Optical Effects of Special Relativity
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Uploaded on Sep 8, 2007
The video shows photorealistic representations of reduced c scenes. This means that the speed of light has been slowed down from over one billion kilometres per hour to a speed of only one meter per second. The consequences of this fiction have been restricted to optical effects, and allows us to see special-relativistic effects not possible in everyday life.
The first scene is a trip down a highway without any relativistic effects. Note the position and orientation of the structures in the desert.
For the next trip, we enable relativistic aberration. As we accelerate, note that the angular compression creates an initial impression of backwards motion. As we pass the sign, it seems to rotate around. This can be viewed as a Terrell rotation, or as angular aberration keeping the sign in our field of view as we pass it. The back walls of the building are also visible, and extreme distortion is visible on all the objects. Note particularly the sky, steadily shrinking down to the vanishing point.
We now enable Doppler shifting. Note that the red desert is blue-shifted ahead through the green and red, causing a rainbow effect. As the blue of the sky is further blue-shifted, it drains of colour. Near the edges of the image, the opposite happens - the sky takes on a reddish hue and the road is drained of colour as the red desert shifts into the infra-red.
With full relativistic effects (now including the headlight effect) the image quickly turns monotone, with objects near the edge of the screen darkened, and the centre brightly illuminated.
The Terrell effect can be illustrated with this flyby of a cube. Note the orientation of the cube change. Also compare it's apparent position with the position indicated on the HUD map. Remember, we are seeing the cube as it was, not as it is.
If we instead fly through the cube, the structures Terrell rotate independently, seeming to turn the cube inside out. Note that even when we have exited the back of the cube, aberration keeps most of it in view.
Another property of aberration is that it preserves circles - that is, a sphere will always present a spherical outline to any observer regardless of their relative motion. We see this demonstrated by flying a camera around the Earth at high speed. Though the camera is very close to the surface, aberration wraps the Earth into our forward field of view. But because we are so close to the earth, we can see only a small portion of its surface - so small regions, about the size of Borneo seem to bulge out and fill the sphere.
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