  Motivated by the issue of particle-hole symmetry for the composite fermion
Fermi sea at the half filled Landau level, Dam T. Son has made an intriguing
proposal [Phys. Rev. X {\bf 5}, 031027 (2015)] that composite fermions are
Dirac particles. We ask what features of the Dirac-composite fermion theory and
its various consequences may be reconciled with the well established
microscopic theory of the fractional quantum Hall effect and the 1/2 state,
which is based on {\em non-relativistic} composite fermions. Starting from the
microscopic theory, we derive the assertion of Son that the particle-hole
transformation of electrons at filling factor $\nu=1/2$ corresponds to an
effective time reversal transformation (i.e.
$\{\vec{k}_j\}$$\rightarrow$$\{-\vec{k}_j\}$) for composite fermions, and
discuss how this connects to the absence of $2k_{\rm F}$ backscattering in the
presence of a particle-hole symmetric disorder. By considering bare holes in
various composite-fermion $\Lambda$ levels (analogs of electronic Landau
levels) we determine the $\Lambda$ level spacing and find it to be very nearly
independent of the $\Lambda$ level index, consistent with a parabolic
dispersion for the underlying composite fermions. Finally, we address the
compatibility of the Chern-Simons theory with the lowest Landau level
constraint, and find that the wave functions of the mean-field Chern-Simons
theory, as well as a class of topologically similar wave functions, are
surprisingly accurate when projected into the lowest Landau level. These
considerations lead us to introduce a "normal form" for the unprojected wave
functions of the $n/(2pn-1)$ states that correctly capture the topological
properties even without lowest Landau level projection.
