Mach's Principle  

In General > s.a. dark matter; gravitational constant; tests of general relativity [Lense-Thirring]; inertia.
* Qualitative idea: Inertial reference frames are determined by the overall matter distribution (named after Ernst Mach by Albert Einstein); One solution of the rotation problem (why on large scales inertial frames seem not to rotate relative to the average matter distribution in the universe).
* Quantitative version: Formulated by Cocconi & Salpeter, along Einstein's lines; Inertial mass is defined in terms of the total mass distribution; The proposal can be tested by experiments that measure preferred frame effects, which would be produced by deviations from a uniform mass distribution.
* Strong form: Spacetime does not exist without matter.
* And mass / inertia: Inertia may be direction-dependent, if the universe is anisotropic; The rest mass of a particle in the Universe can be taken to be a measure of its long-range collective interactions with all other particles inside the horizon.

And Gravity > s.a. emergent gravity; gravitational thermodynamics.
* Prediction: In addition to inertia possibly being direction-dependent, the gravitational constant G may vary with t.
* In general relativity: Although Mach's principle was one of the main motivations behind Einstein's formulation of general relativity, it is incorporated only in part in the final theory; Distant stars affect geometry, but flat, empty space still has an affine structure; Dynamically, it can be formulated in a precise way in terms of the integral form of Einstein's equation (> see formulations).
* In quantum gravity: We don't know yet, but it may be incorporated better than in general relativity, if the vacuum corresponds to gab = 0.
@ In general relativity: Gürsey AP(63); Wheeler in(63), in(64); Brill & Cohen PR(66); Ozsváth & Schücking AP(69) [rotating solutions of Einstein's equation]; Isenberg PRD(81) [specific spacetimes]; Rosen in(81); Tod GRG(94); Lynden-Bell et al MNRAS(95); Assis & Graneau FP(96); von Borzeszkowski & Treder FP(96) [vs principle of general relativity]; Wesson et al IJMPD(02); Wagh gq/02 [spatial scale invariance]; Khoury & Parikh PRD(09)ht/06 [implementation with bulk + boundary matter]; Martín et al gq/07; Newburgh AJP(07)may [history, absolute space and general relativity]; Hartman & Nissim-Sabat AJP(07)sep-a0807 [limits of applicability]; Mashhoon & Wesson AdP(12), response Barbour AdP(12)-a1108; Mashhoon & Wesson AdP(12)-a1108; Berman 12; McLaughlin a1206-wd [topological interpretation]; Telkamp a1404-GRF [relational approach to reconciling Mach's principle with Einstein's general relativity]; Vishwakarma IJGMP(15)-a1508.
@ And frame dragging: Rindler PLA(94); Bondi & Samuel PLA(97)gq/96; Prasanna CQG(97)gq/96; Bičák et al PRD(04)gq/03; Schmid gq/04 [vorticity perturbations of FLRW models], PRD(06) [cosmological gravitomagnetism], PRD(09)-a0801, a0806-proc [and FLRW perturbations]; Vassallo & Hoefer a1901-in.
@ Related topics: Das a1206 [Machian gravity theory]; Singleton & Wilburn IJMPD(16)-a1607-GRF [Hawking and Unruh radiation as a thermal Mach's principle].

And Other Theories
* Models: Realized in relational models (> see particle models), like the Barbour-Bertotti ones (> see parametrized theories).
@ References: Gryb PRD(09)-a0901 [and Barbour-Bertotti proposal, gauge theory].

References > s.a. mass; Newton's Bucket.
@ General: in Mach 1893; Pirani HPA(56); Cocconi & Salpeter NC(58), PRL(60); Barbour & Pfister ed-95; Lichtenegger & Mashhoon in(07)phy/04 [rev]; Wilczek PT(04)apr, comment Hahne phy/05; Barbour FP(10)-a1007 [two definitions, gauge theory, and causality]; Brans AdP(12); Essén EJP(13) [precise definition, and cosmological energy density]; Shuler PhysEd(15) [mathematical formulation, and Newton's bucket]; Jones GRG(20)-a1710 [the rotation problem].
@ History: Hartman & Nissim-Sabat AJP(03)nov-ap [Mach on Newton and Copernicus]; Newburgh AJP(08)feb [Berkeley's rejection of Newton's notions of absolute space and motion].
@ Related topics: Dicke PRL(61) [test]; Dicke AJP(63)jul [cosmology and field theory]; Rosen AJP(81)mar [extended]; Padmanabhan Pra(90) [and notion of time]; Vishwakarma CQG(02)gq, Lipunov ap/02 [cosmological constant]; Unzicker gq/05 [and variable c]; Lichtenegger & Iorio EPJP(11)-a0910 [and the twin paradox]; Sivaram & Arun a0912; Guendelman & Steiner a1106 [electromagnetic version]; Hartman & Nissim-Sabat a1406 [re Machian geocentrism]; Jannes & Volovik JETPL(15)-a1506 [and the quantum vacuum].

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