I see, hmm then if pi isn’t a conserved quantity, how could it possibly show up in Einsteins field equations?
Well length is "frame-dependent" in SR, and yet the Lorentz equations still contain variables for x, y and z. Even if the circumference of a rotating disk were to be equal to pi*diameter*gamma in the disk perimeter's 'frame', then the equation still contains pi.
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Maybe the circumference expands instead of contracts. Please Register or Log in to view the hidden image!
spin; If heat is applied to a nut bound to a bolt via rust, the nut expands radially allowing it to be removed. If energy is applied to a disk causing it to rotate at high angular velocities, it would expand radially. I see similarities.
Ehrenfest paradox, Wikipedia Grøn states that the resolution of the paradox stems from the impossibility of synchronizing clocks in a rotating reference frame.[15]If observers on the rotating circumference try to synchronise their clocks around the circumference to establish disc time, there is a time difference between the two end points where they meet. The modern resolution can be briefly summarized as follows: Small distances measured by disk-riding observers are described by theLangevin-Landau-Lifschitz metric, which is indeed well approximated (for small angular velocity) by the geometry of the hyperbolic plane, just as Kaluza had claimed. For physically reasonable materials, during the spin-up phase a real disk expands radially due to centrifugal forces; relativistic corrections partially counteract (but do not cancel) this Newtonian effect. After a steady-state rotation is achieved and the disk has been allowed to relax, the geometry "in the small" is approximately given by the Langevin–Landau–Lifschitz metric.
Thanks!! Is it permissible to rewrite the born line element in terms of linear velocity, as v = ω r ? https://en.wikipedia.org/wiki/Born_coordinates#Radar_distance_in_the_small
