Mach's Principle

If you think about Mach's Principle, it actually brings attention to some logical contradictions -- at least from a pure relativistic perspective.  If you accept a universal coordinate system, then all your problems go away.

If you are alone in an empty universe, how is rotation defined?  For that matter, how is acceleration defined?  (Again, if you accept a universal coordinate system, then all your problems go away.)

You are standing in a field looking at the stars. Your arms are resting freely at your side, and you see that the distant stars are not moving. Now start spinning. The stars are whirling around you and your arms are pulled away from your body. Why should your arms be pulled away when the stars are whirling? Why should they be dangling freely when the stars don't move?

Why dowould physicists work so hard to avoid the possibility of a universal coordinate system?