The Definition of Mach’s Principle

Barbour, Julian

doi:10.1007/s10701-010-9490-7

Cited by 32 publications

(44 citation statements)

References 27 publications

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“…Complementarily, Mach's principle has been reformulated in order to include the conformal symmetry in recent years [6]. Therefore, since in Brans-Dicke theory it is always possible to have G constant in a frame, the Machian character of this theory seems to be more transparently manifest by the conformal symmetry rather than by the variable-G.…”

Section: A On the Physical Equivalence Of Conformal Framesmentioning

confidence: 99%

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A generalized Weyl structure with arbitrary non-metricity

et al. 2019

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A Weyl structure is usually defined by an equivalence class of pairs (g, ω) related by Weyl transformations, which preserve the relation ∇g = ω ⊗ g, where g and ω denote the metric tensor and a 1-form field. An equivalent way of defining such a structure is as an equivalence class of conformally related metrics with a unique affine connection Γω, which is invariant under Weyl transformations. In a standard Weyl structure, this unique connection is assumed to be torsion-free and have vectorial non-metricity. This second view allows us to present two different generalizations of standard Weyl structures. The first one relies on conformal symmetry while allowing for a general non-metricity tensor, and the other comes from extending the symmetry to arbitrary (disformal) transformations of the metric.1 The usual definition of the non-metricity tensor is Q = ∇g.

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Section: A On the Physical Equivalence Of Conformal Framesmentioning

confidence: 99%

“…The reason for the conformal transformation of the metric has a strong motivation in Mach's principle. In fact, other authors refer to such physical invariance as a guidance towards deeper formulations of gravity, even in a Riemannian setting (see for instance [2][3][4][5][6]).…”

Section: Introductionmentioning

confidence: 99%

A generalized Weyl structure with arbitrary non-metricity

et al. 2019

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“…It is possible to overstate the apparent conflict between the absolute and relational viewpoints; both are likely to appear as complementary aspects of any eventual unified theory when gravitational and other degrees of freedom are taken into account as part of the "matter and energy content" of the Universe [94,95]. Such a theory may need to be formulated on the assumption of a finite (spatially closed) Universe if it is to account for inertia in a self-consistent way [96]. Despite a widespread view to the contrary, such a possibility is fully compatible with observational cosmology and likely to remain so for the forseeable future [97].…”

Section: Cosmologymentioning

confidence: 99%

Spacetime, spin and Gravity Probe B

Overduin

2015

Class. Quantum Grav.

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Abstract. It is more important than ever to push experimental tests of gravitational theory to the limits of existing technology in both range and sensitivity. This brief review focuses on spin-based tests of General Relativity and their implications for alternative, mostly non-metric theories of gravity motivated by the challenge of unification with the Standard Model of particle physics. The successful detection of geodetic precession and frame-dragging by Gravity Probe B places new constraints on a number of these theories, and increases our confidence in the theoretical mechanisms underpinning current ideas in astrophysics and cosmology.

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“…For simplicity, we work with R = √ ̺ in following. According to relations (28)and (42), the third term of relation (28) after expansion is proportional to ( R) 2 R 2 , which is related to the powers m = −2, n = 0 and p = 2 in the condition (37). This term ( R) 2 R 2 can be written in another form which we investigate it in the following.…”

Section: ∇M(x)mentioning

confidence: 99%

Some Clarifications on the Relation Between Bohmian Quantum Potential and Mach’s Principle

Rahmani

Golshani

2017

Int J Theor Phys

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Mach's principle asserts that the inertial mass of a body is related to the distribution of other distant bodies. This means that in the absence of other bodies, a single body has no mass. In this case, talking about motion is not possible, because the detection of motion is possible only relative to other bodies. But in physics we are faced with situations that are not fully Machian. As in the case of general theory of relativity where geodesics exist in the absence of any matter, the motion has meaning. Another example which is the main topic of our discussion, refers to Bohmian quantum mechanics, where the inertial mass of a single particle does not vanish, but is modified. We can call such situations in which motion or mass of a single particle has meaning, pseudo-Machian situations. In this paper, we use the Machian or pseudo-Machian considerations to clarify under what circumstances and how a Machian effect leads us to Bohmian quantum mechanics. Then, we shall get the Bohmian quantum potential and its higher order terms for the Klein-Gordon particle through Machian considerations, without using any quantum mechanical postulate or operator formalism.Keywords Bohmian quantum mechanics · Mach's principle · quantum potential PACS 03.65.Ca · 03.65.Ta · 04.20.Cv · 45.20.Jj

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The Definition of Mach’s Principle

Cited by 32 publications

References 27 publications

A generalized Weyl structure with arbitrary non-metricity

A generalized Weyl structure with arbitrary non-metricity

Spacetime, spin and Gravity Probe B

Some Clarifications on the Relation Between Bohmian Quantum Potential and Mach’s Principle

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