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I don't think space has any fixed points, regardless of the methods one uses to try and discover one. Everything is relative motion and relative acceleration for two or more objects.
That's what I never really understood, if there's a maximum / speed of light, could you not fire a beam in an arbitrary x/y/z axis, measure it somehow, and then use that info to determine what speed and direction you are going?
Speed of light is a constant. For everyone. Because it's linked to time, which is part of 3D space.
Let's say you are standing still. Shoot a laser straight out in front of you. Measure the speed, you get c, the speed of light.
Now, start running forward at 10 mph. Shoot the laser again. Measure the speed. You still get c. Not c + 10, but exactly c.
Run backwards shoot laser out in front of you. Still exactly c.
Because your personal time/clock has changed by moving so that you end up measuring the speed of light the same.
Anyone looking at you, regardless of their relative motion to you will also measure your laser at c.
It's just how the universe is.
Also, speed of light isn't really the best term. More like maximum speed of the universe. Light just happens to travel at that speed because it has no mass. Everything with no mass travels at that speed.
I just want to add that apart from time dilation, velocity also causes length contraction wherein an object will be measured as shorter when it's moving relative to the observer versus from its own rest frame. I've always found it (and time dilation) to be very unintuitive to reason about with my monkey brain - relativity in general is just super weird.
It hurts my head and I kinda like it