I can't find anything online about this, maybe I'm just dumb, but I was wondering, if you put a propeller inside of a air tight, water tight box, and turned it on, would it propel the box? If not, why?
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No, it wouldn't work. Because when you switch on the propeller, it will propel some stuff(like air or water depending on what you are propelling) backwards. So it seems like the propeller will get some push in forward direction and gain some momentum, but because you have a closed container so the stuff will collide the walls which will decrease the momentum that it gained earlier and will again come back to initial state. Another way to see this is that there are no external forces on the system (box + propeller) so it would not accelerate according to Newton's Second Law $F_{external} = ma $ .
You might think what about the energy that I will supply to the propeller to rotate it, where will it go, who will consume it? Answer: The energy you spent in propelling will heat up the stuff you are trying to propel. Your stuff particles will move in random directions after having enough collisions with their neighbors making total momentum to zero but will have some non-zero total randomized kinetic energy which is the measure of temperature.
