The uncertainty principle

Heisenberg's simple idea declares why atoms do not implode, how the sun is able to shine and the vacuum of space is not empty

The uncertainty principle is among the the most famous (and also probably most misunderstood) concepts in physics. It demonstrates that there is a fuzziness in nature, an elementary limit to the things we could know about the behaviors of quantum particles and, consequently, the tiniest scales of nature.

Of these scales, the most we can hope for is to compute or calculate probabilities for where things are and just how they are going to behave. As opposed to Isaac Newton’s clockwork universe, wherein every thing follows clearly identifiable laws on how to move and forecast is simple once you know the starting conditions, the uncertainty principle enshrines an amount of fuzziness into quantum theory. Werner Heisenberg‘s simple idea declares why atoms do not implode, how the sun is able to shine and, surprisingly, that the vacuum of space is not actually empty.

Quantum physics

This uncertainty is a very odd and unexpected result from quantum physics. Until this time, no one had ever made any sort of prediction that knowledge was somehow inaccessible on a fundamental level. Sure, there were technological limitations to how well a measurement was made, but Heisenberg’s uncertainty principle went further, saying that nature itself doesn’t allow you to make measurements of both quantities beyond a certain level of precision.

The uncertainty principle states that we can not measure the position ( x ) and the momentum ( p ) of a particle with undeniable accuracy. The more accurately we know one of those values, the less accurately we know the other. Multiplying together the errors in the measurements of these values (the errors are represented by the Greek letter “delta” ) has to give a number greater than or equal to half of a constant called “h-bar”. This is equal to Planck’s constant (usually written as h) divided by 2π. Planck’s constant is an important number in quantum theory, a way to measure the granularity of the world at its smallest scales and it has the value 6.626 x 10-34 joule seconds.

Quantum tunneling

Heisenberg’s concept can also clarify a form of nuclear radiation known as alpha decay. Alpha particles are two protons and two neutrons discharged by some heavy nuclei, for instance uranium-238. Typically these are bound inside the heavy nucleus and would need plenty of energy to break the bonds holding them in place. However, because an alpha particle inside a nucleus possesses a really distinct velocity, its position is not so well-defined.

This means that there is a small, yet non-zero, possibility that the particle could, at some point, find itself outside the nucleus, despite the fact that it technically does not have sufficient energy to escape. When this occurs – a process metaphorically known as “quantum tunneling” because the escaping particle has to somehow dig its way through an energy barrier that it cannot leap over – the alpha particle escapes and we see radioactivity.

A similar quantum tunneling process happens, in reverse, at the centre of our sun, where protons fuse together and release the energy that allows our star to shine. The temperatures at the core of the sun are not high enough for the protons to have enough energy to overcome their mutual electric repulsion. But, thanks to the uncertainty principle, they can tunnel their way through the energy barrier.

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