Three-Dimensional Geometry as Carrier of Information about Time

Baierlein, Ralph; Sharp, David H.; Wheeler, John Archibald

doi:10.1103/physrev.126.1864

Cited by 224 publications

(318 citation statements)

References 6 publications

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“…This theory is (full) conformal gravity, as can be confirmed by Legendre transformation and BSW elimination [14] to recover the Lagrangian of Sec. 3.…”

Section: Hamiltonian Formulation and Alternative Theoriesmentioning

confidence: 76%

“…The question arises of how one can obtain a 3-metric and associated canonical momenta that satisfy the constraints. A first method, which corresponds to the logic of the best-matching procedure and uses Lagrangian variables, was proposed by BSW in the same paper [14] in which they presented the BSW action (5). Freely specify g ij ,ġ ij and try to solve for ξ i .…”

Section: Summary Of York's Workmentioning

confidence: 99%

“…In RWR [11], the local square root is in the Baierlein-Sharp-Wheeler (BSW) form [14] for the action for GR,…”

Section: Inroductionmentioning

confidence: 99%

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Scale-invariant gravity: geometrodynamics

Anderson

Barbour²,

Foster

et al. 2003

Class. Quantum Grav.

194

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We present a scale-invariant theory, conformal gravity, which closely resembles the geometrodynamical formulation of general relativity (GR). While previous attempts to create scaleinvariant theories of gravity have been based on Weyl's idea of a compensating field, our direct approach dispenses with this and is built by extension of the method of best matching w.r.t scaling developed in the parallel particle dynamics paper by one of the authors. In spatially-compact GR, there is an infinity of degrees of freedom that describe the shape of 3-space which interact with a single volume degree of freedom. In conformal gravity, the shape degrees of freedom remain, but the volume is no longer a dynamical variable. Further theories and formulations related to GR and conformal gravity are presented.Conformal gravity is successfully coupled to scalars and the gauge fields of nature. It should describe the solar system observations as well as GR does, but its cosmology and quantization will be completely different.

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“…This theory is (full) conformal gravity, as can be confirmed by Legendre transformation and BSW elimination [14] to recover the Lagrangian of Sec. 3.…”

Section: Hamiltonian Formulation and Alternative Theoriesmentioning

confidence: 76%

Section: Summary Of York's Workmentioning

confidence: 99%

See 1 more Smart Citation

Scale-invariant gravity: geometrodynamics

Anderson

Barbour²,

Foster

et al. 2003

Class. Quantum Grav.

194

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“…3 outlines the 3-space approach, which consists largely of a systematic examination of Baierlein-Sharp-Wheeler (BSW) [7] geodesic-type actions. We identify the two key principles of such actions: best matching (a universal method to implement 3-dimensional diffeomorphism invariance) and a local square root (taken at each space point before integration over 3-space).…”

Section: Introductionmentioning

confidence: 99%

Interacting vector fields in relativity without relativity

Anderson¹,

Barbour²

2002

Class. Quantum Grav.

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Barbour, Foster andÓ Murchadha have recently developed a new framework, called here the 3-space approach, for the formulation of classical bosonic dynamics. Neither time nor a locally Minkowskian structure of spacetime are presupposed. Both arise as emergent features of the world from geodesic-type dynamics on a space of 3-dimensional metric-matter configurations. In fact gravity, the universal light cone and Abelian gauge theory minimally coupled to gravity all arise naturally through a single common mechanism. It yields relativity -and more -without presupposing relativity. This paper completes the recovery of the presently known bosonic sector within the 3-space approach. We show, for a rather general ansatz, that 3-vector fields can interact among themselves only as Yang-Mills fields minimally coupled to gravity.

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“…18 However, the arising metric still defines proper times for all world lines (Wheeler's many-fingered time), and the evolving spatial metric can itself be regarded as a many-fingered physical clock. 19 Although there are many different time-like foliations of the same spacetime, each one defines a parametrizable succession of states, and this dynamical construction allows in general the formulation of a unique initial value problem -hence an initial condition of low entropy. There are also mathematically consistent non-relativistic Machian ("relational") theories.…”

Section: A Brief History Of Timelessnessmentioning

confidence: 99%