Mach’s principle and the structure of dynamical theories

Barbour, Julian; Bertotti, B.

doi:10.1098/rspa.1982.0102

Cited by 183 publications

(297 citation statements)

References 9 publications

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“…As we show below, these conditions match the intuition that only relational degrees of freedom of the Universe should have physical significance [4][5][6]. A total angular momentum J tot and a total energy E tot would define, respectively, an external frame in which the Universe is rotating and an absolute unit of time.…”

supporting

confidence: 49%

Arrow of Time Emerges in a Gravitational System

Carlip¹

2014

Physics

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It is widely believed that special initial conditions must be imposed on any time-symmetric law if its solutions are to exhibit behavior of any kind that defines an "arrow of time." We show that this is not so. The simplest nontrivial time-symmetric law that can be used to model a dynamically closed universe is the Newtonian N-body problem with vanishing total energy and angular momentum. Because of special properties of this system (likely to be shared by any law of the Universe), its typical solutions all divide at a uniquely defined point into two halves. In each, a well-defined measure of shape complexity fluctuates but grows irreversibly between rising bounds from that point. Structures that store dynamical information are created as the complexity grows and act as "records." Each solution can be viewed as having a single past and two distinct futures emerging from it. Any internal observer must be in one half of the solution and will only be aware of the records of one branch and deduce a unique past and future direction from inspection of the available records. DOI: 10.1103/PhysRevLett.113.181101 PACS numbers: 04.40.-b, 04.20.-q Many different phenomena in the Universe are time asymmetric and define an arrow of time that points in the same direction everywhere at all times [1]. Attempts to explain how this arrow could arise from time-symmetric laws often invoke a "past hypothesis": the initial condition with which the Universe came into existence must have been very special. This is based on thermodynamic reasoning, which seems to make a spontaneous emergence of an arrow of time very unlikely. Although thermodynamics works very well for subsystems, provided gravity is not a dominant force, self-gravitating systems exhibit "antithermodynamic" behavior that is not fully understood. Since the Universe is the ultimate self-gravitating system and since it cannot be treated as any subsystem, its behavior may well confound thermodynamic expectations.In this Letter, we present a gravitational model in which this is the case. In all of its typical solutions, internal observers will find a manifest arrow of time, the nature of which we are able to precisely characterize. We emphasize that in this Letter we make no claim to explain all the various arrows of time. We are making just one point: an arrow of time does arise in at least one case without any special initial condition, which may therefore be dispensable for all the arrows. In this connection, we mention that in Ref.[2] (Sec. II), Carroll and Chen conjectured that the thermodynamic arrow of time might have a time-symmetric explanation through entropy arrows much like the complexity and information arrows we find.The model.-The Newtonian N-body problem with vanishing total energy E tot ¼ 0, momentum P tot ¼ 0, and angular momentum J tot ¼ 0 is a useful model of the Universe in many respects [3]. As we show below, these conditions match the intuition that only relational degrees of freedom of the Universe should have physical significance [4][5][6]. A tot...

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supporting

confidence: 49%

Arrow of Time Emerges in a Gravitational System

Carlip¹

2014

Physics

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“…We hope to use a 'top-down' approach: to start from firm classical theory and deduce features of the quantum universe. However, we start from space rather than spacetime for relational reasons [13,47,11,9] and to illustrate the potential naivety of presupposing and extending spacetime structure. The great problems of quantizing gravity are hopelessly interrelated, so that adding to a partial resolution to tackle further problems can spoil that partial resolution [48].…”

Section: Discussionmentioning

confidence: 99%

“…Our so-called 3-space approach developed out of an earlier attempt [13] to implement Mach's idea of a relational dynamics directly in a constructive dynamical theory, in contrast to Einstein's indirect approach through generalization of the RRP to the GRP. For the direct approach, superspace is the natural relational arena for geometrodynamics.…”

Section: Inroductionmentioning

confidence: 99%

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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“…To compensate for the possible coordinate change in going between neighbouring 3-geometries, correction terms have been added to each of the bare velocitiesġ ab in T g . One can think of this as Bertotti and Barbour's method for achieving 3-diffeomorphism invariance [16,1]. It is appropriately called best matching because the variation with respect to ξ i can be seen as implementing a best matching of two infinitesimally-differing 3-dimensional configurations on a compact manifold; the aim of this is to bring the two configurations as close as possible to congruence and then define the residual difference between them as a measure on superspace.…”

Section: Relativity Without Relativitymentioning

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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Mach’s principle and the structure of dynamical theories

Cited by 183 publications

References 9 publications

Arrow of Time Emerges in a Gravitational System

Arrow of Time Emerges in a Gravitational System

Scale-invariant gravity: geometrodynamics

Interacting vector fields in relativity without relativity

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