Lienar vs rotary motion

[Physicist248]

TL;DR

If linear motion is relative, how come that rotary motion is absolute? And if it is not absolute what is is relative to?

Reference: https://www.physicsforums.com/forums/special-and-general-relativity.70/post-thread

If linear motion is relative, how come that rotary motion is absolute? And if it is not absolute what is is relative to?

 

[Dale]

If linear motion is relative, how come that rotary motion is absolute?

Geometrically it is for the same reason that an angle requires two straight lines but a curved line can make definite angles with itself.

In spacetime speed is represented by an angle between two worldlines. A straight line (representing inertial motion) doesn’t have an angle with respect to itself, but a curved line (representing accelerated motion) does.

 

[Halc]

In spacetime speed is represented by an angle between two worldlines. A straight line (representing inertial motion) doesn’t have an angle with respect to itself, but a curved line (representing accelerated motion) does.

Good example of why proper acceleration is absolute.

If linear motion is relative, how come that rotary motion is absolute?

As for rotation, I suppose it is because the physics of a rotating frame is different than that of an inertial frame (relative to which linear motion is defined). So for example, in a rotating frame, objects at rest tend not to stay at rest. The one frame in which they do (locally) stay at rest is the one frame relative to which the rotation rate is defined. That makes it absolute.

This cannot be done for linear motion. There is no (local) test one can make that determines one's absolute linear motion.