  We review the different proposals which have so far been made for the
holographic principle and the related entropy bounds and classify them into the
strong, null and weak forms. These are analyzed, with the aim of discovering
which may hold at the level of the full quantum theory of gravity. We find that
only the weak forms, which constrain the information available to observers on
boundaries, are implied by arguments using the generalized second law. The
strong forms, which go further and posit a bound on the entropy in spacelike
regions bounded by surfaces, are found to suffer from serious problems, which
give rise to counterexamples already at the semiclassical level. The null form,
proposed by Fischler, Susskind, Bousso and others, in which the bound is on the
entropy of certain null surfaces, appears adequate at the level of a bound on
the entropy of matter in a single background spacetime, but attempts to include
the gravitational degrees of freedom encounter serious difficulties. Only the
weak form seems capable of holding in the full quantum theory.
  The conclusion is that the holographic principle is not a relationship
between two independent sets of concepts: bulk theories and measures of
geometry vrs boundary theories and measures of information. Instead, it is the
assertion that in a fundamental theory the first set of concepts must be
completely reduced to the second.
