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.

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

[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?

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, 201412 yr by xyzt