Grounded cognition states that mental representations of concepts consist of experiential aspects. For example, the concept "cup" consists of the sensorimotor experiences from interactions with cups. Typical modalities in which concepts are grounded are: The sensorimotor system (including interoception), emotion, action, language, and social aspects. Here, we argue that this list should be expanded to include physical invariants (unchanging features of physical motion; e.g., gravity, momentum, friction). Research on physical reasoning consistently demonstrates that physical invariants are represented as fundamentally as other grounding substrates, and therefore should qualify. We assess several theories of concept representation (simulation, conceptual metaphor, conceptual spaces, predictive processing) and their positions on physical invariants. We find that the classic grounded cognition theories, simulation and conceptual metaphor theory, have not considered physical invariants, while conceptual spaces and predictive processing have. We conclude that physical invariants should be included into grounded cognition theories, and that the core mechanisms of simulation and conceptual metaphor theory are well suited to do this. Furthermore, conceptual spaces and predictive processing are very promising and should also be integrated with grounded cognition in the future.