where F α α β β ≡ ≡ ∂ ∂ α α A β β − − ∂ ∂ β β A α α , ◻ ◻ ≡ ≡ g μ μ ν ν ∇ ∇ μ μ ∇ ∇ ν ν , and ∇ ∇ μ μ is a standard, 4D covariant derivative. It shows that the electromagnetic field is a source for the scalar field. Note that the scalar field cannot be set to a constant without constraining the electromagnetic field. The earlier treatments by Kaluza and Klein did not have an adequate description of the scalar field and did not realize the implied constraint on the electromagnetic field by assuming the scalar field to be constant.