The Cartesian Diver: Sinking and Floating on Command

The demo: a bottle, a bubble, and your thumb

Build a Cartesian diver in two minutes. Fill a rigid, flexible bottle (a 1 or 2 litre PET soda bottle is ideal) to the brim with water. For the diver, use anything that traps a small pocket of air and floats just barely: a glass eyedropper, a bent drinking straw pinched at one end, a ketchup or soy-sauce packet, or the cap of a pen. Adjust it until it hovers at the surface, only a whisker of it breaking through. Screw the cap on tight so no air gap remains at the top.

Now squeeze the sides of the bottle. The diver hesitates, then dives to the bottom. Ease off, and it climbs back up. With practice you can make it hang motionless at any depth, balanced on a knife-edge of pressure. The magic is that your hand never touches the diver, yet you control it with millimetre precision from outside a sealed container.

• The trick to a good diver: it must be almost neutrally buoyant when relaxed, so that a tiny loss of displaced volume tips it over into sinking.
• Why a full bottle: water is nearly incompressible, so your squeeze goes entirely into the diver's air pocket rather than being absorbed by a spare gas gap.

Two laws doing all the work

The diver is a marriage of two of the oldest results in physics. Archimedes' principle (c. 250 BCE) says the upward buoyant force equals the weight of the fluid displaced. For a diver of total mass m displacing a volume V of water of density ρ_w, the net vertical force is:

F = ρ_w · g · V − m · g

If F > 0 it rises, if F < 0 it sinks, and if F = 0 it hovers in neutral buoyancy. Crucially, V is the sum of the diver's rigid volume plus the volume of its trapped air pocket. The rigid part cannot change, but the air pocket can.

That is where Boyle's law (Robert Boyle, 1662) enters. For a fixed amount of gas at constant temperature, pressure times volume is constant: P·V_air = constant. Push the surrounding pressure up and the bubble shrinks; the water rushes in to fill the space, the total displaced volume V drops, buoyancy falls, and the diver sinks. Release the pressure and the bubble springs back to full size, buoyancy returns, and the diver rises. The air pocket is a soft spring that Boyle's law tunes with your thumb.

Pascal's principle: how the squeeze reaches the bubble

There is a third law hiding in plain sight: Pascal's principle (Blaise Pascal, 1653). A pressure change applied to an enclosed, incompressible fluid is transmitted undiminished to every point in that fluid. When you squeeze the walls, you cannot compress the water itself in any meaningful way (its bulk modulus is about 2.2 GPa, so a 10% squeeze in air-terms is invisible in water), so the pressure rise appears everywhere at once, including at the mouth of the diver's air pocket.

This is why the effect feels instantaneous and why it works regardless of where the diver happens to be floating. It also explains a subtle design rule: the bottle must be full. Any air gap at the top is far more compressible than the water, so it would soak up your squeeze like a cushion, and the diver would barely respond. Remove that cushion and every joule of your grip is delivered straight to the bubble.

The numbers: how hard, how much, how fast

Put real values on it. Take a modest diver made from a glass eyedropper: total mass m ≈ 4.2 g, with about 1.7 mL of glass (glass density ≈ 2500 kg/m³) and a trapped air pocket of about 2.5 mL. In water (ρ_w = 1000 kg/m³) those volumes displace just enough to make it neutrally buoyant, so it floats on the very edge of sinking.

• How hard you squeeze: to compress the air pocket by about 10%, Boyle's law demands P₂ = P₁ / 0.90, a pressure rise of ΔP ≈ 11 kPa, roughly 0.1 atmosphere. That is a firm but easy squeeze, equivalent to descending about 1.15 m in a real dive.
• How much displacement you lose: shrinking a 2.5 mL bubble by 10% removes 0.25 mL of displaced water. That is 0.25 g of buoyant support lost.
• The force that sinks it: losing 0.25 mL of displacement removes about ρ_w·g·ΔV ≈ 2.5 millinewtons of upward force, roughly a quarter of a gram-force. Tiny, but on a neutrally balanced diver it is decisive.

Notice how leveraged the effect is: a few percent change in a bubble, driven by a tenth of an atmosphere, tips a floating object into a sinking one. That sensitivity is exactly why the diver must be tuned to hover almost perfectly when relaxed.

