Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik

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   You cannot know at the same time, however good your instruments, exactly where a particle is and exactly how fast it moves. It is not a clumsy instrument but a property of every wave, and it is precisely what keeps atoms from collapsing.

   Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik · 1927

   Like a short beep with no clear note, a well-localised particle cannot have a precise speed.

   Werner Heisenberg was 25 when he wrote, in 1927, that the position and the speed of a particle cannot both be known to arbitrary precision. His first explanation was a microscope: to see an electron you must hit it with light, and the hit pushes it. The picture is useful but incomplete. The uncertainty remains with no instrument at all, because it comes from the particle behaving like a wave. Think of sound. A very short beep, like a click, tells you exactly when it happened, but it has no clear note: it is a blend of many frequencies. A long note, held for a few seconds, has a precise pitch, but you can no longer say ‘when’ it was, because it is spread out in time. No sound is both very short and perfectly in tune. In the same way, a matter wave squeezed into a small place has very mixed speeds, and a wave with a precise speed is spread over a large region. This leads to something important: atoms do not collapse. The electron is attracted to the nucleus and would like to fall into it. But if it were squeezed too close, its speed would become very uncertain, which means very large on average, and it would carry too much energy of motion. The atom finds a balance between the attraction and this ‘jitter’ imposed by uncertainty, and that balance sets its size. For everyday objects the effect is so tiny that you never feel it.

   “The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa.”

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