Mach's Principle

In General > s.a. dark matter; gravitational constant; tests of general relativity [Lense-Thirring]; inertia.
* Idea: Inertial reference frames are determined by the overall matter distribution.
* Quantitative version: Formulated by Cocconi & Salpeter; 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.
* In general relativity: Incorporated only in part; Distant stars affect geometry, but flat, empty space still has an affine structure; Dynamically, 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 g_ab = 0.
* In other models: Realized in relational models (> see particle models), like the Barbour-Bertotti ones (> see parametrized theories).
* Strong form: Spacetime does not exist without matter.
* Predictions: Inertia may be direction-dependent, if the universe is anisotropic; The gravitational constant G may vary with t.

References
@ 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.
@ History: Hartman & Nissin-Shabat AJP(03)ap [Mach on Newton and Copernicus]; Newburgh AJP(08)feb [Berkeley's rejection of Newton's notions of absolute space and motion].
@ 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 ht/06 [implementation with bulk + boundary matter]; Martin et al gq/07; Newburgh AJP(07) [history, absolute space and general relativity]; Schmid a0806-in [and frame dragging].
@ And frame dragging: Rindler PLA(94); Bondi & Samuel PLA(97)gq/96; Prasanna CQG(97)gq/96; Bicak et al PRD(04)gq/03; Schmid gq/04 [vorticity perturbations of FRW], PRD(06) [cosmological gavitomagnetism], a0801 [perturbations of FRW].
@ Related topics: Dicke PRL(61) [test]; Dicke AJP(63) [cosmology and field theory]; Rosen AJP(81) [extended]; Padmanabhan Pra(90) [and notion of time]; Vishwakarma CQG(02)gq, Lipunov ap/02 [cosmological constant]; Unzicker gq/05 [and variable c].

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