The special theory of relativity describes space, time and motion.
For relativistic effects to become noticeable, motion must occur at nearly
the speed of light. Since the speed of light is in excess of a billion
kilometers per hour, such motion is far beyond our everyday experience.
With fast computers, however, the experience of motion
at nearly the speed of light can be simulated.
Here we present a simulation using a detailed three-dimensional model
of the old city centre of Tübingen. In the simulation we reduce
the speed of light in “virtual Tübingen” to 30 kilometers per hour:
We can then ride a bike through the city at nearly the speed of light.
One of the fundamental statements of the special theory
of relativity is length contraction. From Albert Einstein's
seminal paper of 1905 on the special theory of relativity
(where V is the speed of light):
A rigid body that, when measured at rest, has the shape of a sphere,
therefore in motion has - when observed from the frame at rest - the
shape of an ellipsoid of rotation with the axes
While the Y- und Z-dimensions of the sphere (and therefore of
every rigid body of arbitrary shape) do not appear modified by the motion,
the X-dimension appears shortened by the factor
1 : √(1 - v2/V2)
, i.e. the more the greater v. For v = V all moving
objects – observed from the frame “at rest” – shrink to two-dimensional
Fig. 1 Illustration by G. Gamov :
The biker (and with him the observer) moves down the road at
nearly the speed of light and sees the houses contracted.
So should we image a fast moving object to look contracted
in the direction of motion?
Taken literally, Einstein's statement means just that.
And this notion was in fact illustrated by the physicist George Gamov
in his 1940 book “Mr. Tompkins in Wonderland” [2,3].
There he writes about a virtual
world in which the speed of light is only 30 km/h, so that
even a biker can move at nearly the speed of light.
This biker sees the houses at the roadside allegedly as shown
in figure 1, contracted in the direction of motion.
However, this picture is entirely wrong.
It is wong because Gamov did not take the consequences of the
finite speed of light into account.
In everyday life we may to all intents and purposes pretend that
the speed of light is infinite, since we are always concerned
with much smaller velocities.
But when a velocity close to the speed of light is involved, this is not
justified any more. On the contrary, what we should see in this case
would be substantially influenced by the fact that light
propagates at a finite speed.
Fig. 2 Houses on the market place of Tübingen.
This is the view of a cyclist who passes by slowly
(much slower than c) from the left to the right and
looks to the side over her left shoulder.
that a cyclist going at nearly the speed of light
have of houses on the roadside is shown in figures 2 to 4
(in the figure captions
we employ the usual symbol c for the reduced speed of light, too).
Figure 2 shows the houses as seen by an observer at rest or in slow
Fig. 3 View of the contracted houses according to Gamov.
The relative velocity is 0.9 c.
When moving by at nearly the speed of light,
a measurement of the shape of the houses would
reveal them to be contracted in length as described by Einstein.
A view of the contracted houses
according to Gamov is shown in figure 3.
Fig. 4 This is how a cyclist would see
the houses on the market
place of Tübingen when passing by at 0.9 c from left to right
and looking sideways over her left shoulder.
But when the fast cyclist looks at the houses,
then she sees them rotated and distorted (figure 4).
Surprisingly, it has taken a long time to realize that
an observer at nearly the speed of light must see her surroundings
distorted. After all, it was in 1676 that the observations of
Olaf Römer established that light propagates with a finite speed.
But it was not until 1924 that Anton Lampa  described the
visual effects for the first time.
Later, the work of Roger Penrose  and James Terrell 
was the starting point for a large number of investigations
(see  for an overview over the literature).