  Observed at z = 4.601 and with L_bol = 3.5 x 10^14 Lsun, W2246-0526 is the
most luminous galaxy known in the Universe, and hosts a deeply-buried active
galactic nucleus (AGN)/super-massive black hole (SMBH). Discovered using the
Wide-field Infrared Survey Explorer (WISE), W2246-0526 is classified as a Hot
Dust Obscured Galaxy (Hot DOG), based on its luminosity and dust temperature.
Here we present spatially resolved ALMA [CII]157.7um observations of
W2246-0526, providing unique insight into the kinematics of its interstellar
medium (ISM). The measured [CII]-to-far-infrared ratio is ~2 x 10^-4, implying
ISM conditions that compare only with the most obscured, compact starbursts and
AGN in the local Universe today. The spatially resolved [CII] line is
strikingly uniform and very broad, 500-600 km/s wide, extending throughout the
entire galaxy over about 2.5 kpc, with modest shear. Such a large, homogeneous
velocity dispersion indicates a highly turbulent medium. W2246-0526 is unstable
in terms of the energy and momentum that are being injected into the ISM,
strongly suggesting that the gas is being blown away from the system
isotropically, likely reflecting a cathartic state on its road to becoming an
un-obscured quasar. W2246-0526 provides an extraordinary laboratory to study
and model the properties and kinematics of gas in an extreme environment under
strong feedback, at a time when the Universe was 1/10 of its current age: a
system pushing the limits that can be reached during galaxy formation.
