Length contraction

Summary

Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGerald contraction (after Hendrik Lorentz and George Francis FitzGerald) and is usually only noticeable at a substantial fraction of the speed of light. Length contraction is only in the direction in which the body is travelling. For standard objects, this effect is negligible at everyday speeds, and can be ignored for all regular purposes, only becoming significant as the object approaches the speed of light relative to the observer. History History of special relativity Length contraction was postulated by George FitzGerald (1889) and Hendrik Antoon Lorentz (1892) to explain the negative outcome of the Michelson–Morley experiment and to rescue the hypothesis of the stationary aether (Lorentz–FitzGerald contraction hypothesis). Although both

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Contraction measurements of cardiomyocytes grown on silicon cantilevers

Arnaud Bertsch, Philippe Renaud, Philipp Stücklin, Mina Todorova

2007

In the rod and hole paradox as described by Rindler (1961 Am. J. Phys. 29 365–6) ('length contraction paradox'), a rigid rod moves at high speed over a table towards a hole of the same size. A bystander expects the rod to fall into the hole, but a co-moving observer expects it to pass unhindered over the hole. According to the accepted solution as first described in that paper, the entire rod must fall somewhat into the hole and therefore cannot remain rigid when the hole moves underneath it. We present an improved approach that is based on retardation due to speed of stress propagation, and in which proper stiffness is not affected. After showing how to solve the similar but simpler car and hole paradox, we find with the same approach that the rod as depicted in Rindler's paper will not fall into the hole as was claimed and that it may pass practically unhindered over it.

2005

The LHeC and the CLIC Drive Beam share not only the high-current beams that make them prone to show instabilities, but also unconventional lattice topologies and operational schemes in which the time sequence of the bunches varies along the machine. In order to asses the feasibility of these projects, realistic simulations taking into account the most worrisome effects and their interplays, are crucial. These include linear and non-linear optics with time dependent elements, incoherent and coherent synchrotron radiation, short and long-range wakefields, beam-beam effect and ion cloud. In order to investigate multi-bunch effects in recirculating machines, a new version of the tracking code PLACET has been developed from scratch. PLACET2, already integrates most of the effects mentioned before and can easily receive additional physics. Its innovative design allows to describe complex lattices and track one or more bunches accordingly to the machine operation, reproducing the bunch train splitting and recombination to and from multiple beamlines. After some initial testing, PLACET2 has been applied to the LHeC Energy Recovery Linac design in order to complete the first end-to-end tracking simulation. The transport of the beam to the dump has been verified in presence of incoherent synchrotron radiation, wakefields and beam-beam effect. Unexpected high radiation losses have been found in specific sections of the lattice, solutions have been proposed to improve both the machine performance and the beam quality. These include a new design of the spreading sections and return arcs based on combined function magnets. The detector bypass, that was originally missing, have now been designed and integrated in the lattice. Tracking simulations have also been performed for PERLE, which have been developed to validate on a smaller scale the technology and the operation of the LHeC. Its performances have been assessed and the design has been consolidated and improved. The work at CTF3 focused on the Combiner Ring. Its length plays a crucial role in the phase structure of the combined beam and must be carefully tuned. The control of the ring length by means of optics scaling, has been measured on the machine and reproduced with the PLACET2 model. Moreover the code has been used to verify a multi-bunch instability that appeared during the commissioning of the ring.

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