March 2022
A Comment on the "Photon position operator with commuting components" by Margaret Hawton
We show that the position operator with commuting components proposed by M. Hawton [M. Hawton, Phys. Rev. A {f 59}, 954 (1999)] and developed in subsequent papers does not have all of the properties required for a photon position operator. Depending on the exact interpretation of the results it either concerns a triplet of massless spin zero part...
July 2020
On the existence of the time operator in mathematical quantum theory
The purpose of this thesis is to answer the question about the existence of the time operator in mathematical quantum theory. The issues of time itself and, primarily, the time operator in non-relativistic and relativistic quantum mechanics are discussed.
February 2022
June 2023
Plotinus, Category Theory and Quantum Theory
In this paper, we embark on a nuanced journey that threads the strands of philosophy, mathematics, and physics together through the robust lens of category theory. Our mission is to present novel interpretations of Plotinus's theory of the soul, Proclus's Neoplatonic Syllogistic, and Bohm's theory of wholeness and the implicate order. Furthermore, we explore the connections between these theories and quantum field theory, as well as Hegel's philosophical thought.
Category theory, with its focus on morphisms and structures, is ideally suited to shed light on the abstract connections across these disciplines. Through this theoretical framework, we aim to reveal the intrinsic parallels, weave a unifying narrative, and provide a common ground for interdisciplinary dialogue.
We begin our exploration with Plotinus's philosophical work, wherein he proposes a comprehensive model of the Soul and its intricate relationships with the Body and Intellect. This tripartite model provides a fertile ground to apply the principles of category theory, offering new insights into Plotinus's metaphysics.
We then turn to Proclus's Neoplatonic Syllogistic, a sophisticated system of logic that further develops the ideas of Plotinus. The structure of Proclus's syllogistic is remarkably akin to the categorical compositions, which invites an exciting avenue for research.
On the other side of the spectrum, we delve into the world of physics with Bohm's theory of wholeness and the implicate order, which presents a revolutionary perspective on the universe's interconnectedness. By recasting these concepts within the framework of monoidal categories, we attempt to marry Bohm's philosophical musings with the precise language of mathematics.
Our analysis further extends to quantum field theory, an essential pillar of modern physics. We explore how category theory can provide a new mathematical lens to interpret quantum fields, potentially bridging the gap between quantum mechanics and general relativity.
In the realm of philosophy, we consider Hegel's idealist thought as an extension of Plotinus's metaphysics. Hegel's dialectical method and his concepts of the Absolute Idealism can be seen as a philosophical analogue to the abstract reasoning in category theory, offering interesting parallels and conceptual cross-fertilization.
To bolster our study, we draw on the works of prominent scholars like Blumenthal and Hutchinson on Plotinus, Richard Martin's analyses of Proclus's syllogistic, and G. MacIsaac's thesis on Proclus's philosophy.
Through the amalgamation of these diverse ideas, we aim to demonstrate the profound potential of category theory as a universal language that can elucidate and unify disparate theoretical realms. Our hope is to stimulate fresh discussions among these domains, catalyze innovative thought, and encourage further research into this intriguing interdisciplinary landscape.
