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Research Warning | Pieces of Eight is a work in progress, and might contain errors or speculative material. If you arrived at this page to help with a standard academic syllabus (i.e. you're at school or college), then this material is probably not for you. If you are here to help with research-level work, then please proceed with caution, and (as with all material on the web) try to carefully measure the value of the information you find here. |
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About ‘Pieces of Eight’ | Pieces of Eight is the working title of a project to develop a fundamental representation model for physics. Two papers have been presented, and a further paper is due for PIRT XI, September 2008. The author continues to refine this work.
- “Algebra of a Three-fold Symmetry for Fundamental Physics” work-in-progress presented to PIRT XI (British Society for the Philosophy of Science, Physical Interpretations of Relativity Theory XI, Imperial College, London, 13 September 2008).
- “Gravity in Symmetrical Context of Space-Time”, PIRT X (British Society for the Philosophy of Science, Physical Interpretations of Relativity Theory X, Imperial College, London, 9 September 2006).
- “A Development of ‘The Fundamental Parameters of Physics’”, ANPA 20 (Alternative Natural Philosophers' Association, Cambridge, 1998).
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Algebra of a Three-fold Symmetry for Fundamental Physics (2008) | | Informal Description |
 | | "May we have the next slide, please..." - Tom Lehrer |
Based on the early work of Peter Rowlands, we use three 'properties' that seem fundamental to everything, and treat them literally as an abstract space of three axes in which waves operate: the building blocks for paravectors and Clifford algebra, along with a quantisation wave that represents how solutions are found physically by our universe. The basic algebra of an interaction in this space is found to be a 'phase operator', which quickly yields Lie group algebra, the Clifford Algebras, the physical model for bosons and fermions (particles, their fields, and their relation to universal vacuum), and Feynman's path integral formulation. We extend a physical model for how the universe works in basic terms, which includes Noether's Theorem, an Exclusion Principle, a mapping to the Dirac algebra, and a definition of how fermions and bosons interact - all of which have been deduced and re-derived from our first assumptions. We offer a mapping to the Dirac alrebra, a QCD-like geometry for hadrons (including residual strong - nuclear - force), a description of classical macroscopic physics in terms of the model, and relativistic effects in extreme situations and in very close proximity to fermions. On a 'softer' note, we engage a brief 'metaphysical' proposition about the nature of the 3D space and the human experience of it, in the context of this representation (the step from the abstraction of the fundamental model to our understanding is not obvious!), and also examine the meaning of time in the causal network, and the precision that various differential techniques can offer. Interesting developments should come from an analysis of the algebra, which has scope to extend quantum field theory to include variables missing from the Standard Model. [work-in-progress, est. 18pp A4] |
| Abstract |
Three fundamental properties (a=parity, b=conservation, c=dimensionality)[2,7] are used as independent bases for an absolute phase space {a,b,c}[6], in which a phase operator is the basis for all sub-physical interactions. Representative number types are determined by {a,c}, after Hestenes and Clifford, and the given phase algebra leads naturally to symmetric conservation (Noether) and applications of group theory (Lie, etc). All bosons are bound pairs of continuous modal waves, and a fermion event occurs where two bosons (four wavefunctions) locally have only two waves at conserved (-b) phase; the remaining nonconserved waves describe its vacuum field. To unambiguously resolve systems having more than two members, we deduce a 'general exclusion principle' that requires out-of-phase local states, and generates the (latent) nonconserved (not -b) bosonic domain with non-local solutions that form the macroscopic physical structure. Significantly, this identifies the sub-physical (point-local) phase space, the quantum phase interactions that provide the 'nonconservation bridge' to the macroscopic, and an integral basis for the Euclidian 3D space we readily understand, in parallel with action and gauge theory. From this, we propose a useful field unification, which naturally mixes parameters like gravity, space, proper local time, and charges (strong, weak, and electric), offering many perspectives for analysis. We use the model to examine qualitative structures in QCD, QED, and nuclear forces. Finally, some interpretations are offered in terms of this representation for the fundamental or derived nature of the energy states and processes known to physics, including correlations with - and additions to - the Standard Model. |
| Downloadable assets |
| Assets will appear here after submission. |
| Presentation (with speaker's notes) | Originally created in PowerPoint, this is a low-res PDF version with descriptive notes (764 KiB, PDF). |
| Abstract and Introduction | The first two sections of the paper. Sections 3 to 10 will be published at a later date. Late edit: the structure of the paper has changed since this PDF was published to this website (and to the conference), so the final paper will contain more material in the introductory sections. |
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Gravity in Symmetrical Context of Space-Time (2006) | | |  | |
Research Warning | Please note that some ideas have been improved since the writing of the 2006 paper, which contains some errors, and many clearly-labelled speculations. Readers are advised to await publication of the 2008 paper, which is a better-informed work. |
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PIRT X (British Society for the Philosophy of Science, Physical Interpretations of Relativity Theory X, Imperial College, London, 9 September 2006). |
| Abstract |
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Three fundamental properties (“properties”) derived directly from fundamental symmetry violations, in combination, give rise to absolute energy states (“parameters”) of {space, time, mass, charge}, and four other energy states. A differential view of symmetry violations leads to energy transformations between energy states, summarised as ‘product numbers’. Their necessary balance defines closed groups, of arbitrary order. Simple closed groups yield useful results, the simplest being 14 possible closed 4-member groups (“4-groups”) of parameters. Four conceptual levels of operation are defined for convenience, through which a single * operation combines violations from unity (Level 0) through fundamental symmetries and unitary interactions (Levels 1 and 2), to our macroscopic quantitative experience of physics (Level 3), where space becomes a practically physical expression, and the concept of number incidentally arises. Gravity is one of the eight possible energy states, having a fundamental symmetry relationship with the other seven parameters.
A set of symmetry violations in a concise 6-member group allow the ‘creation’ of space during a process of nilpotent instantiation of matter, as expressed alongside the transformation of energy states in other parameters in the closed group.
Space is non-rigid yet statistically orthogonal at macrolevel, a situation arising from its non-conserved nature, allowing macro-level relativistic transformations from fundamental symmetry violations, unifying the quantum and macroscopic, while remaining faithful to the principles of general relativity.
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| Downloadable assets |
| Supplement 2: Slides | Some presentation slides (PDF of a PowerPoint file). |
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A Development of 'The Fundamental Parameters of Physics' (1998) | Author's Note: As the ANPA presentation was an initial exploration (with some statements that have since been revised), only extracts will be shown where relevant to later material. |
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| © 2008 John Valentine, All rights reserved. | |  |