In this paper, we aim to model 3D scene geometry, appearance, and the underlying physics purely from multi-view videos. By applying various governing PDEs as PINN losses or incorporating physics simulation into neural networks, existing works often fail to learn complex physical motions at boundaries or requiring object priors such as masks or types. In this paper, we propose NGV to learn physics of complex dynamic 3D scenes without needing any object priors. The key to our approach is to introduce a physics code followed by a carefully designed divergence-free module for estimating a per-Gaussian velocity field, without relying on the inefficient PINN losses. Extensive experiments on two public datasets and a newly collected challenging real-world dataset demonstrate superior performance of our method for future frame extrapolation and motion segmentation. Most notably, our investigation into the learned physics codes reveals that they truly learn meaningful 3D physical motion patterns in the absence of any human labels in training.