Cosmological implications of the Machian principle

The famous idea of Ernst Mach concerning the non-absolute but relational character of particle inertia is taken up in this paper and is reinvestigated with respect to its cosmological implications. From Thirring’s general relativistic study of the old Newtonian problem of the relativity of rotations in different reference systems, it appears that the equivalence principle with respect to rotating reference systems, if at all, can only be extended to the system of the whole universe, if the mass of the universe scales with the effective radius or extent of the universe. A reanalysis of Thirring’s derivations still reveals this astonishing result, and thus the general question must be posed: how serious this result has to be taken with respect to cosmological implications. As we will show, the equivalence principle is, in fact, fulfilled by a universe with vanishing curvature, i.e. with a curvature parameter, which just has the critical density , where is the Hubble constant. It turns out, however, that this principle can only permanently be fulfilled in an evolving cosmos, if the cosmic mass density, different from its conventional behaviour, varies with the reciprocal of the squared cosmic scale. This, in fact, would automatically be realized, if the mass of each cosmic particle scales with the scale of the universe. The latter fact, on one hand, is a field-theoretical request from a general relativistic field theory which fulfills H. Weyl’s requirement of a conformal scale invariance. On the other hand, it can perhaps also be concluded on purely physical grounds, when taking into account that as source of the cosmic metrics only an effective mass density can be taken. This mass density represents the bare mass density reduced by its mass equivalent of gravitational self-binding energy. Some interesting cosmological conclusions connected with this fact are pointed out in this paper.     

THOR dummy chest deflection response in oblique and lateral far-side sled tests

Abstract

Objective: The focus of this study is side impact. Though occupant injury assessment and protection in nearside impacts has received considerable attention and safety standards have been promulgated, field studies show that a majority of far-side occupant injuries are focused on the head and thorax. The 50th percentile male Test Device for Human Occupant Restraint (THOR) has been used in oblique and lateral far-side impact sled tests, and regional body accelerations and forces and moments recorded by load cells have been previously reported. The aim of this study is to evaluate the chestband-based deflection responses from these tests.

Methods: The 3-point belt–restrained 50th percentile male THOR dummy was seated upright in a buck consisting of a rigid flat seat, simulated center console, dashboard, far-side side door structure, and armrest. It was designed to conduct pure lateral and oblique impacts. The center console, dashboard, simulated door structure, and armrest were covered with energy-absorbing materials. A center-mounted airbag was mounted to the right side of the seat. Two 59-gage chestbands were routed on the circumference of the thorax, with the upper and lower chestbands at the level of the third and sixth ribs, respectively, following the rib geometry. Oblique and pure lateral far-side impact tests with and without airbags were conducted at 8.3 m/s. Maximum chest deflections were computed by processing temporal contours using custom software and 3 methods: Procedures paralleling human cadaver studies, using the actual anchor point location and actual alignment of the InfraRed Telescoping Rods for the Assessment of Chest Compression (IR-TRACC) in the dummy on each aspect—that is, right or left,—and using the same anchor location of the internal sensor but determining the location of the peak chest deflection on the contour confined to the aspect of the sensor; these were termed the SD, ID, and TD metrics, respectively.

Results: All deformation contours at the upper and lower thorax levels and associated peak deflections are given for all tests. Briefly, the ID metrics were the lowest in magnitude for both pure lateral and oblique modes, regardless of the presence or absence of an airbag. This was followed by the TD metric, and the SD metric produced the greatest deflections.

Conclusion: The chestbands provide a unique opportunity to compute peak deflections that parallel current IR-TRACC-type deflections and allow computation of peak deflections independent of the initial point of attachment to the rib. The differing locations of the peak deflection vectors along the rib contours for different test conditions suggest that a priori attachment is less effective. Further, varying magnitudes of the differences between ID and TD metrics underscore the difficulty in extrapolating ID outputs under different conditions: Pure lateral versus oblique, airbag presence, and thoracic levels. Deflection measurements should, therefore, not be limited to an instrument that can only track from a fixed point. For improved predictions, these results suggest the need to investigate alternative techniques, such as optical methods to improve chest deflection measurements for far-side occupant injury assessment and mitigation.