Tape the other bottle on top of the one with water in it. Make sure the spouts are lined up.
Turn the bottles over so that the one with water is on top. See how the water has a hard time going down.
To make the water go down into the other bottle, swirl the bottles in a circular motion really fast. Don't shake it up and down or it won't work. The water should swirl into the bottom bottle.
This is why it works: When you swirl the bottle, the water starts to move in a circle. When the water moves fast enough, it pushes out against the bottle and leaves a hole in the middle. There's no water in the hole, only air. The hole allows the air from the bottom bottle to come up to the top bottle. When the air moves, there's then space in the bottom bottle, which makes room for the water from the top to flow into the bottom.
This sort of water movement, with the special hole in the middle, is usually called a whirlpool. A tornado happens in air and a whirlpool happens in water. So, it is really a "Whirlpool in a Bottle."