4. As shown in the figure, in the square $A B C D$ with side length 2, $E$ is the midpoint of $A B$. Now, $\triangle A E D$ and $\triangle B E C$ are folded along $E D$ and $E C$ respectively, so that $E A$ and $E B$ coincide, forming a tetrahedron. The volume of this tetrahedron is $\qquad$
In the figure, $\triangle SCD$ is an equilateral triangle with a side length of 2, so $SF = \sqrt{3}$. From $EF \cdot SH = SE \cdot SF \Rightarrow SH = \frac{\sqrt{3}}{2}$, thus $V_{S-ECD} = \frac{1}{3} \cdot 2 \cdot \frac{\sqrt{3}}{2} = \frac{\sqrt{3}}{3}$.