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.
New Perspectives on the Relativistically Rotating Disk and Non-Time-Orthogonal Reference Frames
The rotating disk problem is analyzed on the premise that proper interpretation of experimental evidence leads to the conclusion that the postulates upon which relativity theory is based, particularly the invariance of the speed of light, are not applicable to rotating frames. Different postulates based on the Sagnac experiment are proposed, and from these postulates a new relativistic theory of rotating frames is developed following steps similar to those initially followed by Einstein for rectilinear motion. The resulting theory agrees with all experiments, resolves problems with the traditional approach to the rotating disk, and exhibits both traditionally relativistic and non-relativistic characteristics. Of particular note, no Lorentz contraction exists on the rotating disk circumference, and the disk surface, contrary to the assertions of Einstein and others, is found to be Riemann flat. The variable speed of light found in the Sagnac experiment is then shown to be characteristic of non-time-orthogonal reference frames, of which the rotating frame is one. In addition, the widely accepted postulate for the equivalence of inertial and non-inertial standard rods with zero relative velocity, used liberally in prior rotating disk analyses, is shown to be invalid for such frames. Further, the new theory stands alone in correctly predicting what was heretofore considered a “spurious” non-null effect on the order of 10−13 found by Brillet and Hall in the most accurate Michelson-Morley type test to date. The presentation is simple and pedagogic in order to make it accessible to the non-specialist.
New Low-Profile Applicators for Local Heating of Tissues
A new type of low-profile applicator is described giving efficient power transfer to tissue with low leakage. It consists of a resonant element spaced from a ground plane by low-loss material having high relative permittivity and some relative permeability. This combination is covered by similar material which can be placed in direct contact with the tissue to be heated, or separated from it by a water bolus as required. Laboratory measurements using phantom materials show that these applicators are well matched and produce well defined and relatively uniform heating profiles. Applicators having maximum dimensions of 3-15 cm covering the frequency range 1000-100 MHz, respectively, are described. Penetration depths of at least 4 cm at 100-200 MHz are achieved. Tests on anesthetised pigs and some clinical assessment have confirmed the usefulness of this compact low-frequency type of applicator and have shown that performance compares favorably with that of other recently reported types. The design can be optimized for treatment of specific sites, and suitable choice of dimensions and electrical characteristics of the layer material allow the low-profile concept to be extended over a wide range of operating frequencies.