IMAGES DEMONSTRATING
THE EFFECTS OF SPECIAL
RELATIVITY
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Consider the scene below, an infinite plane of coloured square tiles, with
a polar coordinate grid sky. Note the information presented in the Head-Up
Display overlaid on the image; the speed appears in the top right corner
as a fraction of the speed of light, and the corresponding Lorentz factor
in the bottom left corner. The map appearing in the bottom left corner
indicates the camera position as the origin of the green
velocity vector and blue view pyramid, which indicates the field of view
of the camera if it was stationary.
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When looking down, the camera sees the tiled plane as a square grid
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However, if the camera moves rapidly down, special relativity dictates
that light subtends a lesser angle with the direction of motion. Consequently,
the horizon, previously a great circle, becomes a smaller circle in front
of the camera, and as the light 'bunches' ahead, the tiles appear brighter.
Doppler shifting also changes the colour of the tiles.
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If the situation is reversed and the camera recedes rapidly, the tiles
appear magnified. They are also severely redshifted, and dimmed by their
expansion. The centre of the image has been brightened to partially compensate
for these effects.
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We now look in the other direction, directly up. We see the coordinate
grid as series of radial lines and concentric circles.
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We now move rapidly up. Observe the same effects at work as on the tiles;
the horizon becomes visible as a circle, the sky has contracted and rings
of colour are visible as the green bands are redshifted and blueshifted.
Note that the tiles become visible at the edges of the image, giving the
illusion of movement along a cylinder. Note also that the motion has no
effect on radial angle; it acts equally on concentric rings of light.
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When we move rapidly down, the sky expands to such an extent that the central
ring lies outside our field of vision and even when brightened,
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A classic derivation in geometrical optics is that of the appearance of
a grid moving perpendicular to the viewer. Setting the camera moving parallel
to the tiles, we can replicate these conditions, as motion is relative,
and observe an identical pattern. The image has been partially brightened
to allow these effects to be seen.
