  A proposal for resolving the black hole information paradox was recently put
forward by 't Hooft in the form of his firewall transformation. Although this
proposal has begun to gain some limited traction, its physical foundation is
still somewhat obscure. Here we develop a classical Hamiltonian analog, which
is oriented towards quantization, by using the canonical formalism developed by
Arnowitt, Deser, and Misner (ADM). We use a model of two null, spherical shells
in a Schwarzschild black hole background, and within our ADM formalism we are
able to characterize the dynamics of the entire system, especially at the point
of collision, and we reproduce the related Dray-'t Hooft-Redmount formula.
Finally, we are able to find a classical analog for 't Hooft's firewall
transformation. Unlike 't Hooft's firewall transformation and previous
classical analogs, the classical firewall transformation we obtain is free from
approximation and maintains the coordinate independence of the ADM formalism.
We leave to future work the quantization of the theory.
