Mach's principle is the proposition that the inertial properties of an object-its resistance to acceleration-are determined by the distribution of mass and energy throughout the rest of the universe, rather than by motion relative to an independent, absolute space. The phrase was coined by Albert Einstein in reference to ideas advanced by the physicist and philosopher Ernst Mach, though the precise content of “Mach's principle” is itself contested, and no single canonical statement of it commands universal agreement; see machs-principle-formulation-viewpoint. The principle is closely tied to debates over the Principle of Inertia and over whether reference frames can be considered physically equivalent, a question also raised in discussions of Ptolemaic System - Reference Frame Equivalence Viewpoint.

Mach's principle originated as a critique of Isaac Newton's bucket argument, which Newton used to argue for the existence of absolute space. Mach proposed instead that inertial effects, such as the concave water surface in Newton's rotating bucket, arise from the rotation of the water relative to the bulk of distant matter in the universe-the “fixed stars”-rather than relative to absolute space itself.

Einstein was influenced by Mach's critique during the development of general relativity and hoped that the theory would embody Mach's principle fully. However, it is widely recognized among physicists that general relativity does not fully implement Mach's principle in the form Mach or Einstein originally envisioned; solutions exist within general relativity, such as Willem de Sitter's empty-universe model and Kurt Gödel's rotating-universe model, that appear to permit inertial frames even in the absence of significant surrounding matter. The question of whether general relativity should nonetheless be regarded as Machian-for instance on the grounds that frame-dragging effects such as the Lense-Thirring effect demonstrate a genuine influence of distant matter on local inertial frames-is treated in detail at machs-principle-general-relativity-viewpoint.

The historical development of these ideas, including Newton's bucket experiment, Mach's critique, and the principle's influence on Einstein, is treated at greater length at machs-principle-history.

There is broad agreement among physicists that general relativity does not incorporate Mach's principle in a complete or unambiguous form, and that the principle, as originally stated by Mach, is not a precisely defined physical law but rather a heuristic or philosophical guideline that influenced the development of relativity theory. See machs-principle-incompleteness-consensus. There is no comparable consensus on what a fully Machian theory would look like, whether one is necessary, or whether the principle is still scientifically useful-these questions remain matters of ongoing viewpoint and debate.

• Strong Machian viewpoint: holds that a correct theory of physics must fully derive inertia from the distribution of matter in the universe, and that general relativity's failure to do so completely is a genuine deficiency. See machs-principle-strong-machian-viewpoint.
• Weak or partial Machian viewpoint: holds that general relativity is “Machian enough,” citing frame-dragging and related effects as sufficient embodiment of Mach's core insight, even if idealized non-Machian solutions exist mathematically. See machs-principle-weak-machian-viewpoint.
• Skeptical or eliminativist viewpoint: holds that Mach's principle is not a well-defined physical principle at all, but a cluster of loosely related and sometimes mutually inconsistent ideas that has outlived its usefulness as a guide to physical theory. See machs-principle-skeptical-viewpoint.
• Absolute-space revivalist viewpoint: associated with some interpretations of Newtonian mechanics and certain modern theories, holds that inertial effects can be understood relative to a privileged structure (whether termed absolute space, a background spacetime, or an ether-like medium) without requiring reference to distant matter at all. This view has some overlap with broader debates about absolute versus relative motion found in discussions of Geocentrism Physics and Geocentrism - Modern Viewpoint. See machs-principle-absolute-space-viewpoint.
• Alternative-theory viewpoint: holds that fully Machian alternatives to general relativity, such as Brans-Dicke theory or other scalar-tensor theories, better realize Mach's principle and should be considered serious alternatives or supplements to standard general relativity. See machs-principle-alternative-theories-viewpoint.

• The relationship between Mach's principle and Geocentrism has occasioned dispute, as some proponents of geocentrist cosmology have invoked Machian reasoning to argue for the physical permissibility of an Earth-centered reference frame; mainstream physicists have generally rejected this application of the principle. See machs-principle-geocentrism-controversy.

• machs-principle-history
• machs-principle-formulation-viewpoint
• machs-principle-general-relativity-viewpoint
• machs-principle-incompleteness-consensus
• machs-principle-strong-machian-viewpoint
• machs-principle-weak-machian-viewpoint
• machs-principle-skeptical-viewpoint
• machs-principle-absolute-space-viewpoint
• machs-principle-alternative-theories-viewpoint
• machs-principle-geocentrism-controversy
• Principle of Inertia
• Geocentrism
• Geocentrism Physics
• Geocentrism - Modern Viewpoint
• Ptolemaic System - Reference Frame Equivalence Viewpoint

1. Ernst Mach, *The Science of Mechanics: A Critical and Historical Account of Its Development*, trans. Thomas J. McCormack (Chicago: Open Court Publishing, 1893).
2. Albert Einstein, “Prinzipielles zur allgemeinen Relativitätstheorie,” *Annalen der Physik* 55 (1918): 241-244.
3. Julian B. Barbour and Herbert Pfister, eds., *Mach's Principle: From Newton's Bucket to Quantum Gravity* (Boston: Birkhäuser, 1995).
4. Hermann Bondi and Joseph Samuel, “The Lense-Thirring Effect and Mach's Principle,” *Physics Letters A* 228, no. 3 (1997): 121-126.
5. Carl H. Brans and Robert H. Dicke, “Mach's Principle and a Relativistic Theory of Gravitation,” *Physical Review* 124, no. 3 (1961): 925-935.