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?