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 *g*_{ab} = 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.

@ __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 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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