Spatial generalization in robot world models depends on whether action representations capture the physical relationships that remain valid across changing spatial configurations. Yet different coordinates can describe the same interaction, whereas similar motions can produce different outcomes when local physical conditions change. How these distinctions affect learned prediction remains insufficiently understood. This study evaluates matched action representations defined in world, object, and surface coordinate frames using a controlled robotic peeling benchmark. Global pose and contact relocation experiments reveal a cost associated with limited training data when equivalent interactions receive different spatial descriptions. Removing information about peel thickness creates an irreducible ambiguity because identical predictive inputs can correspond to different material removal outcomes. Coordinates defined relative to the surface improve consequence prediction and counterfactual action selection under accurate local observations, but learned predictors remain vulnerable to uncertainty in the coordinate frame. Joint centering of the surface and tool removes sensitivity to translation of their common origin, whereas incorrect contact geometry and actual execution deviations introduce different failure mechanisms. These results show that effective spatial generalization depends on preserving the relationships between actions and states that determine physical consequences, rather than simply minimizing coordinate variation. This perspective provides a principled basis for designing robot world models that reuse physical knowledge across spatial configurations while retaining the distinctions essential to prediction and planning.

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