I have a question regarding the well known fact that General Relativity is not a conformal invariant theory or to put it in other words about the fact that it is conformal variant:
What are the physical assumptions in General Relativity about the gravitation that make the resulting formulation of gravity to be conformal variant?
I am not asking about a mathematical reasoning because that is obvious:
One performs a conformal transformation and he can check that the action and field equations are not invariant under this transformation. This mathematical part is obvious for me.
I am asking what is the physical assumption that make this happen? What physical property of gravity (which is absent in Electromagnetic interaction) makes it conformal variant (at least in GR)? is it weak equivalence principle? is it the requirement of the Corresponding principle? or what? there should be some physics behind this, it can't be a mere mathematical coincidence ...