  In this thesis, I introduce a new bottom-up approach to quantum field theory
and collider physics, beginning from the observable energy flow: the energy
distribution produced by particle collisions. First, I establish a metric space
for collision events by comparing their energy flows. I unify many ideas
spanning multiple decades, such as observables and jets, as simple geometric
objects in this new space. Second, I develop a basis of observables by
systematically expanding in particle energies and angles, encompassing many
existing observables and uncovering new analytic structures. I highlight how
the traditional criteria for theoretical calculability emerge as consistency
conditions, due to the redundancy of describing an event using particles rather
than its energy flow. Finally, I propose a definition of particle type, or
flavor, which makes use of only observable information. This definition
requires refining the notion of flavor from a per-event label to a statistical
category, and I showcase its direct experimental applicability at colliders.
Throughout, I synthesize concepts from particle physics with ideas from
statistics and computer science to expand the theoretical understanding of
particle interactions and enhance the experimental capabilities of collider
data analysis techniques.
