A Triadic Theory of Elementary Particle Interactions and Quantum Computation (review)

The work and its authors

The book under review is quite an unusual production in more ways than one. It is the fruit of a remarkable collaboration between a theoretical physicist (Ralph Beil) and a well-known philosopher and Peirce scholar (Kenneth Ketner). Beil and Ketner (from now on B&K) are undertaking an ambitious program to develop a new interpretation of quantum theory and ultimately of the entire standard model of particle physics. Their efforts are partially based on Peirce’s relational logic along with several of his other philosophical ideas, suitably combined with some original conceptions in theoretical physics which Beil has been proposing since earlier publications. B&K have previously collaborated on a physics article, “Peirce, Clifford and Quantum Theory” (2003)¹ and jointly hold United States Patent 6,819,474 (2004). This patent records their invention of the trisistor, a new quantum switching device to be used in quantum computation and conceived as a technological application of ideas advanced in their book.

It is not clear why the authors decided to publish this work as a bound monograph instead of as an article in a professional journal. The length of the text—including figures, tables and bibliography—is scarcely fifty pages, and B&K have not taken advantage of the monograph format by including an index or a supplemental glossary that defines the many and difficult technical terms used. These choices may consequently restrict the potential readership of a work requiring thoughtful examination by physicists and philosophers alike. A future, publicly accessible electronic version would go a long way in remedying these shortcomings.

The Work’s Contents

There is a one-page preface, followed by a brief introduction that acquaints the reader with many of Peirce’s scientific and philosophical achievements and supplies references for further study. That, with very few exceptions, Peirce’s ideas were not influential in the development of 20th century physics is noted. B&K hope to rectify this situation with the introduction of the models advanced in the work at hand. Following an introductory outline is an enumeration of the topics to be covered in the remaining sections II through VII.

Section II outlines Peirce’s theory of relations and explains clearly the framework on which the proposed models are built. Emphasis is placed on triadic structures displayed in diagrammatic form, on their paradigmatic instantiation within the sign relation, and on the features of valence and bonding. The irreducibility of triadic to dyadic relations is also emphasized. Peirce’s conception of the relational nature of reality and his use of the term existence to refer to a special case of reality are also duly explained.

Section III, entitled “Time Symmetry, Advanced Potentials and Needle Radiation,” introduces these three concepts through extremely condensed characterizations buttressed with abundant references to the physics literature. Time symmetry refers to the fact that fundamental theories contain no counterpart to our common-sense distinction between the forward and backward directions in time. Advanced potentials result from the associated fact that the equations of classical and quantum electrodynamics admit forward (retarded) as well as backward (advanced) solutions, according to the two time directions. While consideration of these two concepts is quite prominent and of wide-ranging consequences in contemporary philosophy of science, needle radiation (developed by Einstein) is an almost forgotten conception. While spherical radiation propagates in all directions, needle radiation travels along a linear path as a narrow wave bundle of limited extension, thus serving as a model for an elementary particle in the authors’ proposals.

Section IV, “Physical Preliminaries,” surveys at breathtaking speed several other facts and assumptions on the dispersion and spreading of wave packets, which B&K require for developing a quantum theory concerning individual particles instead of probabilities.

Section V, “Triadic Relations and Elementary Particles,” is the centerpiece of the work. B&K conceive elementary particles as chains of bonded signs that are somehow embodied in space-time. These triadic...