Quantum tunnelling

An example of an implication of the uncertainty principle (as well as wave-particle duality) is a phenomenon known as quantum tunneling. Quantum tunneling is also known as barrier penetration. This is one of the more bizarre results of quantum mechanics. This is when particles can borrow energy from their surroundings, thus, allowing particles to tunnel through walls or barriers. The energy also must be given back by a specified time. 

These are actual particles tunneling through potential energy barriers. These are barriers that classical entities can't move through. Without quantum tunneling, atomic nuclei could never decay by emitting alpha particles. This was proposed by George Gamow in 1928. The alpha particle has a small (however, non-zero) probability of tunneling through and escaping the nucleus. 

This is one of the major difference between Einstein's classical theory of gravity with quantum mechanics. There is a finite probability that particles may tunnel (or make a quantum leap) through impenetrable barriers. 

This is a stunning prediction of the quantum theory. This prediction has had spectacular success at the quantum level. We can't imagine a world without these quantum leaps through barriers, or tunneling as it is known. 

There is a simple experiment to demonstrate the correctness of quantum tunneling. You begin by placing an electron in a box. Typically, the electron would not have enough energy to penetrate the walls of the box. If classical physics holds, then the electron will never leave the box. However, in quantum mechanics, this electron will have a probability wave that spreads through the box and even oozes into the outside world. This oozing can be calculated with the Schrodinger wave equation. The idea is that there is a small probability that the electron is positioned somewhere outside of the box. There is a small but finite probability that the electron will tunnel its way through the wall of the box.

Quantum tunneling also has implications for "impossible" events. For example, I can calculate the probability that I will tunnel through the wall into the next room. However, we would have to wait longer than the lifetime of the universe for these kinds of transitions to occur.