The Hamiltonian formulation of General Relativity: myths and reality

A conventional wisdom often perpetuated in the literature states that: (i) a 3+1 decomposition of space-time into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation of General Relativity (GR); (ii) the canonical treatment unavoidably breaks the symmetry between space and time in GR and the resulting algebra of constraints is not the algebra of four-dimensional diffeomorphism; (iii) according to some authors this algebra allows one to derive only spatial diffeomorphism or, according to others, a specific field-dependent and non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac [Proc. Roy. Soc. A 246 (1958) 333] and of ADM [Arnowitt, Deser and Misner, in "Gravitation: An Introduction to Current Research" (1962) 227] of the canonical structure of GR are equivalent. We provide some general reasons why these statements should be questioned. Points (i-iii) have been shown to be incorrect in [Kiriushcheva et al., Phys. Lett. A 372 (2008) 5101] and now we thoroughly re-examine all steps of the Dirac Hamiltonian formulation of GR. We show that points (i-iii) above cannot be attributed to the Dirac Hamiltonian formulation of GR. We also demonstrate that ADM and Dirac formulations are related by a transformation of phase-space variables from the metric $g_{\mu\nu}$ to lapse and shift functions and the three-metric $g_{km}$, which is not canonical. This proves that point (iv) is incorrect. Points (i-iii) are mere consequences of using a non-canonical change of variables and are not an intrinsic property of either the Hamilton-Dirac approach to constrained systems or Einstein's theory itself.Comment: References are added and updated, Introduction is extended, Subsection 3.5 is added, 83 pages; corresponds to the published versio

Minimum joint space width and tibial cartilage morphology in the knees of healthy individuals: A cross-sectional study

<p>Abstract</p> <p>Background</p> <p>The clinical use of minimum joint space width (mJSW) and cartilage volume and thickness has been limited to the longitudinal measurement of disease progression (i.e. change over time) rather than the diagnosis of OA in which values are compared to a standard. This is primarily due to lack of establishment of normative values of joint space width and cartilage morphometry as has been done with bone density values in diagnosing osteoporosis. Thus, the purpose of this pilot study is to estimate reference values of medial joint space width and cartilage morphometry in healthy individuals of all ages using standard radiography and peripheral magnetic resonance imaging.</p> <p>Design</p> <p>For this cross-sectional study, healthy volunteers underwent a fixed-flexion knee X-ray and a peripheral MR (pMR) scan of the same knee using a 1T machine (ONI OrthOne™, Wilmington, MA). Radiographs were digitized and analyzed for medial mJSW using an automated algorithm. Only knees scoring ≤1 on the Kellgren-Lawrence scale (no radiographic evidence of knee OA) were included in the analyses. All 3D SPGRE fat-sat sagittal pMR scans were analyzed for medial tibial cartilage morphometry using a proprietary software program (Chondrometrics GmbH).</p> <p>Results</p> <p>Of 119 healthy participants, 73 were female and 47 were male; mean (SD) age 38.2 (13.2) years, mean BMI 25.0 (4.4) kg/m². Minimum JSW values were calculated for each sex and decade of life. Analyses revealed mJSW did not significantly decrease with increasing decade (p > 0.05) in either sex. Females had a mean (SD) medial mJSW of 4.8 (0.7) mm compared to males with corresponding larger value of 5.7 (0.8) mm. Cartilage morphometry results showed similar trends with mean (SD) tibial cartilage volume and thickness in females of 1.50 (0.19) μL/mm²and 1.45 (0.19) mm, respectively, and 1.77 (0.24) μL/mm²and 1.71 (0.24) mm, respectively, in males.</p> <p>Conclusion</p> <p>These data suggest that medial mJSW values do not decrease with aging in healthy individuals but remain fairly constant throughout the lifespan with "healthy" values of 4.8 mm for females and 5.7 mm for males. Similar trends were seen for cartilage morphology. Results suggest there may be no need to differentiate a t-score and a z-score in OA diagnosis because cartilage thickness and JSW remain constant throughout life in the absence of OA.</p

Trabecular bone patterning in the hominoid distal femur

In addition to external bone shape and cortical bone thickness and distribution, the distribution and orientation of internal trabecular bone across individuals and species has yielded important functional information on how bone adapts in response to load. In particular, trabecular bone analysis has played a key role in studies of human and nonhuman primate locomotion and has shown that species with different locomotor repertoires display distinct trabecular architecture in various regions of the skeleton. In this study, we analyse trabecular structure throughout the distal femur of extant hominoids and test for differences due to locomotor loading regime

Relevanz antagonistischer Muskelkräfte für die Weite des Subakromialraumes

Webster Eva's (ex George Wroot) 'Wheel-em In' roll ups game stall photographed at Lincoln Fair, 25 April 1964. Digitisation and record funded by the Pilgrim Trust