# Mach's principle

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In theoretical physics, particularly in discussions of gravitation theories, Mach's principle (or Mach's conjecture[1]) is the name given by Albert Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach. The hypothesis attempted to explain how rotating objects, such as gyroscopes and spinning celestial bodies, maintain a frame of reference.

The proposition is that the existence of absolute rotation (the distinction of local inertial frames vs. rotating reference frames) is determined by the large-scale distribution of matter, as exemplified by this anecdote:[2]

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?

Mach's principle says that this is not a coincidence—that there is a physical law that relates the motion of the distant stars to the local inertial frame. If you see all the stars whirling around you, Mach suggests that there is some physical law which would make it so you would feel a centrifugal force. There are a number of rival formulations of the principle, often stated in vague ways like "mass out there influences inertia here". A very general statement of Mach's principle is "local physical laws are determined by the large-scale structure of the universe".[3]

Mach's concept was a guiding factor in Einstein's development of the general theory of relativity. Einstein realized that the overall distribution of matter would determine the metric tensor which indicates which frame is stationary with respect to rotation. Frame-dragging and conservation of gravitational angular momentum makes this into a true statement in the general theory in certain solutions. But because the principle is so vague, many distinct statements have been made which would qualify as a Mach principle, some of which are false. The Gödel rotating universe is a solution of the field equations that is designed to disobey Mach's principle in the worst possible way. In this example, the distant stars seem to be revolving faster and faster as one moves further away. This example does not completely settle the question of the physical relevance of the principle because it has closed timelike curves.

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