An Illusion to the Eye: The Aberration Effect

Anyone who has taken a ride in a car during a thunderstorm would have noticed that the rain drops seemed to have been coming from the front of the car instead of from the sky above. This is known as the aberration of rain. Imagine that these raindrops are now photons. If we are travelling very close to the speed of light, similar distortions of rays of photons will become obvious. The faster we travel, the more distorted objects would appear.

Imagine that you are standing beside a road and a double decker bus is zooming pass you. As the speed of light is very large, you would not expect any strange events occurring. Now let say we turn on the SOL Control System so that the speed of light is lowered to 100 km/h and a bus is moving past you at 70 km/h. We will observe three different aspects of aberration.

The Distortion of Scales in the Direction of Motion

The diagram above shows the bus moving past directly in front of you. As light has a finite speed, light rays take time to travel to your eyes. Since the middle of the bus is nearer to you, light rays from B would reach your eyes much sooner than light rays from its front and rear. By the time the light rays from A and C reaches your eyes, the bus would have moved forward.

The second diagram above shows what you would observe of the bus at that time. In order for light rays from C and A to reach your eyes at the same time as light rays from B, they have to be emitted some time in the past. Hence, the front and rear of the bus would appear to be displaced backwards with respect to the middle of the bus. In the diagram, they are represented by points C' and A' respectively. To you, the bus actually seems compressed in front and stretched out to the back. In other words, there is distortion of scale in the direction of motion. Now let us view this in person to understand it better.


Start the bus: MPEG movie (936K) or still frames

What happened to Lorentz contraction? When we are determining the length of an object, we first find out the coordinates of its two ends simultaneously and take the difference. In this case, the measured length of the object will be the same as the length as calculated using the Lorentz contraction formula. However, Lorentz contraction may not be visible because light from different ends of the object may not arrive at your eyes at the same time. It is only when the object is directly in front of you that you will see the Lorentz-contracted length of the object. When the object is approaching, it appears longer than this and when the object is speeding away, it appears shorter.

Hyperbolic Distortion of Vertically Inclined Objects

On the other hand, the visual distortion does not only occur in the line of motion. The bus is also distorted in the vertical direction.

From the figure above, we can see that light rays from the top and bottom of the bus will take a longer time to travel to our eyes compared to light rays from the middle, because of the longer distances they have to cover. Hence, the light rays from the top and bottom of the bus have to be emitted some time back in the past so as to arrive at the observer with the light rays from the middle of the bus simultaneously. As a result, a vertical line will appear to take the shape of a hyperbola to the observer.

An analogous example to illustrate the two effects is to use a grid. Diagram 4 shows a stationary grid directly in front of you and diagram 5 shows the same grid moving at 99% the speed of light pass you.

These two effects become more pronounced when you are nearer the bus.

If you are getting confused, why not look at the actual scene?


Start the bus: MPEG movie (940K) or still frames

Apparent Rotation of Objects Travelling at High Speeds

In addition to the two types of distortions described above, there is also an apparent horizontal rotation of the bus. This rotation can be understood from the following diagram:

Light rays point C to your eye are normally intercepted by material in the car so you cannot see it. When the car moves rapidly enough, it moves "out of the way" of this ray so that you see point B and all other points between A and B. Hence, we will not only see a contracted side of the bus, but also the back of the bus. Similarly, the light rays emitted from the front of the bus will be blocked when the bus moves forward. As a result, the front of the bus may not be visible to the observer under such circumstances. Apparent to the observer, the front of the bus may seem to be rotated away from him while the back of the bus is rotated towards him.

To sum this up, let us see what will happen to the bus when all three effects occur simultaneously.


Start the bus: MPEG movie (921K) or still frames

Here is the view from the bus itself.


Start the bus: MPEG movie (741K) or still frames

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