We introduce multi-task Visuo-Tactile World Models (VT-WM), which capture the physics of contact through touch reasoning. By complementing vision with tactile sensing, VT-WM better understands robot-object interactions in contact-rich tasks, avoiding common failure modes of vision-only models under occlusion or ambiguous contact states, such as objects disappearing, teleporting, or moving in ways that violate basic physics. Trained across a set of contact-rich manipulation tasks, VT-WM improves physical fidelity in imagination, achieving 33% better performance at maintaining object permanence and 29% better compliance with the laws of motion in autoregressive rollouts. Moreover, experiments show that grounding in contact dynamics also translates to planning. In zero-shot real-robot experiments, VT-WM achieves up to 35% higher success rates, with the largest gains in multi-step, contact-rich tasks. Finally, VT-WM demonstrates significant downstream versatility, effectively adapting its learned contact dynamics to a novel task and achieving reliable planning success with only a limited set of demonstrations.