  The strange-metal phase of the cuprate high temperature superconductors,
above where the superconductivity sets in as a function of temperature, is
widely considered more exotic and mysterious than the superconductivity itself.
Here, based upon detailed angle resolved photoemission spectroscopy
measurements of Bi$_2$Sr$_2$CaCu$_2$O$_8$$_+$$_\delta$ over a wide range of
doping levels, we present a new unifying phenomenology for the non-Fermi liquid
normal-state interactions (scattering rates) in the nodal direction. This new
phenomenology has a continuously varying power law exponent (hence named a
Power Law Liquid or PLL), which with doping varies smoothly from a quadratic
Fermi Liquid to a linear Marginal Fermi Liquid and beyond. Using the extracted
PLL parameters we can calculate the optics and resistivity over a wide range of
doping and normal-state temperature values, with the results closely matching
the experimental curves. This agreement includes the presence of the
$"$pseudogap$"$ temperature scale observed in the resistivity curves including
the apparent quantum critical point. This breaks the direct link to the
pseudogapping of antinodal spectral weight observed at similar (but here argued
to be different) temperature scales, and also gives a new direction for
searches of the microscopic mechanism at the heart of these and perhaps many
other non-Fermi-liquid systems.
