==== Light Speed! ==== DESCRIPTION This is a simulator designed to illustrate relativistic effects on the appearance of objects moving at ultra-high velocities. It simulates a geometrical lattice object traveling at a given speed in a straight line through space. Specifically, the object moves along the x-axis of this space, in the positive-x direction; at time t=0, the object is precisely centered on the origin. The simulator displays, in essence, a still image of the vicinity of the origin snapped at the exact moment that the object is *seen* to be at the origin; i.e. the moment that light reflected off the object, when the object was exactly at the origin (at t=0), eventually reaches the camera. This moment will usually be a few billionths of a second after t=0, accounting for the time needed for the light to traverse this distance. (The camera's info display will explicitly indicate the time of the snapshot, to 0.001 microsecond accuracy). Light Speed! will allow you to move around and see interactively how the object appears to change with observer position. At low velocities, this isn't much the case, but up in the several-million-meters-per-second range, the object as viewed from one angle to another can vary significantly. To get started, drag the slider at the right of the window upward. Relativistic effects will immediately become noticeable. Click and drag in the graphics window to move around. CONTROLS Most interactive control is performed with the mouse. By holding down a particular button, and dragging the pointer around, various camera motions can be obtained: Left button: Revolve camera around view target Shift key + Left button: Revolve view target around camera Middle button: Translate camera left, right, up or down Right button: Dolly in or out The first and last motions are generally the most useful. Should the camera become difficult to control at any point, it may be re-initialized by selecting Camera -> Reset View. THEORY Light Speed! takes into account the following consequences of special relativity: 1. Lorentz contraction (fast objects appear shorter) 2. Doppler red/blue shift (the Doppler effect on light/color) 3. Headlight effect (redistribution of reflected light) 4. Optical aberration (warping due to the finite speed of light) A lengthier treatment of the above phenomena, complete with the formulae used (really, they're not that bad!) may be found in the file MATH. LIMITATIONS The only major weakness of this simulator is color. The Doppler shifts produced are only approximations, and in certain cases may be wildly inaccurate. If color fidelity is a must, Antony Searle's BACKLIGHT raytracer program may be a better choice. (See the Acknowledgements section below for details). REQUIREMENTS Light Speed! requires the X Window System with OpenGL or Mesa3D support, as well as the GTK+ libraries to function. Compilation will additionally need Janne Lof's GtkGLArea widget. See the file INSTALL for details. ACKNOWLEDGEMENTS I would like to thank Antony Searle, of the Australian National University, for allowing me to make use of the Doppler-shift code from his well-received relativistic raytracer, BACKLIGHT. This program illustrates relativistic effects via a four-dimensional raytracing engine, and I highly recommend it in case greater scientific rigor or creative flexibility is desired. You may find it at: http://www.anu.edu.au/Physics/Searle/ ========================================= Daniel Richard G. //