The proper time is defined to be the time measured between two events in an inertial reference frame in which the two events occur at tiresome location in that frame. Consider a distant star that is assumed to be at rest with respect to the Earth. an astronaut is assigned the taslt of travelling to the distant star. The events for this journey are defined as: a Astronaut leaves Earth a Astronaut arrives at star The astronaut travels to the star from the Earth in an inertial frame .5", while the astronomers on Earth remain in inertial frame 5'. The astronaut is carrying a clock at his origin. The astronaut is measuring the proper time for this journey because the times are measured by a clock that is at the same location in reference frame .5" [the origin]. In contrast astronomers on the Earth do not measure the proper time between the events because the events occur at different positions in frame 3. Notice that although the astronomers cannot measure the proper time between the defined eve nts, they can calculate it. Identifying the proper time cannot be done without reference to events. Based on the derivation in the warmup. and the similar discussion in Knight, the equation for proper time is: a: = l31fll ,3: [Knight Eq. see] Here a: is the time measured by an observer in any reference frame 5' other than the one in which the proper time is being measured. 1. You observe two events that. in your reference frame 5. are separated in space by its and in time by it. Starting with equation 36.9 in Knight for the proper time, show that an equivalent way of expressing the proper time between the two events from your frame alone is: aw = Eliot]? [xfj