& -{\vec{E}}^{T} \\
    \hline
    {\vec{E}} & {}^{\star}{\vec{B}} \\
      \end{array}
    \right)\, .$$

    The unification of electricity and magnetism into a single interaction is the first paradigm of modern unification of interactions: the unification requires (or produces) a bigger group of symmetry because the equations of each field were invariant only under the Galilean group and the full set of Maxwell’s equations are invariant under the Poincaré group. This had to be so: if two interactions are different manifestations of a single interaction, there must exist transformations that do not change the equations of the theory and transform one interaction into the other.

    Had the Special Theory of Relativity been proposed before Maxwell’s equations, the latter could have been discovered by imposing Poincaré invariance on the incomplete equations of electricity and magnetism. However, the importance of symmetry principles was discovered much later.

    Observe that the Principle of (Special) Relativity applied to Newtonian gravity implies the existence of gravitomagnetism and the combination of both into a single relativistic field of interaction. This interaction is not yet General Relativity, but contains its seeds.

2.  ${\rm \bf Space}\bigoplus{\rm \bf Time}
    \stackrel{{\rm \bf Einstein, Minkowski}}{\Longrightarrow}  {\rm \bf Spacetime}$

    $$t,\,\,  \vec{x}
    \,\,\longrightarrow\,\, (x^{\mu})\equiv (c t, \vec{x})\, .$$

    