Why does a diver sink inside a sealed bottle without being touched?

The Corning Museum of Glass describes Cartesian divers as demonstrations of density and buoyancy. They also featured in itinerant glassworkers’ entertainments. A surviving advertisement promoted figures that seemed to obey spoken commands.

The useful comparison concerns the condition changed outside the vessel. The name ‘Cartesian’ alone is not evidence that Descartes invented the apparatus.

The Exploratorium uses a sealed condiment packet containing an air bubble. Raising pressure compresses that air and reduces the water displaced by the packet. Water entering the packet is not the key process in this version. This differs from the water-admitting glass design described in Kenyon College’s apparatus archive.

We retain that relationship in an air pocket plus a fixed-volume component. Gas amount and total diver mass stay constant in step one. We neglect air mass, membrane thickness and elasticity. The drawing does not reproduce a real condiment packet or glass figure.

This idealised calculation fixes temperature and gas amount. Change the total pressure around the pocket—absolute pressure—from 100 to 125 kPa. Air volume falls from 5 to 4 cm³. The same air occupies less space; it has not escaped.

NASA’s explanation of Boyle’s law relates constant-temperature pressure and volume through their constant product. Here 100×5 and 125×4 both equal 500. kPa measures pressure and cm³ measures volume. These are our chosen example values.

The whole diver is submerged. The fixed component occupies 1 cm³, so 5 cm³ of air makes 6 cm³ in total, while 4 makes 5 cm³. Taking water density as 1 g/cm³ gives displaced-water masses of 6 and 5 g.

Buoyant force equals the displaced water’s weight. With diver mass fixed at 5.5 g, displacing 6 g of water gives an upward resultant; displacing 5 g gives a downward one. The displayed +0.5 g and −0.5 g are mass differences, not forces measured in grams.

Step two starts afresh at 100 kPa. Keep 5 cm³ of air and the 1 cm³ fixed component, so the diver still displaces 6 g of water. This time compare total diver masses of 5.5 and 6.5 g.

At 5.5 g the diver is lighter than its displaced water and the resultant points up. At 6.5 g it points down. We assume different fictional component materials with the same external volume. We do not add real ballast while silently ignoring its extra volume. Pressure and mass are changed in separate steps.

The pictured diver stays at the same submerged position. Its arrow is the resultant force direction if released there from rest. Bubble compression and an actual downward journey are separate questions. A sinking diver still experiences upward buoyancy.

The model helps separate conditions behind a surprising bottle demonstration. It omits changing depth, drag, membrane elasticity, temperature changes and contact with the bottom or surface. An explanation for one diver type should not be treated as the internal mechanism of every design.