Integrating AI into the physical layer is a cornerstone of 6G networks. However, current data-driven approaches struggle to generalize across dynamic environments because they lack an intrinsic understanding of electromagnetic wave propagation. We introduce the Wireless World Model (WWM), a multi-modal foundation framework predicting the spatiotemporal evolution of wireless channels by internalizing the causal relationship between 3D geometry and signal dynamics. Pre-trained on a massive ray-traced multi-modal dataset, WWM overcomes the data authenticity gap, further validated under real-world measurement data. Using a joint-embedding predictive architecture with a multi-modal mixture-of-experts Transformer, WWM fuses channel state information, 3D point clouds, and user trajectories into a unified representation. Across the five key downstream tasks supported by WWM, it achieves remarkable performance in seen environments, unseen generalization scenarios, and real-world measurements, consistently outperforming SOTA uni-modal foundation models and task-specific models. This paves the way for physics-aware 6G intelligence that adapts to the physical world.