Advantages of Three-Dimensional Space-Time Frames

Abstract

Time dilation and length contraction formulas are derived in Special Relativity. However, these phenomena cannot be visualized in four-dimensional space-time frames. From the time dilation formula, we can derive a relationship between space and time for a pair of inertial frames and, in turn, construct three-dimensional space-time frames based on this relationship. Furthermore, length contraction can be shown on these frames. Since space and time are inseparable, neither time dilation nor length contraction can be fully understood unless discussed together. We apply three-dimensional space-time frames to describe the motion of an object in the twin paradox. Using the concept of the center of mass of a pair of inertial frames, we are able to determine who is on the rest frame of a pair of inertial frames. This example demonstrates the advantage of three-dimensional space-time frames over four-dimensional space-time frames in describing relativistic motion.