  Discrepancies in the low-energy quasiparticle dispersion extracted from angle
resolved photoemission, scanning tunneling spectroscopy and quantum oscillation
data are common and have long haunted the field of quantum matter physics.
Here, we directly test the consistency of results from these three techniques
by comparing data from the correlated metal Sr$_2$RhO$_4$. Using established
schemes for the interpretation of the experimental data, we find good agreement
for the Fermi surface topography and carrier effective masses. Hence, the
apparent absence of such an agreement in other quantum materials, including the
cuprates, suggests that the electronic states in these materials are of
different, non-Fermi liquid like nature. Finally, we discuss the potential and
challenges in extracting carrier lifetimes from photoemission and quasiparticle
interference data.
