  In this work, we find the light front densities for momentum and forces,
including pressure and shear forces, within hadrons. This is achieved by
deriving relativistically correct expressions relating these densities to the
gravitational form factors $A(t)$ and $D(t)$ associated with the energy
momentum tensor. The derivation begins from the fundamental definition of
density in a quantum field theory, namely the expectation value of a local
operator within a spatially-localized state. We find that it is necessary to
use the light front formalism to define a density that corresponds to internal
hadron structure. When using the instant form formalism, it is impossible to
remove the spatial extent of the hadron wave function from any density, and --
even within instant form dynamics -- one does not obtain a Breit frame Fourier
transform for a properly defined density. Within the front formalism, we derive
new expressions for various mechanical properties of hadrons, including the
mechanical radius, as well as for stability conditions. The multipole ansatz
for the form factors is used as an example to illustrate all of these findings.
