.

Per our follow up discussion on another thread ("Synchronizing rotating clocks"), there is another convention that does work by sending signals only around the rim, see post 70 linked here: https://www.physicsforums.com/showthread.php?t=732892&page=4. Interestingly, even though the signals only go around the rim, they likely also synchronize the clocks on the rim to an axis centered inertial coordinate system -- despite there being no signals sent from the axis or from any other point at rest with respect to the axis.