Brans-Dicke theory reduces to general relativity as ; a large but finite value is…

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Schwarzschild spacetime and the tests of general relativity · Schwarzschild spacetime and the tests of general relativity

The Geometry of Gravity, Ch Solar-system tests, the PPN framework and alternative theories

Problem

Brans-Dicke theory reduces to general relativity as ωBD→∞\omega_{\rm BD}\to\infty; a large but finite value is still a distinct scalar-tensor theory. ((a)) Brans-Dicke theory does not build its field equations from the metric alone. Name the assumption made when the Einstein field equations were set up that this drops, and say in one sentence what extra physical ingredient it adds. ((b)) A proposed astrometric mission would measure the light-deflection coefficient γPPN\gamma_{\rm PPN} at the solar limb (where GM⊙/R⊙c2=2.1×10−6GM_\odot/R_\odot c^2 = 2.1\times10^{-6}) to a precision δγPPN=5×10−7\delta\gamma_{\rm PPN} = 5\times10^{-7}. Brans-Dicke theory with ωBD=1.0×105\omega_{\rm BD}=1.0\times10^{5}, a value allowed by the Cassini bound ωBD>4×104\omega_{\rm BD}>4\times10^4, predicts γPPN=(1+ωBD)/(2+ωBD)\gamma_{\rm PPN} = (1+\omega_{\rm BD})/(2+\omega_{\rm BD}). Compute the predicted deviation 1−γPPN1-\gamma_{\rm PPN} and decide whether the proposed mission's precision is, in principle, sufficient to distinguish this theory from general relativity.

Browse the problem library