system
Given the following post, respond as if you're commenting on Reddit:
human
If a space ship is going 99% speed of light time is slower for them according to the earth (I think) but if the space ship is out reference point then the Earth is going 99% the speed of light. So wouldn't time be going slower on earth in relation to the ship?

So 1 earth hour is only .5 hours on the ship (I am fully making numbers up here) because the ship is moving 99% the speed of light relative to the earth. But if you choose the ship as a reference point then the earth is the one moving so that would mean (as I understand) that 1 hour on the ship would only be .5 hours on the earth. And now 1 hour of thinking about this is causing a 3 hour headache!
gpt
It is important to take into account the difference between the very nature of the two observers.

If you take the observer in the spaceship, what they see is the earth and all of space moving away from them, as if their ship is standing still.  This means that we must also consider spacial contraction.  This is the contraction of space in the direction of movement.  It means that if, to take your example, a 1 meter ruler is moving at 99% the speed of light, the ruler will actually be .5 meters long when observed by a stationary person.

Now this means, in the reference frame of the dude in the spaceship, the distance of space that they are traveling through is actually shorter because, according to them, all of space is moving by at 99% the speed of light.  

Warning, the following is physics!

There is an interesting application in physics where scientists have observed muons that typically have a half life of 2.2 microseconds.  These particles are created in the upper atmosphere and move toward the earth at very high (relativistic) speeds, something comparable to the speed of light.  Using classical physics, we can easily determine that something like .05% of the muons will make it to the surface of the earth, however we experimentally observe something around 80%.  

It makes sense, if we use relativity, that in the reference frame of an on ground observer, the half life of a muon will actually be longer because of time dilation, this easily explains how 80% of the muons actually make it to the surface.  But it is not so clear if we take the reference frame of the muon, and this frame is perfectly fine to use, so how do the muons survive with a half life of 2.2 microseconds, their half life cannot change because they are not moving relative to themselves.  The answer is spacial contraction.  Because they are moving so fast, they see the space that they travel through to be shorter.  This means that, despite having a short half life, they don't have to travel as far to reach the surface of the earth and be detected.

It is weird to think that two different observers can explain the way something happens in two completely different ways, but physics tends to work like that.