Copenhagen, part 3

Now for the contributions that Niels Bohr and Werner Heisenberg made to quantum mechanics.

Werner Heisenberg introduced the uncertainty principle in 1927: one cannot precisely know both the position and momentum of a subatomic particle at the same time. In fact, the more precisely one knows one quantity, the less precisely one knows the other.

This was a revolutionary idea. It is a basic premise of science that if one knows the present state of a system, one can use the laws of motion to predict future states. Scientists had previously assumed that any limitation in their ability to predict future states (think predicting the weather) was due to a combination of: a) the inexactness of their instruments in measuring the present state, and b) the sheer complexity of the calculations. What Heisenberg said was that in addition to those limitations, there are inherent limitations on what is knowable about the present state, at least at the subatomic level, even if we had perfect instruments.

Niels Bohr made many contributions to quantum mechanics. The contribution which figures prominently in the play is the principle of complementarity: any quantum object has both a wave nature and a particle nature, and there is a trade-off between them. Hence the wave-particle duality of subatomic particles described in the previous post. Furthermore it is the act of measurement, of observing, that determines what is manifested.

One aspect of both of these principles is that the world is not deterministic, as was thought by previous generations of scientists such as Sir Isaac Newton. The world is probabilistic, at least at the subatomic level. Quantum outcomes can be predicted only as probabilities.

This way of thinking about quantum mechanics became known as the Copenhagen Interpretation.

Heisenberg was mathematically gifted; he invented the matrix algebra used in one formulation of quantum mechanics. Bohr was more inclined to describe things in words. (According to the play, so that Margrethe could understand.) But as Heisenberg aptly noted, "Our words don't fit." (source, p. 150)