  We use the interpolating coordinates studied by Hornbostel to investigate a
transition from equal-time quantization to light-front quantization, in the
context of two-dimensional $\phi^4$ theory. A consistent treatment is found to
require careful consideration of vacuum bubbles, in a nonperturbative extension
of the analysis by Collins. Numerical calculations of the spectrum at fixed box
size are shown to yield results equivalent to those of equal-time quantization,
except when the interpolating coordinates are pressed toward the light-front
limit. In that regime, a fixed box size is inconsistent with an accurate
representation of vacuum-bubble contributions and causes a spurious divergence
in the spectrum. The light-front limit instead requires the continuum
momentum-space limit of infinite box size. The calculation of the vacuum energy
density is then shown to be independent of the interpolation parameter, which
implies that the light-front limit yields the same spectrum as an equal-time
calculation. This emphasizes the importance of zero modes and near-zero modes
in a light-front analysis of any theory with nontrivial vacuum structure.
