Rigid motion revisited: rigid quasilocal frames
Bibliographic record
Abstract
In this first of a series of papers we will introduce the notion of a rigid quasilocal frame (RQF) as a geometrically natural way to define a 'system' in the context of the dynamical spacetime of general relativity. An RQF is defined as a two-parameter family of timelike worldlines comprising the worldtube boundary (topologically ) of the history of a finite spatial volume, with the rigidity conditions that the congruence of worldlines is expansion-free (the 'size' of the system is not changing) and shear-free (the 'shape' of the system is not changing). This definition of a system is anticipated to yield simple, exact geometrical insights into the problem of motion in general relativity. It begins by answering, in a precise way, the questions of what is in motion (a rigid two-dimensional system boundary with topology S 2 , and whatever matter and/or radiation it happens to contain at the moment), and what motions of this rigid boundary are possible. Nearly a century ago Herglotz and Noether showed that a three-parameter family of timelike worldlines in Minkowski space satisfying Born's 1909 rigidity conditions does not have the 6 degrees of freedom we are familiar with from Newtonian mechanics, but a smaller number—essentially only 3. This result curtailed, to a large extent, subsequent study of rigid motion in special and (later) general relativity. We will argue that in fact we can implement Born's notion of rigid motion in both flat spacetime (this paper) and arbitrary curved spacetimes containing sources (subsequent papers)—with precisely the expected 3 translational and 3 rotational degrees of freedom (with arbitrary time dependence)—provided the system is defined quasilocally as the two-dimensional set of points comprising the boundary of a finite spatial volume, rather than the three-dimensional set of points within the volume.
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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 | 0.001 | 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 | 0.007 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".