On the universality of Maxwell’s equations

Einstein’s theory of relativity is based on the Principle of Equivalence, Hilbert’s on invariant theory and the calculus of variations. The two paradigms are not equivalent. Using the universality of Maxwell’s equations, Hilbert’s variational method is used to determine the energy–momentum tensor uniquely, and to show that general relativity can be formulated on the basis of Maxwellian, rather than specific physical force fields. A unified field theory is proved in which the Maxwellian force fields are all on an equal footing, distinct from the geometric field.