The fact that quantum mechanics and general relativity are seemingly incompatible hampers our current understanding of the laws of physics.

The efforts of generations of scientists conceived formidable approaches to fill such a gap, but the problem is that we are very far from any possibility of an experimental test. Here we will investigate a new approach for to the physical description of a photon. This approach is aimed to demonstrate that some of the mentioned novel and sophisticated concepts are testable in the laboratory.

This grant is an investment to develop experimental tests of quantum gravity concepts and for obtaining inspiration for their use in practical applications. The most important physical theories are valid from the scale of the single atom to the astronomical distances. These theories have been developed by reasoning on simple experiments in the laboratory, and our hypothesis is that this may also be true for quantum gravity.

The idea is based on recent generalizations of the uncertainty principle, and on re-formulating optical propagation in a way that naturally includes ideas of quantum gravity and noncommutative geometry. This formulation may largely enrich our description of the photon.

In this optical analogue, we will test some concepts of the generalizations of quantum mechanics arising from quantum gravity. We also hope to be inspired by these investigations to develop novel applications, in particular, in the field of microscopy.

The outputs are: (i) a one-dimensional mathematical formulation of the photon propagation equations in term of the generalized uncertainty principle; (ii) a theory based non-commutative geometry enabling to treat the propagation of ultra-focused time beam; (iii) the design of laboratory experiments to test quantum gravity ideas; (iv) the first quantum gravity inspired applications.

The goal is changing our vision of light with an enduring impact in fundamental physics.