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Unformatted text preview: INVESTIGACI ´ ON REVISTA MEXICANA DE F ´ ISICA 52 (1) 70–73 FEBRERO 2006 Uniformly accelerated observers in special relativity G.F. Torres del Castillo Departamento de F´ ısica Matem´atica, Instituto de Ciencias, Universidad Aut´onoma de Puebla, 72570 Puebla, Pue., M´exico C.I. P´erez S´anchez Facultad de Ciencias F´ ısico Matem´aticas, Universidad Aut´onoma de Puebla, Apartado postal 1152, 72001 Puebla, Pue., M´exico Recibido el 25 de octubre de 2005; aceptado el 9 de enero de 2006 The red shift for an electromagnetic wave measured by two observers in a uniformly accelerated frame, which, according to the equivalence principle, should correspond to a gravitational red shift, is calculated as well as the bending of light rays. Keywords: Special relativity; red shift; bending of light rays. Se calcula el corrimiento al rojo para una onda electromagn´etica medido por dos observadores en un sistema de referencia uniformemente acelerado, el cual, de acuerdo con el principio de equivalencia, debe corresponder a un corrimiento al rojo gravitacional, as´ ı como la desviaci´on de rayos de luz. Descriptores: Relatividad especial; corrimiento al rojo; desviaci´on de rayos de luz. PACS: 03.30.+p; 04.20.q 1. Introduction Just like in Newtonian mechanics, in the special theory of rel ativity the inertial frames of reference play an essential role (see, for example, Refs. 1,2) and the Lorentz transformations give the relationship between the spacetime coordinates of events measured in two different inertial frames. However, in Newtonian mechanics, as well as in special relativity, one can make use of noninertial reference frames. In fact, the equivalence principle states that, in the absence of gravita tional fields, a reference frame that is linearly accelerated is locally identical to a reference frame at rest in a gravitational field. In particular, making use of the equivalence principle, it is possible to derive the existence of a gravitational red shift for electromagnetic waves and of a bending of the light rays by considering their propagation viewed from an accelerated frame in the absence of a gravitational field (see, for example, Refs. 35). References 3 and 4 contain computations of these effects based on Newtonian relations. The aim of this paper is to find, in the context of spe cial relativity, the red shift for an electromagnetic wave, mea sured by two observers in a uniformly accelerated frame sep arated by a fixed distance, and the trajectory of a light ray. In Sec. 2 we derive the relationship between the spacetime co ordinates of events measured by an inertial frame and a ref erence frame whose origin has a constant acceleration with respect to an instantaneously comoving inertial frame (see also Refs. 68). This coordinate transformation is employed in Sec. 3 to find the exact red shift formula and the bending of light rays....
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This note was uploaded on 05/17/2011 for the course PHYSICS 123 taught by Professor Hayes during the Spring '07 term at Harvard.
 Spring '07
 Hayes
 Special Relativity

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