Monadic characterization of the rational order

Let $R$ denote the rational order, and let $M$ be an order.

Rational-order conjecture. There is a monadic sentence $\psi$ such that

$$R\models\psi$$

and

$$M\models\psi$$

imply that $M$ and $R$ have the same monadic theory.

The source marks this assertion as confirmed by Gurevich, so it is recorded as solved rather than open.