Say I get on a Sci-Fi speed Rocket Ship and leave Earth at .999999% the Speed of Light to me I travel for 21 minutes reach Mars then U-Turn back to Earth for another 21 minutes at 0.999999% the Speed of Light again. Back on Earth if I compared my watch to someone else’s would my watch be slightly ahead or slightly behind?
Like if I’m the one traveling I’d expect their watch to be slightly ahead of mine because slightly less time has passed. But at the same time from my frame of view. Earth and my bussy with the watch just shot away from me for 21 minutes and then returned and came back 21 minutes later so my watch should be ahead of theirs since they were the one traveling.
In: Physics
The object traveling at 99.99% of C (not .99999% of C, which would be less than 1 percent of the speed of light) would have a slower clock because fractionally less time has passed for them.
However, this is not the whole story, Einstein’s general relativity predicts that time will travel more slowly the closer you get to a massive object. So, if you were to only consider ‘kinetic time dilation’ (the dilation due to speed mis-match) then GPS satellites should be 7 microseconds **slower** than a clock on earth because they (the satellites) are moving faster than we are. However, since the satellites are further away from a massive object than we are, the clocks move **faster** than ground based clocks by 47 or so microseconds. Take the difference and the clocks in GPS satellites are 38 microseconds **faster** than an earth based clock per day. GPS needs to be in the 20 to 30 nanoseconds of precision, which is 1000 times smaller than the difference caused by time dilation.
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