The permanent versus determinant conjecture is a major problem in complexity theory that is equivalent to the separation of the complexity classes VP and VNP. Mulmuley and Sohoni suggested to study a strengthened version of this conjecture over the complex numbers that amounts to separating the orbit closures of the determinant and padded permanent polynomials. In that paper it was also proposed to separate these orbit closures by exhibiting occurrence obstructions, which are irreducible representations of GL_{n^2}(C) that occur in one coordinate ring of the orbit closure, but not in the other. We prove that this approach is impossible. However, this does not rule out the general approach to the permanent versus determinant problem via multiplicity obstructions. (Joint work with Ikenmeyer and Panova)