Abstract of Full Paper Presented at the 10th Asian Technology Conference in Mathematics
December 12-19, 2005, South Korea

Motion of Particles Described in a Three-Dimensional Space-Time Frame

Tower Chen
Mathematical Sciences
University of Guam


Abstract: The motion of a particle moving in space can be decomposed into three directions, but it is difficult to describe all three directions in a single three-dimensional space frame with respect to time. In mathematics, we can locate a point in a plane by (x, y) in the rectangular cartesian coordinate frame and also by (r, úc) in the polar coordinate frame, where x equals to r(cosúc) and y equals to r(sinúc). In physics, we can describe the motion of a particle moving in one dimension in the rectangular cartesian frame with x-axis as location coordinates and y-axis as time coordinates of the particle by (x, t). Can we describe its motion in a polar coordinates frame? The proposed 3-D S-T is constructed similar to a polar coordinate frame to solve this problem. In the proposed three-dimensional space-time frame (3-D S-T), space is represented by perpendicular three axes (x, y, and z), but time is represented by spheres of different radii with the origin of the space axes as their center. The radii of the spheres representing time are set to equal the velocity of the medium used to transmit messages in the system multiplied by time. Any particleíŽs motion in space can be described in a chosen 3-D S-T frame by selecting the proper medium for transmitting messages. This paper will illustrate how to graph motion of particles in this 3-D S-T frame using the graph-function of the MATLAB program. In Special Relativity, a 3-D S-T frame can be constructed to describe the motion of the other frame by choosing light as a medium for transmitting messages, then geometric lines can represent time dilation and length contraction clearly in this 3-D S-T frame. The proposed 3-D S-T frame is an alternate coordinate system that can be used to describe the motion of particles, and it may provide additional understanding of space and time.

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