The length of an object can only be determined when the endpoints of the object can be located simultaneously. In any particular inertial reference frame, the only measuring device that can do this is at rest. Therefore, the proper length of any object in an inertial reference frame is the length of that object when it is at rest in that frame. Based on the derivation in lecture, the equation for proper length is: Lo I' We typically think of a tape measure or ruler as the measuring device. Any ruler that is at rest in a reference frame can measure the proper length. L' is the length measured in any reference frame S'other than the one in which the proper length is being measured. 3. Reconsider the events from the previous question. The Sun emits a high-energy particle that travels to the Earth. The Sun and Earth are at rest relative to each other. According to observers on the Earth, the Sun is 150 million km away and it takes the particle 12 minutes to reach the Earth, where it is absorbed by a molecule in the Earth's atmosphere. In which of the following inertial reference frames (neglecting effects due to rotation, orbital motion, etc.) can the proper length of a ruler stretching between the Earth and the Sun (a very long ruler!) be used to measure the separation? Briefly justify your answer. i. the Sun ii. the Earth iii. a fast space ship at rest relative to the particle. iv. something else.