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).

* __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].

@ __Related topics__: Das a1206
[Machian gravity theory]; Singleton & Wilburn 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].

@ __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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send feedback and suggestions to bombelli at olemiss.edu – modified 11 jul
2016