Abstract
Special relativity in five dimensions à la Kaluza - Klein with two basic constants, the speed of light and the Planck length, is revised in order to substantiate the interpretation recently given to a version of the Einstein equations of general relativity extended to extra space dimensions as the quantum law of a geometry - matter duality. The formalism of the electromagnetic field in five dimensions and in the absence of gravitation is next reviewed to argue that the U(1) symmetry of the fifth dimension cannot be identified with electromagnetism itself, so that a unification of gravity and electromagnetism à la Kaluza - Klein is not possible. The five-dimensional general theory of relativity is finally considered to discuss electromagnetism in gravitational fields.
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