What is the physical process when you uncork a bottle in a shoe hitting a wall? When you want to uncork for example a champagne bottle you can put it in shoe and hitting the bottom of the shoe against a wall. By this the liquid is pushing out the cork. But is this process just a matter of reflected liquid from the bottom on the cork or is there also something special going on? 
 A: Wine bottles have a small quantity of air trapped within them. When the bottle is accelerated towards the wall, the air bubble is also accelerated towards it. On contact, the bubble gets compressed between the heel of the shoe at one end and the wine at the other. This reduces the total volume within the bottle creating a tiny vacuum as well as a low pressure region at the opposite end, near the cork.
When the air stops being compressed (in between impacts), the pressure goes back to normal and - if you do this rapidly enough - the pressure changes induce the process of cavitation in the wine. In other words, the gases dissolved in the wine are released forming pockets of air (or 'vapour cavities') near the neck because it is a low-pressure area. As the region returns to its original pressure, the bubbles implode, generating a shock wave that pushes against the cork, slowly forcing it out of the bottle with each successive impact.
Here's a nice little video with an explanation, including frames from a high-speed camera showing the actual creation of these bubbles.
A: The cavitation answer is incorrect. It's conservation of momentum and the fact that the wine is relatively incompressible. Here's a detailed explanation citing a fluid dynamics professor: 
https://www.npr.org/sections/thesalt/2014/03/25/283927259/can-you-open-wine-with-shoe-open-yes-but-it-ain-t-pretty
