On the Response of a Particle Detector in a Circular Motion

characterized by an effective temperature which differs from the temperature associated with the response for L by a factor of 7[/13 at most (d. the paragraph following Eq. (22) below), but did not arrive at a conclusive statement as to the relation between the two responses. In this letter we point out that a precise relation exists, not between the responses for CM and for L, but between those for CM with speed v and for "the combined motion of a uniform linear acceleration and a uniform translation with speed v in the direction perpendicular to the acceleration" (hereafter called L T ). We begin with an elementary observation. Let the radius of the circle for CM be R. Then, in the limit of large R, CM looks like LT. Let us define CM and L T precisely and examine this geometrical analogy more closely. In what follows the parameter r denotes the proper time of the world line, and r=(1-v 2 )-1/2. We use the natural units. The trajectory of CM is given in the Minkowski coordinates by