The hypothesis attempted to explain how rotating objects, such as gyroscopes and spinning celestial bodies, maintain a frame of reference.
[a][2] 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".
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.
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 Mach's words, the principle is embodied as follows:[5] [The] investigator must feel the need of... knowledge of the immediate connections, say, of the masses of the universe.
In this view, the apparent forces that seem to permit discrimination between relative and "absolute" motions should only be considered as an effect of the particular asymmetry that there is in our reference system between the bodies which we consider in motion, that are small (like buckets), and the bodies that we believe are still (the earth and distant stars), that are overwhelmingly bigger and heavier than the former.
It is then not clear, in the passages from Mach just mentioned, if the philosopher intended to formulate a new kind of physical action between heavy bodies.
Most physicists believe Mach's principle was never developed into a quantitative physical theory that would explain a mechanism by which the stars can have such an effect.
[7]: 530 A relatively weak formulation is the assertion that the motion of matter in one place should affect which frames are inertial in another.
Einstein, before completing his development of the general theory of relativity, found an effect which he interpreted as being evidence of Mach's principle.
If one rotates [a heavy shell of matter] relative to the fixed stars about an axis going through its center, a Coriolis force arises in the interior of the shell; that is, the plane of a Foucault pendulum is dragged around (with a practically unmeasurably small angular velocity).
As for the statement that "inertia originates in a kind of interaction between bodies", this, too, could be interpreted as true in the context of the effect.
Heuristically, the boundary conditions for an asymptotically flat universe define a frame with respect to which inertia has meaning.
At an exit poll of experts, held in Tübingen in 1993, when asked the question "Is general relativity perfectly Machian?
Mach's principle may therefore have a future – but not without the quantum theory.In 1953, in order to express Mach's Principle in quantitative terms, the Cambridge University physicist Dennis W. Sciama proposed the addition of an acceleration dependent term to the Newtonian gravitation equation.
where r is the distance between the particles, G is the gravitational constant, a is the relative acceleration and c represents the speed of light in vacuum.