Endy0816 Posted January 7, 2014 Share Posted January 7, 2014 Does anyone know if a rotating plasma can also undergo time dilation? Been thinking off and on about how it might allow a plasma ball to last longer than one would otherwise expect. Just not sure what the math would look like for a rotating system. Link to comment Share on other sites More sharing options...
xyzt Posted January 7, 2014 Share Posted January 7, 2014 Does anyone know if a rotating plasma can also undergo time dilation? Been thinking off and on about how it might allow a plasma ball to last longer than one would otherwise expect. Just not sure what the math would look like for a rotating system. Particles in a particle accelerator (cyclotron or synchrotron) exhibit time dilation according to the rule: [math]\Delta t'=\frac{\Delta t}{\sqrt{1-(\omega R/c)^2}}[/math] where: [math]\Delta t'[/math] is the elapsed time in the frame attached to the (accelerated) particle [math]\Delta t[/math] is the elapsed time in the frame of the lab, so, clearly [math]\Delta t' > \Delta t[/math] [math]\omega[/math] is the angular speed [math]R[/math] is the radius of the trajectory Link to comment Share on other sites More sharing options...
md65536 Posted January 7, 2014 Share Posted January 7, 2014 [math]\Delta t[/math] is the elapsed time in the frame of the lab, so, clearly [math]\Delta t' > \Delta t[/math]Does this mean that the rotating clock ticks faster than the lab clock? 1 Link to comment Share on other sites More sharing options...
xyzt Posted January 7, 2014 Share Posted January 7, 2014 (edited) Does this mean that the rotating clock ticks faster than the lab clock? Slower, I had the square root inverted by mistake: The derivation is based on the metric for rotating frames: [math](cdt')^2=(1-\frac{\omega^2 R^2}{c^2})(cdt)^2-(dx^2+dy^2+dz^2+2 \omega (xdy-ydx)dt)[/math] for the particular case [math]dx=dy=dt=0[/math] Particles in a particle accelerator (cyclotron or synchrotron) exhibit time dilation according to the rule: [math]\Delta t'=\Delta t \sqrt{1-(\omega R/c)^2}[/math] where: [math]\Delta t'[/math] is the elapsed time in the frame attached to the (accelerated) particle [math]\Delta t[/math] is the elapsed time in the frame of the lab, so, clearly [math]\Delta t' < \Delta t[/math], i.e. the clock in the rotating frame ticks slower than the one in the (inertial) lab, meaning that , in the frame of the lab, the plasma state persists longer than in the frame of the moving particles, exactly as in the muon experiment: [math]\Delta t=\frac{\Delta t'}{ \sqrt{1-(\omega R/c)^2}}[/math] [math]\omega[/math] is the angular speed of the (plasma) particle [math]R[/math] is the radius of the trajectory of the plasma jet Edited January 7, 2014 by xyzt 1 Link to comment Share on other sites More sharing options...
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