Tell me about the definition of a rigid body A rigid body is a concept in physics that refers to an object that does not [[Deformable|deform]] or change shape when subjected to external forces. In other words, a rigid body maintains its size and shape regardless of the forces acting upon it. In reality, there are no perfectly rigid bodies as all materials have some degree of flexibility or elasticity. However, the concept of a rigid body is often used in physics to simplify calculations and understand the behavior of objects under certain conditions. Rigid bodies are characterized by three main properties: 1. Fixed Shape: A rigid body maintains a constant shape and size, meaning its internal distances between particles remain unchanged. 2. Incompressibility: The volume of a rigid body remains constant even under external pressure. This means that the density of a rigid body remains constant as well. 3. No Internal Forces: Rigid bodies do not experience internal forces due to deformation or changes in shape. Any force applied to one part of the body will be transmitted instantaneously throughout the entire object without distortion. The study of rigid bodies is important in various fields, including mechanics, dynamics, and engineering. It allows for the analysis and prediction of motion, stability, and equilibrium of physical systems like bridges, vehicles, and machinery. ## Einstein's idea of a true rigid body [[Albert Einstein]] discussed the concept of a "true" rigid body in his theories of general relativity. In this framework, a "true" rigid body refers to a hypothetical object that is not affected by the curvature of spacetime caused by matter and energy. This concept is important for understanding how spacetime is shaped by matter and how objects move within it. In Einstein's theory, the concept of a true rigid body is used to define what is meant by distance and velocity in curved spacetime. The idea is that if we have a coordinate system that is fixed with respect to the curvature of spacetime, then we can define distances and velocities within that coordinate system as being "true" or unchanged by the curvature of spacetime. This allows us to describe how objects move and interact with each other in a way that is independent of their position in spacetime. The concept of a true rigid body is related to the idea of "inertial reference frames," which are coordinate systems that are not affected by the motion of the observer or the matter in the universe. In general relativity, any object can be treated as an inertial reference frame if it is moving at a constant velocity relative to other objects in the universe. This means that the concept of a true rigid body is not limited to just one specific object, but rather can be applied to any object that is moving at a constant velocity with respect to other objects. ### Response from Bing GPT Albert Einstein, in his theory of relativity, indeed discussed the concept of measurements in space. However, he did not specifically talk about a “true” rigid body to measure the size of space. Instead, he made a significant remark in his 1916 review paper on general relativity that all our measurements amount to the determination of spacetime coincidences, like the coincidence of a pointer with a mark on a scale[(1)](@giovanelliNothingCoincidencesPointcoincidence2021). In the context of special relativity, the concept of a “rigid body” is not straightforward. Physicist [[Max Born]] proposed a Lorentz-invariant definition of a “rigid body”, but it was later clarified by [[Wolfgang Pauli|Pauli]] that while the concept of a rigid body has no place in relativistic mechanics, it is nevertheless useful and natural to introduce the concept of a “rigid motion” of a body[(2)](@RigidRotatingDisk). In essence, Einstein’s theories revolutionized our understanding of space and time, introducing new ways to conceptualize and measure these fundamental aspects of our universe. However, the idea of using a “true” rigid body as a standard measure for the size of space does not align with these theories. Instead, measurements in Einstein’s relativity are more about relationships and coincidences in spacetime. # Conclusion Overall, the concept of a true rigid body is an important tool for understanding how spacetime works according to Einstein’s theory of general relativity. It allows us to define distances and velocities in curved spacetime and to describe how objects move and interact with each other in a way that is independent of their position in spacetime. # References [[@giovanelliNothingCoincidencesPointcoincidence2021]] [[@RigidRotatingDisk]]