A reliable action feasibility scorer is a critical bottleneck in embodied agent pipelines: before any planning or reasoning occurs, the agent must identify which candidate actions are physically executable in the current state. Existing approaches use supervised fine-tuning (SFT) to train action scorers, but SFT treats each candidate independently and does not explicitly teach the model to discriminate between actions that are physically correct and those that are subtly wrong. We propose the Contrastive World Model (CWM), which fine-tunes a large language model (LLM) as an action scorer using an InfoNCE contrastive objective with hard-mined negative examples. The key idea is to push valid actions away from invalid ones in scoring space, with special emphasis on hard negatives: semantically similar but physically incompatible candidates. We evaluate CWM on the ScienceWorld benchmark through two studies. First, an intrinsic affordance evaluation on 605 hard-negative test pairs shows that CWM outperforms SFT by +6.76 percentage points on Precision@1 for minimal-edit negatives -- cases where a single word changes the physical outcome -- and achieves a higher AUC-ROC (0.929 vs. 0.906). Second, a live filter characterisation study measures how well CWM ranks gold-path actions against all valid environment actions during task execution. Under out-of-distribution stress conditions, CWM maintains a significantly better safety margin (-2.39) than SFT (-3.96), indicating that the gold action is ranked closer to the top. These results support the hypothesis that contrastive training induces representations that capture physical feasibility more faithfully than SFT alone.