In analogy with Planck’s construction of fundamental quantities in gravitation, we construct fundamental quantities associated with (1) theories of electrodynamics in which the electromagnetic field has a maximum value (e.g. Born-Infeld theory), and (2) the Fermi interaction. This gives us a maximum intensity of the electromagnetic field, and also reveals a close relationship between the fundamental lengths associated with the gravitational and weak interactions, supporting the connection between these two interactions.

We propose a new approach to describe quantum mechanics as a manifestation of non-Euclidean geometry. In particular, we construct a new geometrical space that we shall call Qwist. A Qwist space has a extra scalar degree of freedom that ultimately will be identified with quantum effects. The geometrical properties of Qwist allow us to formulate a geometrical version of the uncertainty principle. This relativistic uncertainty relation unifies the position-momentum and time-energy uncertainty principles in a unique relation that recover both of (...) them in the non-relativistic limit. (shrink)