Fluid-like volumetric collective motion in drone swarms with navigation, obstacle avoidance, and formation maintenance remains challenging. Existing potential-field-based approaches often lack stability guarantees and are largely restricted to two-dimensional formations. This paper proposes Active Elastic Matter, an extension of the Active Elastic Sheet method that (i) generalizes the elastic interaction model to volumetric 3D formations and (ii) incorporates estimated relative velocities and accelerations using an Extended Kalman Filter. These predictive interaction terms improve stability and robustness in dynamic environments. Simulation results demonstrate that Active Elastic Matter enables 3D formations to navigate narrow passages and dynamic obstacles while maintaining higher order and lower entropy compared to Active Elastic Sheet. Real-world experiments with Crazyflie drones further validate improved stability during narrow passage navigation.