Acceleration can be measured completely locally, velocity can't.
Imagine a pool table on a spaceship. If the spaceship starts to thrust, the pool balls will start to slide backwards. You can measure how fast they accelerated backwards and know how fast the ship is accelerating forwards without needing any point of reference outside the ship. There is no way to determine your velocity without having another point of reference outside the ship, and even if you do that, you still now only know the velocity between the spaceship and the reference.
I understand that. However, I do not really understand why is that so in the laws of nature.
Losely speakimg, we have F=ma. Since a second derivative of position is involved, in the integral forms with velocity and position, we have constants of integration unresolved, which leaves no absolute frame of reference.
So the spacetime somehow has it that absolute measurements are for acceleration, which implies there is an absolute recerence frame for acceleration. I wonder if this implies a higher order relativity is present or waiting to be found.
Rotational motion feels still more strange. Here, even though angular momentum is conserved, rotational velocity still seems absolute. If it weren't, then distance objects in some rotational reference frame would be moving faster than the speed of light, unless there's some relativistic modification to v = omega * r.
If you have a given velocity but no given starting position, then position is the missing constant. If you measure some acceleration and time, you can integrate that into a delta-velocity, but not an absolute velocity.
You can measure your speed against the CMB as an "absolute velocity" (in your local observable universe), but for two locations that are a significant fraction of the width of the observable universe apart, "zero movement" relative to the CMB in each of those locations, will not be zero movement relative to each other, due to the expansion of space in between.
May be a naive question, but why is this so? Is there a different type of 'ether' when we consider acceleration?
Edit: Actually I have the same question for rotational motion too.