Butterflies on the Stretched Horizon

Understand

In this paper I return to the question of what kind of perturbations on Alice's side of an Einstein-Rosen bridge can send messages to Bob as he enters the horizon at the other end.

• By definition "easy" operators do not activate messages and "hard" operators do, but there are no clear criteria to identify the difference between easy and hard.
• In this paper I argue that the difference is related to the time evolution of a certain measure of computational complexity, associated with the stretched horizon of Alice's black hole.
• The arguments suggest that the AMPSS commutator argument is more connected with butterflies than with firewalls.