Cold in quantum

One of the principles of quantum mechanics is called the Heisenberg uncertainty principle, which (colloquially) states that we cannot know where something is and how fast it’s moving at the same time.  This arises because we realised that all things, matter included, have wave-like properties.  


If we think about the familiar kinds of waves, those spreading from a pebble dropped into a pond, for instance, we realise that it doesn’t make sense to say that a wave exists at any one point -- it is necessarily spread out over some region in space.  If we were to “localise” the wave, that is, to make it exist in just one part of the pond at a time, we would need to add together many different waves, all of different wavelengths (and, thus, speeds), to have them add up in just such a way as to have the peaks travel together.  In the former case, we can know that there’s only one speed associated with the wave, but can’t say “where” the wave is; and in the latter, we know where it is, but we can’t say that there’s a particular speed of the wave.

Matter waves are governed by the same principles.  The limit on the knowledge of the positions and speeds is dictated by a universal constant ħ, known as “Planck’s constant,” which describes the fundamental unit of momentum.  Mathematically, we say that the limit of our knowledge of the position 𝜹x and the limit of our knowledge of momentum 𝜹p (where p = mv, and m is the mass, and v is the speed) is the product of the uncertainties in these quantities.

By cooling the atoms, we slow them down.  And when they’re slow, the speeds actually become so small that the uncertainties are also very small, and we start to run into this fundamental limit.  As we run into it, the uncertainty in position increases, eventually to the point where one atoms overlaps the next, and we can no longer give each atom an individual identity -- they start to act together and quantum mechanics governs their behaviour.

© Lindsay J LeBlanc 2013