I have seen a couple of posts on this website of physics students who were puzzled by what the electric displacement vector D in electromagnetic theory represents. This quantity also had me rather puzzled when I was a student and I think I can provide some insight into its significance. The equations div E=4*pi*(rho total)=4*pi*(rho free +rho p) and div P=- rho p are both on rather solid footing. A little algebra gives div (E+4*pi*P)=4*pi*(rho free). Thereby if we define D=E+4*pi*P, then div D=4*pi*(rho free). There is however no measurement device of any kind that can distinguish between the electric field created by free electrical charges from the electric field created by polarization charges. Thereby, after much careful thought, I have come to the conclusion that the electric displacement vector "D" is a very useful mathematical construction, but it is not a physically measurable quantity.