Rotating Disk Physics: SR Reconciles Fast-moving Points?

[PeterDonis]

I would now like to propose a method to measure the geometry of the disc that is indisputably independent of simultaneity issues.

I should also comment that this method is basically equivalent to "radar distance", as defined in the Wikipedia page on Born coordinates that I linked to earlier. A key fact about it is that it is not symmetric for the case of observers at different radii from the center of the disk. (The fact that the observer at the center of the disk measures a different radius than the observer riding on the rim is just one special case of this.)

 

[pervect]

As far as the conventionality of simultaneity goes, let me make one quick remark. I suspect that some 90% of the readers of the thread don't know any physics other than the high school version of Newton's laws. And if you are going to use Newton's laws (F=ma and all that), even in the low speed limit, following the Einstein clock synchronization convention is a "required option". I.e. it's optional whether or not you use it, you'll just get the wrong answers if you don't.

The errors may not be terribly large if your synchronization is "close" to Einstein's, but they'll be there. You'll see issues like two equal masses colliding at equal but oppositely directed velocities (as measured by your chosen synchronization scheme) not coming to rest.

If you are using a formulation of physics that allows for generalized coordinates (for instance a Lagrangian formulation), these remarks do not directly apply - though as I recall it turns out to be a bit trickier than it looks to find the correct Lagrangian when you change your definition of simultaneity.

I think a lot of readers mistakenly assume that simultaneity being "conventional" means that Newton's laws work with the different possible choices, and this isn't the case.