The Quantum Universe_ Everything That Can Happen Does Happen - Brian Cox [26]
Heisenberg’s Uncertainty Principle
Heisenberg’s Uncertainty Principle is one of the most misunderstood parts of quantum theory, a doorway through which all sorts of charlatans and purveyors of tripe4 can force their philosophical musings. He presented it in 1927 in a paper entitled ‘Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik’, which is very difficult to translate into English. The difficult word is anschaulich, which means something like ‘physical’ or ‘intuitive’. Heisenberg seems to have been motivated by his intense annoyance that Schrödinger’s more intuitive version of quantum theory was more widely accepted than his own, even though both formalisms led to the same results. In the spring of 1926, Schrödinger was convinced that his equation for the wavefunction provided a physical picture of what was going on inside atoms. He thought that his wavefunction was a thing you could visualize, and was related to the distribution of electric charge inside the atom. This turned out to be incorrect, but at least it made physicists feel good during the first six months of 1926: until Born introduced his probabilistic interpretation.
Heisenberg, on the other hand, had built his theory around abstract mathematics, which predicted the outcomes of experiments extremely successfully but was not amenable to a clear physical interpretation. Heisenberg expressed his irritation to Pauli in a letter on 8 June 1926, just weeks before Born threw his metaphorical spanner into Schrödinger’s intuitive approach. ‘The more I think about the physical part of Schrödinger’s theory, the more disgusting I find it. What Schrödinger writes about the Anschaulichkeit of his theory … I consider Mist.’ The translation of the German word mist is ‘rubbish’ or ‘bullshit’ … or ‘tripe’.
What Heisenberg decided to do was to explore what an ‘intuitive picture’, or Anschaulichkeit, of a physical theory should mean. What, he asked himself, does quantum theory have to say about the familiar properties of particles such as position? In the spirit of his original theory, he proposed that a particle’s position is a meaningful thing to talk about only if you also specify how you measure it. So you can’t ask where an electron actually is inside a hydrogen atom without describing exactly how you’d go about finding out that information. This might sound like semantics, but it most definitely is not. Heisenberg appreciated that the very act of measuring something introduces a disturbance, and that as a result there is a limit on how well we can ‘know’ an electron. Specifically, in his original paper, Heisenberg was able to estimate what the relationship is between how accurately we can simultaneously measure the position and the momentum of a particle. In his famous Uncertainty Principle, he stated that if Δx is the uncertainty in our knowledge of the position of a particle (the Greek letter Δ is pronounced ‘delta’, so Δx is pronounced ‘delta x’) and Δp is the corresponding uncertainty in the momentum, then
where h is Planck’s constant and the ‘∼’ symbol means ‘is similar in size to’. In words, the product of the uncertainty in the position of a particle and the uncertainty in its momentum will be roughly equal to Planck’s constant. This means that the more accurately we identify the location of a particle, the less well we can know its momentum, and vice versa. Heisenberg came to this conclusion