SESSION: MathematicsMonPM1-R3 |
Rowlands International Symposium (7th Intl. Symp. on Sustainable Mathematics Applications) |
Mon. 21 Oct. 2024 / Room: Marika B2 | |
Session Chairs: Mike Mikalajunas; Student Monitors: TBA |
Peter Rowlands appears to be the only physicist who has written a book on foundational laws in physics [1]. He identifies four fundamental symmetries that are foundational to physics: space, time, mass and charge. A group relationship, a zero-totality condition and a nilpotent Dirac equation are the primary mathematical structures used to build the foundational laws. [2]. The duality between space-time and mass-charge is so exact that any reversal of role between discrete space and continuous time also produces a corresponding reversal of role between continuous mass and discrete charge [3]. One of us has argued that his ‘principle of duality’ is so ubiquitous in both mathematics and physics that it should be promoted into a ‘law’ based on the quantum mechanical law of entanglement [4]. Rowlands identifies three distinct mathematical processes: (A) conjugation, (B) complexification and (C) dimesionalization. Their corresponding physical manifestations are dualistic in nature: (a) conserved/nonconserved, conjugated/nonconjugated, + / –, (b) real/complex (the relativistic duality) and (c) the discrete/continuous, or the dimensional/nondimensional options. A classic case of the discrete/continuous representation is the well-known continuous wave/discrete particle duality. Rowlands’ principle of duality UNITES the theory of general relativity (GR), which is a theory about gravity not a theory of gravity, and quantum mechanics (QM). It does not UNIFY them [5].