A common reply is that the pressure is higher, but why should it be? My friend Bill Weiher, who was trained in physical chemistry gave the following explanation, which I believe.

First the pressure is not greater after shaking. Modern aluminum cans allow a direct verification of this. You can press on the sides of a can and observe the degree of deformation which directly reflects the internal pressure. Try this before and after shaking the can. Then open the can and try again. This is fairly crude but it is easy to convince your self that there is much less than a factor of 2 in the pressure before and after shaking. After opening the pressure difference inside and out vanishes and makes it dramatically easier to deform the can indicating that the resistance of the closed can was due to pressure, not resistance of the metal.

In both cases the pressure in the unopened can is the equilibrium pressure for whatever concentration of CO₂ is in the liquid. It also depends on temperature, but there is insufficient shaking energy to change the temperature much.

Weiher’s explanation is that when the can is shaken the gaseous phase of CO₂ in the can is transformed partly into small bubbles mixed in the liquid. This greatly increases the area of the interface between the gas and liquid phase. When the pressure is released the CO₂ comes out of solution at the interface of the phases. There is much more interface in the shaken can and thus the rate of fizzing is much greater. Effectively liquid expands as a result of the bubbles expanding.

In either case there remains much supersaturated carbonated drink after opening, but less with shaking.