On Mach's principle: Inertia as gravitation

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dc.creatorMartin, J.
dc.creatorRanada, Antonio F.
dc.creatorTiemblo, A.
dc.date2007-03-28
dc.date.accessioned2026-07-07T07:54:13Z
dc.date.available2026-07-07T07:54:13Z
dc.descriptionIn order to test the validity of Mach's principle, we calculate the action of the entire universe on a test mass in its rest frame, which is an acceleration ${\bf g}^*$. We show the dependence of the inertia principle on the lapse and the shift. Using the formalism of linearized gravitation, we obtain the non-relativistic limit of ${\bf g}^*$ in terms of two integrals. We follow then two approaches. In the first one, these integrals are calculated in the actual time section $t=t_0$ up to the distance $R_U=ct_0$. In the more exact and satisfactory second approach, they are calculated over the past light cone using the formalism of the retarded potentials. The aim is to find whether the acceleration $\dot{\bf v}$ in the LHS of Newton's second law can be interpreted as a reactive acceleration, in other words, as minus the acceleration of gravity ${\bf g}^*$ in the rest frame of the accelerated particle ({\it i. e.} to know whether or not ${\bf g}^*=-\dot{\bf v}$). The results strongly support Mach's idea since the reactive acceleration for $Ω_Λ=0.7$ turns out to be about ${\bf g}^*=-1.1 \dot{\bf v}$, in the first approach, and about ${\bf g}^*= -0.7 \dot{\bf v}$, in the second. These results depend little on $Ω_Λ$ if $Ω_Λ<0.9$. Even considering the approximations and idealizations made during the calculations, we deem these results as interesting and encouraging.
dc.description17 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/gr-qc/0703141
dc.identifierhttp://arxiv.org/abs/gr-qc/0703141
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126519
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleOn Mach's principle: Inertia as gravitation
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