Relativistic Rotation in the Large Radius, Small Angular Velocity Limit
Relativistic rotation is considered in the limit of angular velocity approaching zero and radial distance approaching infinity, such that centrifugal acceleration is immeasurably small while tangent velocity remains close to the speed of light. For this case, the predictions of the traditional approach to relativistic rotation using local co-moving Lorentz frames are compared and contrasted with those of the differential geometry based non-time-orthogonal analysis approach. Different predictions by the two approaches imply that only the non-time-orthogonal approach is valid.
Chapter 6 Toward a Consistent Theory of Relativistic Rotation in Relativity in Rotating Frames (Kluwer Academic)
Part 1: Traditional Analysis Conundrums Although most physicists presume the theoretical basis of relativistically rotating systems is well established, there may be grounds to call the traditional analysis of such systems into question. That analysis is argued to be inconsistent with regard to its prediction for circumferential Lorentz contraction, and via the hypothesis of locality, the postulates of special relativity. It is also contended that the traditional analysis is in violation of the continuous and single valued nature of physical time. It is further submitted to be in disagreement with the empirical finding of Brillet and Hall, the global positioning system satellite data, and a light pulse arrival time analysis of the Sagnac experiment. Part 2: Resolution of the Conundrums: Differential Geometry and Non-time-orthogonality It is postulated that physical constraints on time (its continuous and single-valued nature) limit the set of possible synchronization/simultaneity schemes in rotation to one, the “flash from center” scheme. A differential geometry analysis based on this simultaneity postulate is presented in which the rotating frame metric is constrained to be locally non-time-orthogonal (NTO) and due to which, all inconsistencies and disagreements with experiment are resolved. The hypothesis of locality is shown to be invalid for rotation specifically, and generally valid only for non-inertial frames in which the metric can have all null off diagonal space-time components (i.e., time is orthogonal to space.) The analysis approach presented does not contravene traditional relativistic theory for translating systems and makes many (but not all) of the same predictions for rotating systems as does the traditional (time orthogonal) analysis. Part 3: Experiment and Non-time-orthogonal Analysis Experiments performed from the 1880s to the present to test special relativity are summarized, and their relevance to NTO analysis is presented. One test, that of Brillet and Hall, appears capable of discerning between the NTO and traditional approaches to relativistic rotation. It yielded a signal predicted by NTO analysis, but not by the traditional approach. Other evidence in favor of the NTO approach may be inherent in the global positioning system data, and the Sagnac experiment.
Thermal incompatibility analysis of metal-ceramic systems based on flexural displacement data.
The feasibility of simple tests or analytical methods for prediction of residual stress states in metal-ceramic (MC) prostheses has not been demonstrated. Biomaterial metal-ceramic strips have been proposed to provide sensitive measures of transient and residual stress states through the measurement of midpoint deflection after cooling from the ceramic sintering temperature. The objective of this study was to apply the elastic-viscoelastic analogy to calculate transient and residual midpoint deflections in MC biomaterial strips and to compare these values with deflections measured with a beam-bending viscometer (BBV). Calculations and measurements were made for five MC systems that were found from a clinical study to be "thermally compatible" systems. Metal strips, 64 mm in length, 3 mm wide, and either 0.5 mm, 1.0 mm, or 2.0 mm in thickness, were veneered with four 0.25-mm thick layers of opaque porcelain. Midpoint deflection of the MC strips (ceramic oriented in the posterior position) was measured during cooling from an initial temperature of 700 degrees C. In general, the directions of the measured residual deflections did not agree with the "textbook" convention that negative deflections are associated with positive thermal contraction mismatch (alpha(M) - alpha(c) > 0) regardless of metal thickness. For a metal thickness of 0.5 mm, the residual midpoint deflection for all thermal contraction mismatch cases, except one, was positive (upward deflection) whereas the residual midpoint deflections were all negative when the metal thickness was increased to 1 or 2 mm, independent of the thermal contraction mismatch. The best agreement between calculated and measured values of residual midpoint deflection (+16 microns vs. +14 +/- 2.3 microns, respectively was obtained for MC biomaterial strips with a Ni-Cr alloy (0.5 mm thick) while the largest difference (+346 microns vs. +61 +/- 43.8 microns) was obtained for MC bimaterial strips with a Au-Pd allow (0.5 mm thick). In all but one case, changes in deflection direction as a function of metal thickness were correctly predicted by the viscoelastic analysis. The results of this study indicate that a viscoelastic model is useful for estimating thermal compatibility conditions of MC systems.