= Solution
\b[No: the theory predicts zero gravitational deflection of light.] The reason is <conformal preservation of null geodesic paths>. Along a <null geodesic> with tangent $k^i$, the <geodesic equation for a conformally flat metric> reduces to
$$
\frac{dk^i}{d\lambda}+2\frac{d\log\phi}{d\lambda}k^i=0,
$$
because $\eta_{ij}k^ik^j=0$. The acceleration is parallel to the tangent and changes only its parametrization. Equivalently, with $\ell^i=\phi^2k^i$, $d\ell^i/d\lambda=0$, so the unparametrized ray is a straight <null geodesic> of <Minkowski spacetime>. A positive <conformal factor> also preserves local angles, so this straight-path result cannot be hidden by changing the local angle measurement. It contradicts the nonzero solar deflection observed in <gravitational lensing>, while remaining compatible with the <gravitational redshift> in part (b).
Back to article page