P1*V1=P2*V2 Since you basically have a closed system (the diver plus the water bottle) by applying pressure on the bottle, you are effectively transferring this pressure to the cartesian diver. This is because water is pretty much uncompressible. So, because the pressure is increased, the volume of air must decrease. Because we have a closed system, the water goes into the void created by the compressed air, the density increases until it is greater than that of water and it sinks.
Hey im new here and i also need help on the Cartesian Diver. I was just wondering if The air pressure is the same, less than, much less than, greater or much greater than the air pressure outside of the bottle or container before pressure is applied to the container.