extreme time dilation

[thoughtful1]

i was just wondering earlier today about this thought experiment i thought of earlier today, and i had some questions about it:

 

suppose one put a small particle accelerator on a space ship and then had that space ship headed out in to space traveling at a constant speed of 0.99c, then according to einstein's time dilation formula, every second that passes on the spaceship, approximately 7.088 seconds pass back on earth. then, imagine that we rev up the particle accelerator that was put on the spaceship and fling around some muons that have an average lifetime of about 2.197 nanoseconds. now, since we are traveling aboard the spaceship at 0.99c, the lifetime of some stationary muons will already have been extended to about 15.57 nanoseconds, but if we accelerate them so that their speed is also 0.99c, would their lifetimes still be 15.57 nanoseconds? or would their lifetimes be "super-dilated" so to speak so that they would last for a little over 110 nanoseconds?

[swansont]

They would be dilated by whatever factor you get from their speed relative to you. The lifetime will be longer for the earth-based observer who sees their speed as .99999c (or whatever) than the spaceship observer who sees it as .990c

[thoughtful1]

thanks for the response, very useful

[Janus]

i was just wondering earlier today about this thought experiment i thought of earlier today, and i had some questions about it:

 

suppose one put a small particle accelerator on a space ship and then had that space ship headed out in to space traveling at a constant speed of 0.99c, then according to einstein's time dilation formula, every second that passes on the spaceship, approximately 7.088 seconds pass back on earth. then, imagine that we rev up the particle accelerator that was put on the spaceship and fling around some muons that have an average lifetime of about 2.197 nanoseconds. now, since we are traveling aboard the spaceship at 0.99c, the lifetime of some stationary muons will already have been extended to about 15.57 nanoseconds, but if we accelerate them so that their speed is also 0.99c, would their lifetimes still be 15.57 nanoseconds? or would their lifetimes be "super-dilated" so to speak so that they would last for a little over 110 nanoseconds?

 

It depends on the type of accelerator you are using and how it is oriented.

If you had a linear accelerator which accelerated the muons in the direction the ship was traveling, then according to the ship, the muon lifetime would be 15.57 ns and according to the Earth, their lifetime would be 219 ns (as they would traveling at 0.99995c wrt Earth.)

If you your accelerator was pointing in the opposite direction, the lifetime would still be 15.57 ns according to the ship, but would be 2.197 ns according to the Earth( as they would be at rest wrt Earth.

 

If you had a circular accelerator and the axis around which the particles circled was oriented along the direction of the ships motion, then the lifetime onboard ship would be 15.57 ns and the lifetime according to Earth would be ~110 ns.

 

If the axis was perpendicular to the line of motion, then the lifetime on ship would still be 15.57 ns, but the lifetime according to the Earth would vary depending upon which point the muon was in its circuit around the accelerator.