Dean Waters Research

Current Projects

Exploring time-centric perspectives as alternatives to mass-centric and/or energy-centric perspectives

Exploring methods of bridging the static Event-time of QFT Fock States and the more familiar Parameter-Time used in calculations involving evolving wavefront. (Image of the Clifford Hopf Bundle from Roger Penrose's Road to Reality, the core of a twistor)

Twistor Structure

Illustration of the geometry of Roger Penrose's twistor focusing on the concept of 'fibration' which brings the energy-aspect of photon Fock state into 'direct contact' with 'tips' of spin-carrying fibers when they are projected onto the surface of an expanding Complex-Projective Riemann 2-sphere.

In General Relativity, the 2-sphere is also known as the Celestial Sphere.

About Dean

Constructing a toy model of the photon Fock State starting from known behaviors and physical attributes without first choosing a preferred mathematical framework. Modern theory relying heavily on manifolds, this work draws on the geometric intuition and fascination with 'complex number magic' espoused by Roger Penrose in his tome The Road to Reality: A Complete Guide to the Laws of the Universe.

For much of human history, geometry was considered core to mathematical understanding. With the increasing success of pure math and computer calculations, advanced math texts during the era of my education were nearly completely devoid of two things: Helpful Imagery and Practical Applications.

Without Penrose's incredible series of hand drawings, pointing out the geometric intuition behind virtually every mathematical concept from integers to complex-dimensional manifolds, step by step by step, image by image by image until this math-challenged 'kid' found his intellectual home in the world of twistor geometry.