The discussion centers on the desynchronization of clocks in rotating frames, particularly in relation to Earth's rotation. It is established that clocks at rest on the Earth's surface do not agree on simultaneity due to the Sagnac effect, which prevents global Einstein synchronization. Clocks positioned equidistant from the axis of rotation can be synchronized in terms of rate but not via Einstein synchronization, as this method is not transitive in rotating frames. The conversation highlights the complexities of measuring time and simultaneity in non-inertial frames, emphasizing the need for alternative synchronization methods.
PREREQUISITESPhysicists, students of relativity, and anyone interested in the implications of rotating frames on time measurement and synchronization.
pervect said: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.
WannabeNewton said: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.