= Solution
An affinely parameterized <geodesic> $x^\mu(\lambda)$ satisfies
$$
\boxed{
\frac{d^2x^\mu}{d\lambda^2}
+\Gamma^\mu_{\alpha\beta}
\frac{dx^\alpha}{d\lambda}
\frac{dx^\beta}{d\lambda}=0.}
$$
For the <conformally flat metric> $g_{\mu\nu}=\varphi^2\eta_{\mu\nu}$, its <Christoffel symbol>[Christoffel symbols] are
$$
\Gamma^\mu_{\alpha\beta}
=\delta^\mu_\alpha\partial_\beta\log\varphi
+\delta^\mu_\beta\partial_\alpha\log\varphi
-\eta_{\alpha\beta}\partial^\mu\log\varphi.
$$
Let $u^\mu=dx^\mu/d\lambda$. Along a <null geodesic>, $\eta_{\alpha\beta}u^\alpha u^\beta=0$, so the equation reduces to
$$
\frac{du^\mu}{d\lambda}
+2\frac{d\log\varphi}{d\lambda}u^\mu=0.
$$
The acceleration is parallel to the tangent. A change of parameter removes it, leaving a straight null line of the <Minkowski metric>. Thus conformal rescaling changes the affine parameter but not the unparametrized light ray.
Consequently <Nordstrom theory of gravitation> predicts
$$
\boxed{\delta\phi=0}
$$
for light passing a star. This contradicts the observed nonzero deflection and the successful general-relativistic value $4GM/(bc^2)$.
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