  It is believed that a primary principle of the theory of quantum gravity is
the Holographic Principle according to which a physical system can be described
only by degrees of freedom living on its boundary. The generalized covariant
formulation of the principle considers the entropy content on truncated
light-sheets: light-like hypersurfaces of non-positive expansion orthogonally
generated from a boundary. When we construct the truncated light-sheets for
cosmological observers we find a general expression for the minimum cosmic time
interval from the apparent horizon to verify the holographic prescription; this
minimum time is related to quantum effects involved in the entropy computation.
Finally, we arrive to the uncertainty relation from the Holographic Principle,
which suggests a deep connection between general covariance, entropy bounds and
quantum mechanics.
