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
This is the [twin paradox](https://en.wikipedia.org/wiki/Twin_paradox).
Nobody sees their own clock running slower, but they see all moving clocks running slower, at a rate dependent on the relative speed. The trick is, there are *three* inertial frames of reference in this problem, not two: the one in which Earth is at rest, the one in which you’re at rest on the first stage, and the one in which you’re at rest on the way back. You can work the problem in each of these and get the same answer: that your clock is a little behind the stay-at-home clock.
[edit] It didn’t make it into the article, but I think this diagram is helpful:
https://en.wikipedia.org/wiki/Talk:Twin_paradox/Archive_11#/media/File:Twin_5.png
The three frames of reference are the rest frames of the stay-at-home twin, the outbound twin, and the returning twin. The third is translated so that the traveling twin has the same coordinates after turnover as before. The arrows are the twins’ worldlines, the thin lines are their lines of simultaneity at turnover. The dashed diagonal lines show the light cone from the start.
When the traveller says his clock should be ahead of Earth’s, he’s ignoring the time that passed on Earth between points A and C.
Both of you will agree on the time spent in flight. For the guy on earth he will see that you go super fast and your time ticks slow but for you on the spaceship it will feel that the path you are traveling ( earth – mars and back ), has shrunk and earth clock is ticking slow. See this video to for more clarification [https://www.youtube.com/watch?v=6MfJ59lkABY](https://www.youtube.com/watch?v=6MfJ59lkABY). You can also read about twin paradox as already stated in one of the comment.
The object under acceleration would be the one undergoing dilation in the form of time slowing. While you can’t determine who is in motion in the situation of two objects at aconstant velocity, you’d be able to measure your acceleration away from Earth, your deceleration, your acceleration back towards Earth, and your deceleration again.
Comparing to your observations of Earth’s “motion,” and knowledge of dilation effects, you’d be able to calculate that Earth didn’t move (any more than it normally does) and this would agree with measurements in their reference frame (a key concept underpinning relativity).
The premise of the twin paradox is that both frames are *inertial*, which means moving at constant velocity.
The key to dissolving the apparent paradox is acceleration. The ship is the one undergoing acceleration, not the Earth. Acceleration acts like gravity (the equivalence principle), and so the accelerating body undergoes the time dilation.
Why? Because acceleration takes you out of your inertial reference frame, which was initially the Earth’s rest frame. Even though you can never see your own clock ticking slower, the fact that you were accelerated out of Earth’s frame inexorably ties the time dilation to your clock.
Once you decelerate back to the Earth’s frame your clock *must* be behind the Earth’s clock, because Earth remained inertial while you were accelerating.
This problem is often confusing because relativity problems, unless advanced, will say that you accelerate instantaneously. Without acceleration the paradox becomes apparent.
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.
The answers given so far are good but not really ELI5.
So I’ll give it a shot with a boomerang analogy.
When you throw a boomerang, it is accelerating away from you. Yet if you placed a camera on the boomerang, that camera would suggest you are accelerating away from it.
That is the twin paradox.
However, that is really just an optical illusion. In reality, only one object is actually accelerating – the boomerang – while you are stationary.
Time dilation occurs to the person/object being accelerated, not the one which is stationary.
So if we threw the boomerang at 99% the speed of light, what you see and what the camera sees would still be the same as throwing it at any speed. But in terms of actual time dilation, it would occur to the boomerang, not the observer.
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