41
Physics, Astronomy & Cosmology / Re: Time dilation caused by relative motion.
« on: 07/02/2024 01:37:53 »So Alice's and Bob's acceleration are identicalTheir proper acceleration magnitude in my example is identical at all times in the Earth frame. The direction of the acceleration is not identical at all times, so their velocity (and with it, speed) relative to Earth is not always identical, and dilation in SR is all about speed, not about acceleration.
Quote
Is it a complicated (tedious) calculation of all the various relative speeds involved followed by an integration of all the time dilations along the respective paths?For an erratic itenerary, yes, doing it that way always yields the right answer. For simple linear acceleration over a known time, there are shortcuts. I performed no integration to calculate Bob's age after the 7.5 Earth years.
Quote
Are the actual distances travelled by Alice and Bob the same?Not in that example. At no point is Alice moving faster than Bob relative to Earth, but most of the time Bob is moving faster than Alice. Hence he covers more ground.
Relative to a different frame, and the exact same example, I could have Bob and Alice travel the same distance from start to end. This shows that distance traveled is very frame dependent, and the dilation is not a function of it.