The Apparent Velocity and Acceleration of Relativistically Moving Objects

Although special relativity limits the actual velocity of a particle to $c$, the velocity of light, the observed velocity need not be the same as the actual velocity as the observer is only aware of the position of a particle at the time in the past when it emits the detected signal. We consider the apparent speed and acceleration of a particle in two cases, one when the particle is moving with a constant speed and the other when it is moving with a constant acceleration. One curious feature of our results is that in both cases, if the actual velocity of the particle approaches $c$, then the apparent velocity approaches infinity when it is moving toward the observer and $c/2$ when it is moving away from the observer.Comment: 9 pages, LaTeX forma

The effect of recombinant bone morphogenetic protein-2 in revision tibiotalocalcaneal arthrodesis: utilization of the Retrograde Arthrodesis Intramedullary Nail database

Item does not contain fulltextThe use of bone morphogenetic protein-2 (BMP-2) has been recommended for high-risk fusions and nonunion. Patients undergoing revisional tibiotalocalcaneal (TTC) arthrodesis via a retrograde arthrodesis nail to evaluate the influence of BMP-2 on rate of fusion in this high-risk population are presented. A retrospective chart and radiographic review were performed on 23 patients with failed prior fusion attempts at the ankle treated with retrograde intramedullary nailing. Sixteen patients were treated without BMP-2 (None group) and 7 were treated with BMP-2 (BMP group). The primary and secondary end-points were successful fusion, and time to fusion, respectively, with a variety of variables evaluated for influence. Other than the use of BMP-2, there were no statistical differences in the patient population. Overall, 11 of 16 ankles (68.8%) in the None group and 5 of 7 ankles (71.4%) in the BMP group resulted in a stable, functional limb. Rate of complication was similar between the 2 groups (p > .05). Time to radiographic ankle union was 115.2 and 184.0 days in the None and BMP groups (p > .05). The effect of BMP-2 on revisional TTC fusions with retrograde nails is reported here. The overall result as a stable, functional limb was 69.6%, which suggests that revision surgery in this high-risk population is a reasonable consideration. Even though this study was unable to demonstrate statistically significant differences, biologic augmentation with BMP-2 did not increase the complication rate and showed a slightly enhanced salvage rate for revision TTC fusions with an intramedullary nail