Monday, 30 January 2017

Quantum tunnelling

Leaving aside the controversy about whether tunnelling should have only one 'l', quantum tunnelling is a real effect predicted by quantum theory which is impossible to explain with classical physics. It is another example of the way in which the wierd ideas underlying quantum theory are validated by strange effects in the real world.

According to classical physics, an object can't get over a barrier unless it has at least a certain amount of energy. The higher the barrier, the more energy is needed. The rule is black and white- if the object has enough energy it can get over the barrier- if it doesn't it can't. Think of throwing a ball over a wall. Unless you throw it hard enough it won't get over the top.

Quantum theory, on the other hand, says there's always a chance an object will get over a barrier no matter what energy it has. The chances depend on the shape of the object's quantum wave and on the height and thickness of the barrier.

To get an idea of why this happens, remember that every object has an associated wave, and there is a chance that the object could be anywhere within the area covered by its wave- the chance of an object being at a particular point depending upon the height of its wave at that point. Now, one general characteristic of waves is that they never come to an abrupt stop- they always gradually fade away at their edges. When the quantum wave of an object meets the surface of a barrier the wave doesn't suddenly drop to nothing- instead the wave gradually fades away through the space occupied by the barrier. If the barrier is a tall one, and the object doesn't have much energy, then the wave reduces in height very rapidly. On the other hand, if the barrier isn't too high compared with the energy of the object, then the wave will reduce over a greater area. If the barrier is thinner than the area over which the wave reduces to nothing then the wave will continue on the other side of the barrier, meaning that there is a chance that its object can appear there.

Quantum tunnelling explains the rates at which certain radioactive substances emit radiation. Particles at the centre of an atom of radioactive material are held in place by forces that act as a barrier to their escape. They don't have enough energy, in classical terms, to pass over the barrier, but their quantum waves do just manage to extend beyond the effective width of the barrier, so there is a small chance that the particles will appear outside the barrier that is holding them in the atom. The mathematics of quantum theory can predict the decay rates of radioactive materials very precisely.

Quantum tunnelling is routinely exploited in the design of modern electronics, and explains certain effects in biology, such as certain types of DNA mutation.

In theory quantum tunnelling applies to all objects and all barriers, but once objects get much larger than a few atoms the chances of tunnelling get very small. Since humans are trillions of times bigger than atoms, the chances of us tunnelling through barriers are vanishingly small.

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