  In an effort to locate the sites of emission at different frequencies and
physical processes causing variability in blazar jets, we have obtained high
time-resolution observations of BL Lacertae over a wide wavelength range: with
the \emph{Transiting Exoplanet Survey Satellite} (TESS) at 6,000-10,000 \AA\
with 2-minute cadence; with the Neil Gehrels \emph{Swift} satellite at optical,
UV, and X-ray bands; with the Nuclear Spectroscopic Telescope Array at hard
X-ray bands; with the \emph{Fermi} Large Area Telescope at $\gamma$-ray
energies; and with the Whole Earth Blazar Telescope for measurement of the
optical flux density and polarization. All light curves are correlated, with
similar structure on timescales from hours to days. The shortest timescale of
variability at optical frequencies observed with TESS is $\sim 0.5$ hr. The
most common timescale is $13\pm1$~hr, comparable with the minimum timescale of
X-ray variability, 14.5 hr. The multi-wavelength variability properties cannot
be explained by a change solely in the Doppler factor of the emitting plasma.
The polarization behavior implies that there are both ordered and turbulent
components to the magnetic field in the jet. Correlation analysis indicates
that the X-ray variations lag behind the $\gamma$-ray and optical light curves
by up to $\sim 0.4$ days. The timescales of variability, cross-frequency lags,
and polarization properties can be explained by turbulent plasma that is
energized by a shock in the jet and subsequently loses energy to synchrotron
and inverse Compton radiation in a magnetic field of strength $\sim3$ G
