Clinical care is interventional. Physicians must decide how a patient's trajectory is likely to change under competing actions, not only estimate risk under the status quo. Most deployed medical artificial intelligence, however, remains optimized for classification or passive forecasting. We argue that the useful next abstraction is the medical world model, a learned system that represents patient state, models how that state evolves over time, accepts interventions such as drugs, doses, and procedures, and rolls trajectories forward under those interventions. Progress toward this goal is currently fragmented across digital twins, disease-trajectory models, surgical simulators, and generative electronic health record forecasting, with each community addressing a subset of the necessary ingredients. We organize the field with a capability ladder spanning representation, forecasting, single-arm projection, comparative treatment evaluation, and planning. Across imaging, physiology, longitudinal electronic health records, and surgical simulation, a consistent maturity pattern emerges. Representation and forecasting are widespread, narrow treatment-conditioned simulators are appearing, credible counterfactual comparison remains scarce, and validated treatment planners are absent. Once a model simulates what would happen under alternative treatments, causal validity becomes the binding constraint. Scaling data and generative modeling alone will not solve this. Credible medical world models also require explicit action definitions, causal design, and staged clinical validation with regulatory oversight. In this paper, the medical world model is a claims-to-evidence framework for simulation that can inform clinical decisions.