Bibliographic record
Abstract
A new algebra is introduced that is found to be suitable for representing asynchronous action-at-a-distance. This “Natural Vector” representation is based on Hamilton’s quaternions with the four bases constructed from real (4x4) matrices with the scalar component explicitly including the standard square root of minus one, so that natural vectors operate like a simple non-commuting, complex algebra. This algebra can replace calculus in much physics and directly relates the Wave equation, the Continuity equation and the Flow equation together, which are at the center of mathematical physics. This new representation forms the mathematical foundation for a new research programme that challenges several of the basic assumptions of modern physics that are directly related to the metaphysical “Continuum Hypothesis”. This new form of quaternion algebra described here is found to be mathematically simpler than the somewhat similar biquaternions and appears to be the natural algebraic form for describing ‘relativistic’ interactions that implicitly incorporate the asynchronous delays occurring in the electromagnetic interaction. These complex four-component vectors are inherently simpler than other alternatives, such as Clifford algebra or Minkowski 4-vectors – they are more physically transparent than tensor calculus. Natural vectors are always anti-symmetric for two point-particles, so they form a natural fermionic representation even for ‘classical’ electrons; their anti-commutative properties lead naturally into a suitable representation for quantum mechanics. The new focus is on the interaction between two electrons at two different times, rather than other standard theories centered on a single particle or field-point in empty space, at one single time. Asynchronous inter-particle interactions, like those found in electromagnetism, are here represented by natural vectors that are both separable and temporally invariant. This is the first paper in a new research programme investigating the foundations of physics; this programme is aimed to recognize that continuum assumptions in physics (used everywhere since Isaac Newton created calculus for particle motion) needs to be replaced with discrete mathematics. *SPSI, Surrey, B.C. Canada (604) 542-2299* spsi99@telus.net © H. J. Spencer [2016] * (Version 2.6 19-08-2016 Version 1.0 31-7-2007)
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.018 | 0.005 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".