Short version of a cdrom which may be ordered from U. Backhaus.

Galileo, classically retarded | Einstein, relativisticly retarded |
---|---|

The main reason for this surprising effect is the difference between measuring an object and observing it:

means determing positions simultaneously while**Measuring**means combining light which enters the eyes or a camera simultaneously.**observing**

simultanous emittation, registration in succession | emittation in succession, simultanous registration |
---|---|

The finite value of the speed of light has the consequence that parts of an object with different distances to the observer are imaged at different moments in the past that means, in the case of fast moving objects, due to different positions of the object.

During the last years additional effects have been discussed such as the influence of frequency (Doppler effect) and intensity transformation. Most of the publications cause the impression that these effects are specifically relativistic. We want to stress that most of the effects arrise in classical physics similarily although differently pronounced.

We show several computer animations generated by own raytracing routines. They demonstrate the different effects caused by the finite runtime of light, Doppler effect and intensity transformation due to classical and relativistic theory, respectively. Our main aim is to discriminate classical from relativistic effects and to emphasize the reach of classical theory.

We think generating those animations and considering the demonstrated effects is an excellent opportunity to reflect upon different theories and their implications. Additionally, we consider the generation of those pictures and movies as a good example for the interdependence between theoretical reflections, numerical computing and visualization:

- At first, theoretical results serve as guidelines for the development of the computer algorithms.
- The movies then visualize the expected effects.
- Finally, however, they show additional and, maybe, surprising effects thus leading again to theoretical reflections.

The animations below show the relative motion between a camera and a
**cube** or the printed names of "**ALBERT
EINSTEIN**" (relativistic calculations) and "**GALILEO GALILEI**"
(classical calculations), respectively. They distinguish between the following
cases:

- motion of the camera or motion of the object,
- relativistic or classical calculation,
- with or without tracing camera,
- taking into account of the Doppler effect or not,
- taking into account of the aberration of light or not (up to now only grayscale because only 256 colours can be assigned by using the Borland Pascal compiler),
- visualization of the incident flow of energy (only in grayscale, too),

By clicking on one of the following pictures you can download a document with the related little animation. That document additionally offers a link to the related high resolution mpeg video. In this internet version, the mpeg videos are not contained.

## Moving Cube

Those movies can be calculated with the program Wuerfel. ## Moving names

Those movies can be calculated with the program EinsteinG. ## Moving "ALBERT EINSTEIN":

Comparison of the geometric effects at different velocities,relativistic calculation

The movies below contain the same number of pictures per unit time. They compare, therefore, the magnitude and the course of the geometric effects, simultanously.v=0.1c v=0.3c v=0.7c v=0.7c v=0.9c v=0.99c ## Moving "ALBERT EINSTEIN":

For correct representation, two additional effects influencing the brightness of the observed object have to be taken into account:

Light aberration and energy flow- Light emitted isotropically by the moving object is concentrated in
forward direction by
**light aberration**. - Due to Lorentz transformation, the number of photons registrated per unit time, i.e. the light intensity, increases with the relative speed.

slow x-motion y-motion xy-motion without

energy flowwith

energy flow- Light emitted isotropically by the moving object is concentrated in
forward direction by
## ... and now some superluminosity (v=2.0*c),

In classical physics, the speed of light is finite, too. But, contrary to relativistic theory, it doesn't form an upper limit for the speed of moving objects. It makes sense, therefore, to study motions faster than light.

classically retardedmoving object moving camera cube Galilei ## ... and now, accelerated motions in the x-direction

We calculate motion of

**constant local acceleration**:- In the case of relativistic calculation, the motion is shown until v=0.99c.
- In the case of classical calculation, the motion is calculated for
**the same time intervall**and**the same acceleration**. Therefore, speeds far above the speed of light arise.

Such movies can be calculated by the program EinsteinB.

## ... and, finally, the portraits of Einstein and Galileo at v=0.9c

slowly relativistic,

moving cameraclassical,

moving cameraclassical,

moving objectx-motion y-motion Those movies can be generated using the program Galstein.

The essential results of R. Thiel's paper:

are contained in the short version of a speech (in German, too).

last modification: March 28th, 2008