Zenith Grant Awardee
Dr. John Baez
University of California at Riverside
Project Title
Categorifying Fundamental Physics
Project Summary
In ordinary mathematics, and physics as well, equations are fundamental. However, every equation is a half-truth: after all, if the two sides of the equation look different, why are we saying they're the same? 'Categorification' is a fancy name for coming clean on this issue: instead of merely saying that two things are the same, we specify a way of regarding them as the same.
This has surprising consequences. For example, we usually think of quantities like energy as continuously variable, or 'analog'. Quantum mechanics shows there is a certain discreteness built into the world, but it still uses analog ideas. Using categorification, we can phrase large portions of quantum mechanics in a purely discrete way. We want to know how far we can push this.
In addition to thinking about physics in new ways, we shall explore new methods of carrying out research. We intend to share not just our results, but the process by which we find them. We will do this by incorporating a wide range of multi-media into our research, including videos of lectures and seminars made publicly available online.
Technical Abstract
The goal of this program is to develop a radically new understanding of the mathematics underlying physical theories. Our main tool will be categorification. Traditional mathematics takes the concept of equality as fundamental. Categorification replaces equations by isomorphisms: instead of merely saying that two things are the same, we specify a way of regarding them as the same. This is a surprisingly powerful change of viewpoint.
Our program has three components. First, we are developing a version of quantum mechanics in which Hilbert spaces are replaced by purely combinatorial structures. Second, we are categorifying classical mechanics and geometric quantization, which leads naturally to a generalization of these ideas from point particles to extended objects. Third, we are studying the role of 'exceptional' algebraic structures, such as the octonions and exceptional Lie groups, in of particle physics.
In addition to thinking about physics in new ways, we shall explore new methods of carrying out research. We intend to share not just our results, but the process by which we find them. We will do this by incorporating a wide range of multi-media into our research, including videos of lectures and seminars made publicly available online.
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.