Seeing Relativity 10 minutes


We begin with a view of constant proper acceleration through a starfield. This is how space travel to near-light speeds would appear, contrary to the special effects in Star Trek and Star Wars universes. C, the speed of light , is not exceeded.


A sphere (moving at 0.5c) passes over a screen, onto which the title is projected. The sphere leaves a delayed shadow - cast earlier when it was in a different position . Light reflected from the moving sphere is Doppler-shifted, appearing a different colour.


As we enter our reduced c world - where the speed of light is only five meters per second (18 Kilometers per hour) the effects of slow light are apparent even without motion. A flickering streetlamp does not instantly illuminate its surroundings; rather it casts expanding spherical shells of light into space around it, which we can see when they hit a surface.


If we take a flash photograph inside a stationary tram, we can see that the flash does not instantly illuminate the interior, but slowly travels through the tram. As the light must travel from our flash and back to the camera, the illuminated region appears to move radially outward at half the speed of light.


The streetlamp turns on and off. We can see that even though the wall is closer to the streetlamp than the ground, parts of the ground are illuminated first. To understand this, we must take into account not only the distance of the surface to the streetlamp, but also the distance to the camera.
We move to a schematic world where we can track the path of individual photons. As light makes the trip between the lamp, the surface and the camera, the light which follows the shortest path will reach the eye first. As the direct route between lamp and camera is the shortest and thus the fastest, we see the lamp itself turn on before anything else is illuminated. The next quickest route is from the lamp to the ground to the camera, so the ground is illuminated first. The route to the wall is longer, so it appears later.


We now look at moving objects. A tram moving close to the speed of light (0.866c, a Lorentz factor of 2) displays many effects, becoming distorted, and changing colour and brightness. Its shadow also falls at an unusual angle. The effects of distortion (angular aberration), colour (the Doppler effect) and intensity (the Headlight effect) can be separately treated, so for the moment we "enhance" our image, correcting it so only distortion appears. This correction occurs within the large rectangle labelled "computer corrected".


The tram appears to have been shortened, sheared (with the two ends no longer perpendicular to the sides), and slightly bent.

To explain the shear, we again move to the schematic world. As the tram moves close to the speed of light, it is shortened by the Lorentz contraction. This explains why it appears shorter. As the back side of the tram is further from us than the front side, the light takes longer to reach us. Thus the light we see at
any one time must have left the front and back surfaces of the tram at different times.

As the tram is moving at a speed comparable to that of light, this time delay also means that we see the front surface of the bus later and further along the track than the back surface, thus we see a shear.
This effect is known as the Terrell rotation, as the degree of contraction and shear combine to the exact proportions that a rotation would produce.
However, this effect is dependent on the object appearing small and distant. If we are too close to the object its different parts will appear rotated by different amounts, sometimes resulting in extreme distortion.


If we move with the tram, the world around us is subject to the same sort of distortions. While we can understand these in terms of the Terrell effect, there is a more powerful concept - relativistic aberration.
[Also note that when we move with the tram, it seems to be moving faster - this is time dilation at work.]


To understand relativistic aberration, consider the ordinary "real" world. When a vehicle moves though rain, to the vehicle the rain seems to fall at an angle. In an analogous process, photons "falling" into the camera appear to come from different angles as the camera moves at different speeds. As the camera moves faster and faster, photons enter it at increasingly steeper angles. This means that things that would appear behind us if we were in their rest frame are wrapped forward into our field of view. The same,reversed, applies to outgoing photons.


This is why the tram appears small as it approaches us, and large as it recedes from us.


If we accelerate the camera slowly, we can see the distortion increasing, and objects - like the clouds behind us - sliding into our field of view, and the sun moving closer to our direction of motion.


To see what is happening all around us, we use a mercator projection; a map of everything we can see around us. The map is made by "unwrapping" a sphere and stretching the areas at the poles to make the map flat. This is the same kind of map that shows Greenland the size of South America.
Accelerating, we can see that objects behind us increase in size. Even though we are moving away from the houses at the end of the street [left and right edges] they grow larger. The patch of blue sky overhead shrinks to a small circle ahead of us.


