The meeting was controversial, as both men were working on nuclear fission.
No-one knows what was said between the two, but Frayn's play creates three possible scenarios. Each one is believable, but we will never know which - if any of them - is true.
Heisenberg is famous for his 'Uncertainty Principle', which essentially says that as soon you touch or move something, it's never the same again.
This was particularly true when studying the structure of atoms, which is where both Heisenberg and Bohr did much of their early work.
Frayn's play says this is also true of human beings. There are always at least two sides to a story and there is no single truth - just the reality according to each person involved.
Frayn links science to human nature in a way that I found interesting and thought-provoking. There's a parallel between the uncertainty of science and the uncertainty of human relationships.
Ultimately, the play brought home to me the fact that there will never be just one final answer, and also the realisation that one has to accept the need to live with this uncertainty.
Anne Glover is chief executive of Amadeus Capital Partners and chairman of the British Venture Capital Association.