If the physical world is bound by the laws of physics, how can something non-physical interact with something physical? If two objects collide, the movement and force of one object will cause the other object to change its speed and direction. This is a physical law of causation.
However, if we are to believe, as Descartes argues, that the mind influences the body and causes its movements, how would a non-physical thing interact with something physical? It is not compatible with our understanding of modern physics.
Similarly, if the mind were to causally interact with the body, it would require energy to move a physical object. If this was the case, and the non-physical world was interacting with the physical one, science would dictate that the energy levels in the cosmos would be ever increasing as mental energy was constantly being converted to physical energy. But this is not the case.