Returning to the tram we now consider the colour shift. Even at low speeds (0.1c) objects change their colour significantly. Green lamp posts ahead of us look red, behind us they look green. This is the Doppler shift at work.
Just as the direction of motion of photons change when the camera moves, so do the frequencies which we perceive as colour. Objects we move towards appear blueshifted. Objects we move away from appear redshifted. As we go faster, the effect becomes extreme, and we see a rainbow effect as any sharp spectral features pass through the visible band.


If we remove colour correction from our acceleration scenes, we see the world ahead go blue, and the sun darken as we start to see in the ultraviolet and above. This is matched by a reddening behind us. A rainbow ring appears in the sky as the blue colour is shifted through the regions of the spectrum our eye detects as red and green.


Doppler shift effects are seen again in this mercator projection.Though the distribution of energy in spectra means that the Doppler effect will sometimes make an object look darker, this is not the only effect changing the brightness of the tram.


At high speeds, without the protection of computer correction, extreme intensity effects occur, with most parts of the scene too dark or too bright to discern any detail. Because aberration concentrates photons in front of us and spreads them out behind us, objects ahead look brighter and objects behind look dimmer.
Time dilation also means that the shutter of a moving camera is open longer - collecting more light and making the image brighter.
This effect also means that moving light sources concentrate their output along their direction of motion - the headlights on the front and back of this tram are of equal intensity when it is stationary.
We can see that as we accelerate without the benefit of computer correction, we are swiftly overtaken by the effects of relativity, with the scene changing colour and becoming blindingly bright or too dark to make out. At high velocity, the effect is extreme - the camera is subjected to a beam of high energy electromagnetic radiation.


A more subtle effect occurs with shadows. Note that the shadow of the moving tram lies at a steep angle compared with that of other objects. Viewed from above, we can see that because light moves slowly,
shadows are not cast instantaneously. Because the effects of the blocking take time to reach the surface, it can remain illuminated (or vice versa) when it would normally not be.


As the tram accelerates, electromagnetic radiation enters more and more directly from in front. This effect, when combined with the doppler shift towards shorter wavelengths of higher frequencies, would produce a lethal high intensity beam of x-rays and gamma-rays. This is another consequence of near light travel usually ignored in science fiction.



Here is the same intensity effect shown in mercator projection. Note that any information from the outside world enters through a very restricted kind of porthole . What changes would occur in any radi o communication between 2 trams, travelling one behind another ?


Moving light sources also cast unusual shadows ­ because they cast different parts of the shadows from different positions at different times. Note the shape of the shadows cast on the ground. Why does this occur ?


These effects can be seen in the real universe. But the real speed of light is very fast, three hundred thousand kilometers per second. Because relativity effects are most pronounced at very high speeds, the real visual effects of relativity must occur on a much larger scale than the simulations you've just seen. For example : light delay in the "light echoes" of supernovae, the Doppler shift of fast-moving astronomical bodies, and the headlight effect in the incredible brightness of gas jets directed towards us.
While humans cannot yet directly experience these effects, it is possible, though not practical, to build a space ship with today's technology that could travel fast enough to see these effects directly.




Visualising Special Relativity 7 minutes

The first scene is a trip down a highway without any relativistic effects. Note the position and orientation of the structures in the desert. There are several elements superimposed on the video, constituting the head-up display (HUD). The number at the top right is the current camera speed relative to the scene. The number at bottom left is the Lorentz or gamma factor, a measure of the degree of relativistic effects. The image at bottom right is a map of the scene with the camera view-pyramid (position, and field of view) shown in blue, and the camera velocity shown in green.


 

For the next trip, we enable only 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. Look at the difference between our actual postion as viewed from above on the lower right, and our apparent position. 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, adding it to the aberration effects from before. Note that the red desert is blueshifted ahead through the green and red,causing a rainbow effect. As the blue of the sky is further blueshifted, 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. Doppler and intensity effects are disabled. Note the orientation of the cube change. Also compare its 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 orbiting a camera around the Earth at high speed. The camera's position can be seen from above in the lower right hand corner of the screen.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.