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"Contraction-orthogonality" of covariant and contravariant basis Contravariant vectors or just "vectors" are defined as elements of the tangent space at a given point. In practice, they are defined with respect to a coordinate-vector basis $\mathbf{e}_{(i)}$, where $\mathbf{e}_{(i)}$ is the vector tangent to the $i$-th coordinate line. Then they are given, ...


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Perhaps you could explain what exactly led you to question your understanding... The physical meaning of coordinate invariance is pretty simple. It's just that the laws of physics cannot depend upon your choice of coordinates as long as the reference frame you're working in is inertial. So if you were to perform a coordinate transformation from one inertial ...


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The "motion of stuff" is not the same in all reference frames. Each frame has it's own coordinate system, and so the physical process you are looking at will be described by different variables. (This is true even when you think of Galilean coordinate systems). What Griffiths means is that you can use the vector form of Maxwell's equations along with the ...



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