Originally Posted by

**SinceYouAsked**
Cincirob argued ...

1) The LT solns are correct in Gron's analysis, yet cinci has long argued Gron's elliptical shape is wrong because he misapplied the LTs.

2) Gron's rotating disk has a radius of R'=1 per the axle frame observer (A), rolling on a ground moving at v=-0.866c.

3) Cinci introduced an inertial rod, to prove his point ...

4) A records a moving inertial length-contracted rod at height y'= 0.866 (above the disk's axle) to be unit length a L_{A}=1.

5) Per A, when a linear cord of (at y'=+0.866) Gron's rolling disk is momentarily superposed with the moving rod, both then are the length L_{A}=1.

6) The ground observer G moves at -0.866c wrt axle observer A, because the rolling disk's axle translates at 0.866c per the ground observer G.

7) G holds the moving rod at length L_{G} = (L_{A}*1/√(1-v²/c²))*√(1-u²/c²), where u = 2v/(1+v²/c²), so for v=0.866c then L_{G} = (1*2)/7 = 0.28571

OK, so we know that Gron's rolling wheel is only L_{G} = 0.5 long (wrt x at y=y'=0.866) per ground observer G, yet the inertial rod must be L_{G} = 0.28571 per G ... even though they are the same x' length per the axle observer A. Is this a problem, relativistically? No. Yet, cincirob has long argued it an error on Gron's behalf. So while cincirob says the LTs are correct, he also argues that Gron does not apply them correctly under the case of rotation, and thus Gron's theory is all wrong. Hmmm.

Cincirob then points out that the inertial rod must have a proper length of L_{P}*1/√(1-v²/c²) = 1*2 = 2. Given such, he presumes that the length of the disk-cord (of atoms) associated with y=y'=0.866 per A, should have the same proper length (2 units) per the rest length of those atoms per the noon-inertial disk POV itself. Yet, he never concedes that the linear string of disk atoms defined by the axle observer A (in his instant t') must be non-linear in either the non-inertial non-euclidean disk POV and/or the ground POV. Hmmm.

Then, cincirob says Gron never took the various differing motions of the disk atoms into account in his analysis, nor did Gron consider the composed velocity of each individual atom, as though that's a problem of sort. Did Gron ever need to do this in his analysis? Of course not. Did Gron ever care about the proper length of disk cords in the non-inertial disk POV? Of course not, as it was never required. Cincirob says the Gron analysis is wrong, and cannot be validated until all those calculations are done. Hmmm.

Thank You,

SinceYouAsked