  Heisenberg showed in the early days of quantum theory that the uncertainty
principle follows as a direct consequence of the quantization of
electromagnetic radiation in the form of photons. As we show here the
gravitational interaction of the photon and the particle being observed
modifies the uncertainty principle with an additional term. From the modified
or gravitational uncertainty principle it follows that there is an absolute
minimum uncertainty in the position of any particle, of order of the Planck
length. A modified uncertainty relation of this form is a standard result of
superstring theory, but the derivation given here is based on simpler and
rather general considerations with either Newtonian gravitational theory or
general relativity theory.
