Zenith Grant Awardee
Dr. Jenny Harrison
University of California at Berkeley
Project Title
Axioms of Calculus and Mechanics
Project Summary
We present axioms of calculus that unify the discrete and the smooth continuum with applications to fractals, soap films, charged particles, and smooth manifolds. Properties that follow from the axioms include broad generalizations of the integral theorems of calculus that are equally valid for the above domains. A goal for the period of this grant is to establish similar axioms of mechanics that unify the quantum and classical viewpoints.
Technical Abstract
We present axioms of calculus that unify the discrete and the smooth continuum with applications to fractals, soap films, charged particles, and smooth manifolds. Properties that follow from the axioms include broad generalizations of the integral theorems of calculus that are equally valid for the above domains. Emerging from the axioms is a new derivative and integral called prederivative and preintegral. The first takes on the role of weak derivative of distributions and permits us to multiply singular distributions without a contradiction of mathematics. Preintegral together with prederivative suggest a way to formalize conservation of energy in a curved space. Hodge decomposition in our category leads to rigorous proof of the existence of the Coulomb field and Maxwell's equations. A similar proof shows how 2-dimensional shell fields form a dynamic fabric of space. We find new representations of the CCR with physical realism using prederivative and its adjoint. A goal for the period of this grant is to establish similar axioms of mechanics that unify the quantum and classical viewpoints.
QSpace Latest
PressRelease: Shining a light on the roots of plant “intelligence”
All living organisms emit a low level of light radiation, but the origin and function of these ‘biophotons’ are not yet fully understood. An international team of physicists, funded by the Foundational Questions Institute, FQxI, has proposed a new approach for investigating this phenomenon based on statistical analyses of this emission. Their aim is to test whether biophotons can play a role in the transport of information within and between living organisms, and whether monitoring biophotons could contribute to the development of medical techniques for the early diagnosis of various diseases. Their analyses of the measurements of the faint glow emitted by lentil seeds support models for the emergence of a kind of plant ‘intelligence,’ in which the biophotonic emission carries information and may thus be used by plants as a means to communicate. The team reported this and reviewed the history of biophotons in an article in the journal Applied Sciences in June 2024.