Runaway sinking and the art of hovering

Watch closely and you will see the dive accelerate. This is positive feedback. As the diver descends, the water above it adds hydrostatic pressure at a rate of about 9.8 kPa per metre of depth (ΔP = ρ_w·g·h). In a short bottle this extra pressure is small, but it compresses the bubble a little further, which sinks the diver faster, which deepens it more. A diver held just barely below neutral will tend to run all the way to the bottom on its own once it starts.

The mirror image happens on the way up: rising reduces the pressure, the bubble expands, buoyancy grows, and the ascent quickens. This inherent instability is what makes hovering at mid-depth genuinely hard, and it is the same instability real submarines and scuba divers fight constantly. To pause the diver mid-bottle you must feed in just enough squeeze to hold the bubble at exactly the size that gives zero net force, correcting continuously by feel. Master divers of the toy learn to modulate finger pressure the way a submariner trims ballast tanks.

• Neutral buoyancy is a knife-edge: the equilibrium F = 0 is unstable, so no diver sits still without active control.
• Temperature matters too: Boyle's law assumes constant temperature; warm the bottle and the trapped air expands (Gay-Lussac/Charles behaviour), nudging the diver toward floating.

History, and where the physics really lives

The device is traditionally credited to René Descartes and dates to the 1640s, though the physicist Raffaello Magiotti described a nearly identical apparatus in his 1648 tract Renitenza certissima dell'acqua alla compressione, arguing precisely that water resists compression while the trapped air does not. Italian and Venetian glassworkers built ornate glass divers, sometimes shaped as little devils or fish, that danced inside sealed flasks — the reason the toy is also called a "Cartesian devil" or "bottle imp." For three centuries it has been the physics teacher's favourite: a single sealed system that demonstrates buoyancy, gas compressibility, and pressure transmission all at once.

The same mechanism scales up to serious engineering. A submarine dives by flooding ballast tanks to reduce displacement and surfaces by blowing them out with compressed air, changing effective volume just as the diver's bubble does. A fish's swim bladder is a biological Cartesian diver: the fish secretes or reabsorbs gas to hold neutral buoyancy at depth. Cephalopods, submersibles, and even weather-balloon altitude control all play the same game of trading gas volume against displacement. The toy in the bottle is a working model of every one of them.

Misconceptions and a note on safety

The most common wrong explanation is that squeezing "makes the diver heavier." It does not; the diver's mass m never changes. What changes is the volume of water it displaces, because the compressible air pocket shrinks. Weight stays fixed while buoyant support drops, and the imbalance sends it down. Another myth is that the water is being compressed to push the diver; in reality the water is essentially incompressible and merely acts as the messenger that carries your pressure to the bubble.

A third confusion: people expect the effect to depend on the diver being made of a dense material. It does not. Any object that traps a compressible air pocket and hovers near neutral buoyancy works, from a foil sauce packet to a bottle cap. The material only sets how much air you need to trap for balance.

• Safety: the pressures involved are tiny (about 0.1 atm) and a flexible PET bottle handles them easily. There is no meaningful bursting hazard from hand-squeezing a plastic bottle.
• Do not use rigid glass containers and never seal a bottle with a stiff wall you cannot flex, and avoid heating a sealed full bottle, since a fluid that cannot compress will build pressure quickly if you try to force volume into it.
• Troubleshooting: if the diver won't dive, you probably have an air gap at the top or a diver that floats too high; top up the water and retune the diver to hover with only a sliver showing.

What changes when you squeeze the bottle (typical eyedropper-style diver)

Quantity	Relaxed (floating)	Squeezed (sinking)	Physics
Bottle pressure	≈ 101 kPa (1 atm)	≈ 112 kPa (1.1 atm)	Pascal transmits squeeze
Trapped air volume	≈ 2.5 mL	≈ 2.25 mL	Boyle: P·V = constant
Water displaced	Diver weight ≈	Less than weight	Archimedes' principle
Net vertical force	0 (neutral) or up	Downward	F = ρ_w·g·V − m·g
Result	Rises / hovers	Falls to bottom	Buoyancy lost