Rigid bodies are idealizations in physics that do not exist in reality due to the finite speed of force propagation between atoms, which is limited by the speed of sound in solids, not the speed of light. This means that when a torque is applied to a rigid body, the far end does not respond instantaneously, leading to bending rather than pure rotation. The discussion highlights that while classical mechanics uses the rigid body assumption for simplicity, it can lead to inaccuracies in certain scenarios, such as molecular rotation. Textbooks like "A History of Strength of Materials" by Timoshenko can provide historical context on the topic. Ultimately, the rigid body concept serves as a useful approximation in many mechanical analyses despite its limitations.