Spacetime visualization of relativistic effects

ABSTRACT

We have developed an innovative ray-tracing algorithm to describe Relativistic Effects in SpaceTime (“REST”). Our algorithm, called REST-frame, models light rays that have assumed infinite speed in conventional ray-tracing to have a finite speed c in spacetime, and uses general Lorentz Transformation, which connects the spacetime description of a single event in two inertial coordinate systems (frames) that differ by a constant velocity, to perform the relativistic translation and aberration of light rays. In this paper, we report the extension of our previous work for visualizing relativistic motion in spacetime to include relativistic Doppler color shift and the simulation of complex kinematic systems in which objects of different relativistic velocities coexist. Our simulations have produced non-intuitive images showing anisotropic deformation (warping) of space and intensity concentration/spreading of light sources in spacetime. Images of objects undergoing relativistic Doppler shift are also generated. By applying state-of-the-art computation technology and simulation techniques to the earlier quests in Physics that were conducted mainly by thought experiment, we demonstrate, through our new revelations, that REST-frame offers a powerful experimentation tool to study and explore some of the most exciting aspects of the natural world; particularly, the rich physical properties associated with the finite speed of light.

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INDEX TERMS

Primary Classification:
  J. Computer Applications
  J.2 PHYSICAL SCIENCES AND ENGINEERING
      Subjects: Physics

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.2 Nonnumerical Algorithms and Problems
          Subjects: Geometrical problems and computations

  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.3 Picture/Image Generation
          Subjects: Display algorithms
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Curve, surface, solid, and object representations

General Terms:
Algorithms, Experimentation, Theory