The law of conservation does not apply to babies

It's true.  The law of conservation states that in a closed system, mass will be conserved.  It might be converted to a different form (like energy) but it doesn't magically disappear or appear.  This, however, does NOT pertain to babies. Examples:

Sleep Volume - a small baby, that fits comfortably in his tiny bassinet with room to spare will take up 5 times as much space when placed in a bed with his parents.  

Liquid Mass - regardless of how much liquid intake an infant has, his output - be it in the form of drool, pee, or spit up - will be easily twice what was consumed.  

I'm reasonably certain that babies some how tap into extradimensional spaces, perhaps via a worm hole.  It must be something we forget how to do as we get older ...