Walter Lewin in one of his lectures (8.02 lect 5 https://youtu.be/JhV-GOS4y8g?t=25m46s) draws an example of a solid conducting heart.
He then asks whether there would be any charge on the inner surface of the heart or all the charge would be located on the outer surface. He uses a gaussian surface (red) to prove that there cannot be any charge on the inner surface, enclosed within the gaussian surface, since the net flux and therefore electric field is 0.
My question is, how did he come to the conclusion that there can't be any charge on the inner surface? Isn't there a possibility that the charges would align themselves to cancel the fields within the cavity, but also in the area between the two surfaces? Like this (sorry for the messy image):