What is meant by the last line of Copenhagen by Michael Frayn, not according to science, but according to the play itself?
The final line of Copenhagen refers to the "final core of uncertainty at the heart of things."
In this limited space, this question is going to be difficult to fully answer because "uncertainty' is a central theme and, in an interesting complex stylistic choice, reflects many motifs. One motif of uncertainty is Heisenberg's personal uncertainty, another is the uncertainty theory of physics, and a third is the moral uncertainty worrying Hesienberg. For this format, addressing the moral uncertainty troubling Heisenberg is the best single motif to examine.
Bohr With careful casualness he begins to ask the question he's prepared.
Heisenberg Does one as a physicist have the moral right to work on the practical exploitation of atomic energy?
Margrethe The great collision.
Heisenberg is engaged in a project exploring the "practical exploitation of atomic energy," He comes to Copenhagen expressly to ask Bohr the question quoted above. The phrase is not one with a vague, hypothetical meaning, but rather it possesses a specific and well understood meaning. It is a euphemism. Bohr understands this and he understands the euphemism, that is why he stops in his tracks, looks "horrified," and abruptly walks away toward home. The euphemistic phrase "practical exploitation of atomic energy" means, precisely, building an atomic bomb, an atomic weapon of warfare, nothing else. Thus what Heisenberg asks that so horrifies Bohr is: Is it moral for a physicist to build an atomic bomb?
This is Heisenberg's moral dilemma. This is not a moral dilemma for Bohr. He knows the answer within himself already. He is horrified that (1) a bomb is being built and he is horrified that (2) Heisenberg does not know the answer within himself already.
Margrethe [W]hat will be left of our beloved world? Our ruined and dishonoured and beloved world?
Heisenberg But in the meanwhile, in this most precious meanwhile, there [our world] is. ... Our children and our children's children. Preserved, ... By that final core of uncertainty at the heart of things.
The last line, shown in abbreviated context above, refers to Heisenberg's question about moral uncertainty. It refers to how that moment in Copenhagen with a horrified Bohr may have been the pivotal moment in human history that prevented Germany from building and deploying the atomic bomb first and destroying "London ... Paris ... Amsterdam. Perhaps Copenhagen." The last line complexly combines and alludes to all the "uncertainty" motifs but ultimately refers to the moral uncertainty that lies at the heart of all complex human endeavor.