4. Let $O$ be the center of the base $\triangle ABC$ of the regular tetrahedron $P-ABC$. A moving plane through $O$ intersects $PC$ at point $S$, and the extensions of $PA$ and $PB$ at points $Q$ and $R$, respectively. Then the sum $\frac{1}{PQ} + \frac{1}{PR} + \frac{1}{PS}(\quad)$
(A) has a maximum value but no minimum value
(B) has a minimum value but no maximum value
(C) has both a maximum value and a minimum value, which are not equal
(D) is a constant independent of the plane $OPS$
4.D.

Let the regular tetrahedron $P-ABC$ have dihedral angles between each pair of lateral edges as $\alpha$, and the angle between $PC$ and the plane $PAB$ as $\beta$. Then
$$
\begin{array}{l}
V_{S-PQR}=\frac{1}{3} S_{\triangle PQR} h \\
=\frac{1}{3}\left(\frac{1}{2} PQ \cdot PR \sin \alpha\right) PS \sin \beta .
\end{array}
$$

On the other hand, let the distance from $O$ to each face be $d$. Then
$$
\begin{array}{l}
V_{S-PQR}=V_{O-PQR}+V_{O-PRS}+V_{O-PQS} \\
=\frac{1}{3} S_{\triangle PQR} d+\frac{1}{3} S_{\triangle PRS} d+\frac{1}{3} S_{\triangle PQS} d \\
=\frac{d}{3} \cdot \frac{1}{2} PQ \cdot PR \sin \alpha+\frac{d}{3} \cdot \frac{1}{2} PS \cdot PR \sin \alpha+ \\
\frac{d}{3} \cdot \frac{1}{2} PQ \cdot PS \sin \alpha \text {. } \\
\end{array}
$$

Thus, $PQ \cdot PR \cdot PS \sin \beta$
$$
=d(PQ \cdot PR+PR \cdot PS+PQ \cdot PS) \text {. }
$$

Therefore, $\frac{1}{PO}+\frac{1}{PR}+\frac{1}{PS}=\frac{\sin \beta}{d}$ (constant).