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Cosmic rays that strike the top of the Earth’s atmosphere generate a shower of secondary particles that move toward the surface with relativistic speeds. Water Cherenkov detectors (WCDs) on the ground can detect charged muons, which are one of the many particles generated in the shower, with the Cherenkov imaging technique. A large number of these muons travel in WCD tanks near the speed of light in a vacuum, faster than the speed of light in water, and so trigger isotropic Cherenkov radiation, which is detected by the photomultiplier tubes (PMTs) placed inside the tanks. When the radial component of the speed of the muon toward a PMT drops from superluminal to subluminal, the PMT records Cherenkov light from an optical phenomenon known as relativistic image doubling (RID), which causes two Cherenkov images of the same muon to appear suddenly, with both images moving in geometrically opposite directions on the original muon track. The quantities associated with the RID effect can be measured experimentally with a variety of detector types and can be used to find various points on the original trajectory of the muon. In this paper, a detailed study of reconstructing the trajectory of a muon entering a WCD using the RID technique has been presented. It is found that the measurements of standard RID observables enables a complete reconstruction of the trajectory of the muon to a high degree of accuracy with less than 1% error.

When a gamma or cosmic ray strikes the top of Earth's atmosphere, a shower of secondary particles moves toward the surface. Some of these secondary particles are charged muons that subsequently enter Water Cherenkov Detectors (WCDs) on the ground. Many of these muons, traveling near the speed of light in vacuum, are moving faster than the speed of light in water and so trigger isotropic Cherenkov radiation in the WCDs. Inside many WCDs are photomultiplier tubes (PMTs) that detect this Cherenkov radiation. When the radial component of the speed of a muon toward a PMT drops from superluminal to subluminal, the PMT will record Cherenkov light from a little-known optical phenomenon called Relativistic Image Doubling (RID). Were the RID-detecting PMTs replaced by high resolution video recorders, they would see two Cherenkov images of the muon suddenly appear inside the tank, with one image moving with a velocity component toward the recorders, the other away. Even without a video, the RID phenomenon will cause different PMTs to record markedly different light curves for the same muon. In this paper, we present a study hoping to inspire the explicit detection and reporting of RID effects in WCDs. We consider three example cases of muon RIDs in High-Altitude Water Cherenkov (HAWC)-like systems: vertical, horizontal and oblique. Monte Carlo simulations show that RID effects in HAWC-like systems are not rare -- they occur for over 85 percent of all muon tracks., Minor changes but included in an erratum

A popular physics legend holds that scissors can cut paper with a speed faster than light. Here this counter-intuitive myth is investigated theoretically using four simple examples of scissors. For simplicity, all cases will involve a static lower scissors blade that remains horizontal just under the paper. In the first case, the upper blade will be considered perfectly rigid as it rotates around and through the paper, while in the second case, a rigid upper blade will drop down to cut the paper like a guillotine. In the third case, the paper is cut with a laser rotating with a constant angular speed that is pointed initially perpendicular to the paper at the closest point, while in the fourth case, the uniformly rotating laser is pointed initially parallel to the paper. Although details can be surprising and occasionally complex, all cases allow sections of the paper to be cut faster than light without violating special relativity. Therefore, the popular legend is confirmed, in theory, to be true., 6 pages, 9 figures, accepted for publication in Physics Education (un-copyedited version)

Cosmic gamma-ray photons incident on the upper atmosphere create air showers that move to the Earth's surface with superluminal speed, relative to the air. Even though many of these air showers remain superluminal all along their trajectories, the shower's velocity component toward a single Imaging Atmospheric Cherenkov Telescope (IACT) may drop from superluminal to subluminal. When this happens, an IACT that is able to resolve the air shower both in time and angle should be able to document an unusual optical effect known as relativistic image doubling (RID). The logic of RID is that the shower appears to precede its own Cherenkov radiation when its speed component toward the IACT is superluminal, but appears to trail its own Cherenkov radiation when its speed component toward the IACT is subluminal. The result is that the IACT will see the shower start not at the top of the atmosphere but in the middle -- at the point along the shower's path where its radial velocity component drops to subluminal. Images of the shower would then be seen by the IACT to go both up and down simultaneously. A simple simulation demonstrating this effect is presented. Clear identification of RID would confirm in the atmosphere a novel optical imaging effect caused not by lenses but solely by relativistic kinematics, and may aid in the accuracy of path and speed reconstructions of the relativistic air shower., 8 pages, 3 figures, comments welcome