1. One of the objectives of Special Relativity was to make the laws of electricity and magnetism valid for all inertial observers. In particular, Maxwell's wave equation for light's electric field E is given by °E/dn? – (1/c)² E/&? = 0 (a) Show that this equation does not have its mathematical form preserved under Galilean coordinate transformations, i.e., it violates the principle of Galilean relativity. (b) Next, show that this equation is invariant under Lorentz transformations, i.e., it keeps its form and is thus indeed valid for all inertial reference frames in the context of Special Relativity.

1. One of the objectives of Special Relativity was to make the laws of electricity and magnetism valid for all inertial observers. In particular, Maxwell's wave equation for light's electric field E is given by °E/dn? – (1/c)² E/&? = 0 (a) Show that this equation does not have its mathematical form preserved under Galilean coordinate transformations, i.e., it violates the principle of Galilean relativity. (b) Next, show that this equation is invariant under Lorentz transformations, i.e., it keeps its form and is thus indeed valid for all inertial reference frames in the context of Special Relativity.

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