We have learned the following fundamental correspondence relations from basic quantum mechanics: $$E\rightarrow i\hbar\dfrac{\partial}{\partial t} \tag{1}$$ $$\vec{p}\rightarrow-i\hbar \nabla \tag{2}$$
My question is why we take a minus sign in formula $(2)$? I mean we should not take the minus sign from the viewpoint of space-time symmetry. Is there any relationship with special relativity? If we don't take the minus sign in the replacement for momentum, what will happen in quantum mechanics?
