Identical quantum particles (such as Fermions and Bosons) have intriguing statistical properties (Bose statistics and Fermi statistics) that raise serious issues for naive philosophical accounts of identity. The predominant context for interpretive studies of identical particles has been basic quantum mechanics. The PIs propose to develop an interpretive study in the context of quantum field theory, which is more fundamental. The study involves a theory of superselection developed in the algebraic formulation of quantum field theory by Doplicher, Haag, and Roberts. The theory provides a mathematical explaination of superselection, which would otherwise be a postulated set of rules that forbid the preparation of a superposition of states associated with different types of identical particles. They plan to focus attention on two research questions. The first concerns whether superselection theory (in the algebraic formulation of quantum field theory) provides a more fundamental explanation for why systems obey Bose rather than Fermi statistics (for example). The second addresses how scientific results involving identical particles are to be understood in quantum field theory, in light of powerful arguments against the existence of particles.
Intellectual Merit. This project will bring the philosophy of quantum field theory into contact with long-standing problems in the philosophy of quantum mechanics. Quantum field theory has been the source of many novel conceptual problems, particularly (though not solely) having to do with the existence of unitarily inequivalent representations of the theory. This has led to much fruitful research, but also to a lack of engagement between philosophy of quantum field theory and work on quantum mechanics, even in areas where the study of quantum field theory should bear on the older debates. The metaphysics of statistics is one such largely-neglected area.
Broader Impacts This is a deeply interdisciplinary project that brings together aspects of philosophy, modern physics, and mathematics. It proceeds in a spirit of cooperative (rather than critical) exchange between these fields, and it will contribute to enhancing constructive developments at some crucial points of contact between science and philosophy of science. The results of this project will prove to be of interest to mathematicians, physicists, and philosophers of science. The project also integrates teaching and research; the senior researcher plans to teach a graduate seminar on the subject matter of the project; the junior researcher will participate in teaching the course.
Our project explored the so-called "statistics" of quantum theories--usually understood as the property that determines what happens when the theory's particles are interchanged. You might have heard it said that any two fundamental particles of the same type (like two electrons or two photons) are exactly identical. This is because of their statistics. Matter particles like electrons are grouped into a statistical category called fermions, while force-carriers like photons are bosons. This popular gloss on the nature of statistics can't be exactly true, though. In the most realistic quantum field theories, like the ones used to predict high-energy events in accelerators, the picture of reality in terms of "particles" is only a useful approximation. The first stage of our project was to explicate how statistics can be understood precisely in light of the fact that there are no particles, strictly speaking, at the level of our most fundamental quantum theory. This question is philosophically rich because the popular description of statistics in terms of particles has led many philosophers to conclude that the notion of idividuality is somehow altered or eliminated by quantum theory. We have shown that this is not the case, since the particle picture is not entirely accurate. Next we considered an exotic variety of theoretically possible particle known as paraparticles. These are particles which are neither bosons nor fermions, but exhibit some aspects of both types. In nature, there appear to be no paraparticles, which is to say we don't need to posit them in our theories in order to explain known experimental data. This has been seen as a deep mystery, but it has also been claimed that paraparticle theories are always equivalent to theories with ordinary bosons and fermions if one writes them in the correct mathematical notation. These arguments for equivalence have not been very detailed or thorough, however. Exploring this question, we found that the arguments could be made fully rigorous. Therefore, paraparticles are indeed a notational variant of regular boson and fermion theories, and so there is no mystery about their apparent nonexistence. As the reader may have already surmised, this project has been interdisciplinary at its core, drawing from mathematics and physics as well as philosophy. In the long term, we hope that this intellectual cross-pollination will help to improve the climate at the points of interaction between science and the humanities. In the past, much of the contact between humanists and scientists has proceeded in a spirit of criticism. We expect that our project, along with others like it, will lead to progress in the direction of more cooperative and less antagonistic contact.
