Consider the ladder paradox;
Let the length of the barn in its fixed frame be $80m$, and consider the ladder's reference frame which is moving toward the barn with a speed $v$, and in ladder's frame the length of the barn is $20m$.
Now, since both doors of the barn are closed simultaneously in the barn's fixed frame, if we were to write the Minkowski distance between these events, i.e the events that the doors are shut, we get
$$c^2 \Delta t_B^2 - \Delta x_B ^2 = c^2 \Delta t_L ^2 - \Delta x_L^2$$ where $\Delta t_B^2 = 0, \quad \Delta x_B^2 = (80m)^2, \quad \Delta x_L^2 = (20m)^2$, but when we plug these values in the the equation above, we get
$$\Delta t_L^2 < 0,$$ which is not possible.
So where is my mistake in my reasoning? I mean since the doors of the barn are moving with speed $-v$ relative the ladder, the distance between the doors should be smaller, due to length contraction, but this leads to a weird thing as I have explained above.