Suppose $G$ is a finite group and $x, y \in G$. $x$ and $y$ are said to be rational conjugate $x \sim_{r} y$ if and only if $\langle x\rangle$ and $\langle y\rangle$ are conjugate subgroups of $G$. Assume that $A$ is the set of all character values of $G$ and $Q(A)$ is an extension of $Q$ in $A$. Set $H = Gal(\dfrac{Q(A)}{Q})$. Is it true that the orbits of $H$ on conjugacy classes of $G$ are the same as the equivalence classes of $\sim_{r}$? Is there any proof or reference for this result?