1. The problem statement, all variables and given/known data The Lorenz gauge ∂Φ/∂t + ∇. A = 0 enables the Maxwell equations (in terms of potentials) to be written as two uncoupled equations; ∂2Φ/∂t2 - ∇2Φ = ρ 1 and ∂2A/∂t2 - ∇2A = j 2 The tensor version using the Lorenz gauge is, i am told, ∂μ∂μ Aα = jα 3 expanded this is: ∂2Φ/∂t2 - ∇2A = jα 4 where Jα is the 4-current; ρ + J 2. Relevant equations If one adds 1 and 2 one gets two terms not included in 4. Namely; ∂2A/∂t2 - ∇2Φ My query is, what happened to these terms when we go to 3 (or 4). Have I misunderstood the transition from 1 and 2 to the tensor forms? 3. The attempt at a solution If one tries to cancel these terms, or equate their sum to zero, one sees that the first is a vector and the second a scalar. Secondly; ∂2A/∂t2 = ∂E/∂t which > 0 for a time varying field. And ∇2Φ = ∇. E = div E which also is not zero unless no charges are present, which they can be in 3. Any enlightenment would be greatly appreciated.