The movement of molecules from an area of higher concentration to lower concentration without energy or carrier protein is called

Diffusion. While all forms of passive transport move from a higher concentration to a lower concentration, facilitated diffusion uses a carrier protein to move hydrophilic molecules through a membrane. Only normal passive diffusion uses no energy or carrier proteins and moves from a high to low concentration.

Alright, i'm gonna try to explain this as good as possible. the law of conservation is like a collection overtime. it never changes though. no matter how you change the constituent parts.