An elementary particle travels at 0.840c across a solar system that has a diameter of 8.14 × 10^12 m (both measurements in the reference frame S of the solar system). (a) What value does an observer in reference frame S measure for the time interval needed for the particle to cross the solar system? (b) What time interval is needed in the reference frame P of the particle? (c) What is the proper length of the diameter? (d) What is the proper time interval for the particle’s trip across the system? (e) What is the diameter of the solar system in reference frame P?

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Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.