Covariance refers to the invariance of Maxwell's equations under a change of coordinate systems. This means that the equations hold true regardless of the choice of coordinate system used to describe the physical phenomenon.
Checking the covariance of Maxwell's equations is important because it ensures that the equations accurately describe the behavior of electromagnetic fields in any coordinate system. It also allows for the development of a unified theory of electromagnetism that is consistent with the principles of relativity.
There are several methods that can be used to check the covariance of Maxwell's equations, including transformation laws, tensor analysis, and the use of Lorentz transformations. These methods involve manipulating the equations and coordinate systems to ensure that they remain consistent and unchanged.
If Maxwell's equations are not covariant, it would mean that they do not accurately describe the behavior of electromagnetic fields in different coordinate systems. This would lead to discrepancies and inconsistencies in experimental results and could potentially undermine the entire theory of electromagnetism.
Yes, it is possible to prove the covariance of Maxwell's equations using mathematical methods such as tensor analysis and Lorentz transformations. Additionally, the fact that the equations have been successfully applied to numerous experiments and observations in different coordinate systems serves as a strong evidence for their covariance.