  While first-principles calculations with different levels of sophistication
predict a topologically trivial $Z_2$ state for bulk bismuth, some
photoemission experiments show surface states consistent with the
interpretation of bismuth being in a topologically non-trivial $Z_2$ state. We
resolve this contradiction between theory and experiment by showing, based on
quasiparticle self-consistent $GW$ calculations, that the experimental surface
states interpreted as supporting a non-trivial phase are actually consistent
with a trivial $Z_2$ invariant. We identify this contradiction as the result of
a crosstalk effect arising from the extreme penetration depth of the surface
states into the bulk of Bi. A film of Bi can be considered bulk-like only for
thicknesses of about 1000 bilayers ($\approx$ 400 nm) and more.
