# I Mechanical system with de Broglie-like features

#### AVentura

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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