I Mechanical system with de Broglie-like features

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I found a proof for the twisting formula. Using the inverse Lorentz transformation ##t=\gamma_z(t'+v_z x'/c^2)## set ##t'=0## in ##S'## where the cylinder translates. The time ##t## in ##S## we are interested in is one revolution or ##2\pi/\omega##. So ##x'=2\pi c^2/\gamma_z \omega v_z##. My interpretation is this is the distance in ##S'## that time is so un-synchronized that it is one revolution out of phase.

To the observer in ##S'## all of the energy ##E## seen in ##S## is inertial. Maybe the radius is out to infinity and there is only matter translating, or maybe it's spinning too; it doesn't matter . That is how I got:

##\lambda=2\pi c^2 L/\gamma_z E v_z = 2\pi L/p_z##​
 
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