tiny-tim said:Hi DiamondGeezer!
I think that's just "covariance" …
Coordinate independence is a concept in mathematics and physics where the equations or laws of a system remain unchanged regardless of the coordinate system used to describe it. This means that the physical or mathematical phenomena being studied are not dependent on a specific choice of coordinates.
Coordinate independence is important because it allows for a more general understanding of a system or phenomenon. It eliminates the need for a specific coordinate system, which can vary depending on the observer or context, and allows for a more universal understanding that is not limited to a particular coordinate system.
Coordinate independence can be achieved through the use of tensors, which are mathematical objects that are invariant under coordinate transformations. By using tensors, equations and laws can be written in a coordinate-independent form, allowing for a more general understanding of the system.
One example is the laws of electromagnetism, which are expressed in terms of tensors and are therefore coordinate independent. Another example is the principle of relativity in physics, which states that the laws of physics should be the same for all observers regardless of their frame of reference.
Coordinate independence is not always applicable in all systems or phenomena. In some cases, specific coordinate systems may be necessary to accurately describe or analyze a system. Additionally, converting equations or laws into a coordinate-independent form can be mathematically complicated and may require advanced techniques.