# What exactly is the definition of motion and its relation to Mach's conjecture?

The notion of "movement" seems to be well understood in physics. In fact, I don't recall any physics text-book defining motion. Special relativity theory says that there is no absolute frame of reference.

Consider a star (such as the Sun). We say that the Sun is moving at so and so speed with respect to the Milky Way, which is moving at so and so speed with respect to the Andromeda Galaxy, and so on. However, this implies that motion only makes sense if there is a background frame of reference.

In a universe, where there is only one star, what would it mean for the star to rotate around its axis? How could we define this axis? And relative to what would it rotate?

If we can say that the star rotates, then there is some absolute frame of reference. In special relativity, the star would stop rotating if it was isolated from the rest of the universe. This seems to indicate that Mach's conjecture is true, and the existence of astronomical objects far away defines our notion of motion.

Is there any formal definition of motion, especially rotation?

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