  The classical approach to spacetime singularities leads to a simplified
dynamics in which spatial derivatives become unimportant compared to time
derivatives, and thus each spatial point essentially becomes uncoupled from its
neighbors. This uncoupled dynamics leads to sharp features (called "spikes") as
follows: particular spatial points follow an exceptional dynamical path that
differs from that of their neighbors, with the consequence that, in the
neighborhood of these exceptional points, the spatial profile becomes ever more
sharp. Spikes are consequences of the BKL-type oscillatory evolution towards
generic singularities of spacetime. Do spikes persist when the spacetime
dynamics is treated using quantum mechanics? To address this question, we treat
a Hamiltonian system that describes the dynamics of the approach to the
singularity and consider how to quantize that system. We argue that this
particular system is best treated using an affine quantization approach (rather
than the more familiar methods of canonical quantization) and we set up the
formalism needed for this treatment. Our investigation, based on this affine
approach, shows the nonexistence of quantum spikes.
