Brans-Dicke theory gives

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 gives γPPN=1+ωBD2+ωBD\gamma_{\rm PPN} = \dfrac{1+\omega_{\rm BD}}{2+\omega_{\rm BD}}. Using the two-standard-deviation threshold from the Cassini time-delay result, ∣γPPN−1∣<2.5×10−5|\gamma_{\rm PPN}-1| < 2.5\times10^{-5}, this gives ωBD>4×104\omega_{\rm BD} > 4\times10^4. ((a)) Write ωBD\omega_{\rm BD} in terms of the two-standard-deviation threshold δ\delta on ∣γPPN−1∣|\gamma_{\rm PPN}-1|, and check it reproduces ωBD>4×104\omega_{\rm BD} > 4\times10^4 for δ=2.5×10−5\delta = 2.5\times10^{-5}. ((b)) A proposed future mission would improve the precision of the same time-delay measurement by a factor of 20, with the same experimental method and no other change. Find the two-standard-deviation threshold this mission would achieve, and the resulting bound on ωBD\omega_{\rm BD}. ((c)) State, as a ratio, how the bound on ωBD\omega_{\rm BD} scales with an improvement in precision, and check part (b) against this scaling.

Browse the problem library