 Another problem for the Anti-de Sitter spacetime is that a “divergent blueshift” phenomenon occurs. Intuitively, the frequency of any signal Bob sends to Alice is amplified more and more as he goes along. Eventually, even the slightest thermal noise will be amplified to such an extent that communication is all but impossible. So, if the counterexample to Goldbach’s conjecture comes late in the game (or not at all), it is not clear that Alice can ever know this. 