  The canonical approach to quantizing quantum gravity is understood to suffer
from pathological non-renomalizability. Nevertheless in the context of
effective field theory, a viable perturbative approach to calculating
elementary processes is possible. Some non-perturbative approaches, most
notably loop quantum gravity and combinatorial quantum gravity imply the
existence of a minimal length. To circumvent the seeming contradiction between
the existence of a minimum length and the principle of special relativity,
Double Special Relativity introduces modified dispersion relationships that
reconcile the conflict. In this work, we combine these dispersion relationships
with an effective field theory approach to compute the first post Newtonian
correction to the bending of light by a massive object. The calculation offers
the prospect of a directly measurable effect that rests upon both the existence
of a quantized gravitational field and a minimal length. Experimental
verification would provide evidence of the existence of a quantum theory of
gravity, and the fundamental quantization of spacetime with a bound on the
minimal distance.
