In the picture above, a 230 gr. .45 caliber bullet is shown in flight in a high speed photograph. The average speed of such a bullet is about 1000 ft/s. That's just below the speed of sound which is 1116 ft/s. This is quite fast for such objects in our every day world, but not fast enough to observe the strange effects which the theory of special relativity predicts. This theory says, among other things, that as an object approaches the speed of light, c = 983,571,000 ft/s, it actually contracts (or shrinks) in the direction of motion. If we were able to shoot a bullet at a faster speed, say v = .85 c, would a high speed photograph reveal that the bullet is contracted? A high speed photograph is the image produced from the wavefront of light at the location of the camera at an instant in time. This instantaneous wavefront will be composed of light waves emitted from many different points of the object which are at different distances from the camera and therefore are emitted at different times. When the object is set in motion relative to the camera this can create a distortion in the image carried by the instantaneous wavefront. Please note that we are not concerned here with motion blur due to prolonged exposure time, we are interested in the objects image as it would be revealed by the instantaneous wavefront of the light reflected from the object. (For now we are also only interested in the shape or geometry of the image, not in any change of color or brightness.) So how would the bullet above or some other object appear if it were moving past you at .85 c?

The image sequences available for download below were created using point cloud representations of geometrical objects which were then transformed according to the combined effects of the Lorentz transformation and the time of flight delay of light waves as they are emitted from a moving object. This combined transformation projected onto the (x,y,z) coordinates of the point clouds results in a shift of the x coordinates when the object moves in the positive x direction according to (see G. D. Scott and M. R. Viner, Am. J. Phys. 33, 534, 1965)

 

Where β = , γ = , and d is the distance of the objects center from the camera shutter. When the distance d becomes large, this reduces to the well known Terrel "rotation" result:

However, if the object is close to the camera, a nonlinear shearing of the image becomes apparent. The transformed point clouds are then “wrapped” with a VRML surface using Cocone or Geomagic Wrap. In each case the object is moving in the positive x direction from left to right, perpendicular to the line of sight of the camera which is placed a distance d from the object.

The free VRML viewer Immersaview is included with each of the downloads (see Immersaview Keyboard.txt for instructions). Immersaview can be configured to display animated sequences of VRML objects either as a single image or stereoscopically for a GeoWall system.

Relativistic Cube