The Mach Principle (sometimes “Mach's Principle”) is the idea, attributed to physicist and philosopher Ernst Mach, that the inertia of any object is determined by its relationship to the rest of the matter in the universe, rather than being an intrinsic property of the object measured against absolute space. In its broadest form, the principle holds that local inertial frames-the frames in which Newton's laws of motion hold without correction-are themselves determined by the large-scale distribution of mass and energy in the cosmos. The phrase “Mach's Principle” was coined by Albert Einstein, who drew on Mach's critique of Newtonian absolute space while developing general relativity. There is no single canonical statement of the principle; physicists and philosophers have formulated it in a number of non-equivalent ways, and whether general relativity satisfies any given formulation remains disputed. See mach-principle-formulation-viewpoint and mach-principle-debate for discussion of these competing statements.
Mach's original critique, developed in the late nineteenth century, targeted Isaac Newton's bucket argument, which Newton had used to argue for the existence of absolute space. Mach argued that the water's behavior in the rotating bucket could only be understood relative to the fixed stars and the rest of the matter in the universe, not relative to empty space itself. Einstein later cited this critique as an inspiration for general relativity, hoping that the theory would fully implement Mach's idea-that inertial frames would be entirely determined by the mass-energy distribution, with no residual “absolute” structure.
Subsequent analysis has led most physicists to conclude that general relativity is only partially Machian. Solutions exist, such as flat (Minkowski) spacetime with no matter at all, that retain a well-defined inertial structure despite the complete absence of mass-energy, which most physicists take as evidence against a strong reading of the principle. Other features of general relativity, including frame-dragging effects predicted around rotating masses, are often cited as partial confirmations of Machian ideas, and the connection between frame-dragging and Mach's Principle has itself been a subject of analysis. Frame-dragging was measured directly by the Gravity Probe B experiment, with results reported in 2011. The interpretation of such results as genuinely “Machian,” however, is itself contested, since frame-dragging can also be derived without reference to Mach's broader cosmological claims. See mach-principle-history for the historical development of the idea from Newton through Einstein and beyond.