The Appearance of Fast Moving Objects
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auf deutsch
This project has been presented at
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Short version of a cdrom which may be ordered from U. Backhaus.
Galileo, classically retarded | Einstein, relativisticly
retarded
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U. Backhaus, R. Thiel, Universität Koblenz
Abstract
The contraction of fast moving bodies in the direction of their velocity is a
well-known result of special relativity: Different observers get different
results when they measure the length of an object, the shorter the larger the
relative speed between observer and object. Much less known is the fact that
this so called Lorentz-Fitzgerald contraction is invisible in the following
sense: By looking at the moving object or by photographing it one does not
observe it as shortened but, on the contrary, as lengthened and, under
certain conditions, as deformed or twisted.
The main reason for this surprising effect is the difference between
measuring an object and observing it:
- Measuring means determing positions simultaneously while
- observing means combining light which enters the eyes or
a camera simultaneously.
simultanous emittation, registration in succession
| emittation in succession, simultanous registration
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Those animations can be generated by the program Retardierung.
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),
In the case of classical theory, the speed of light has a finite measure but
does not play the role of a limiting velocity. Therefore, some of the
animations show effects arising in classical theory due to superluminal
speeds.
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
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| relativistic, moving camera
| classical, moving camera
| classical, moving object
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x-motion without Doppler effect
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x-motion with Doppler effect
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y-motion without Doppler effect
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y-motion with Doppler effect
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xy-motion without Doppler effect
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xy-motion with Doppler effect
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y-motion without Doppler effect (traced)
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y-motion with Doppler effect (traced)
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Those movies can be calculated with the program
Wuerfel.
Moving names
| slowly
| relativistic, moving camera
| classical, moving camera
| classical, moving object
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x-motion without Doppler effect
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x-motion with Doppler effect
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y-motion without Doppler effect
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y-motion with Doppler effect
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xy-motion without Doppler effect
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xy-motion with Doppler effect
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y-motion without Doppler effect (traced)
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y-motion with Doppler effect (traced)
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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
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v=0.7c | v=0.9c | v=0.99c
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Moving "ALBERT EINSTEIN":
Light aberration and energy flow
For correct representation, two additional effects influencing the brightness
of the observed object have to be taken into account:
- 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
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without energy flow
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with energy flow
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... and now some superluminosity (v=2.0*c),
classically retarded
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.
| moving object | moving camera
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cube
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Galilei
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... 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.
| relativistic, moving camera
vmax=0.99c
| relativistic, moving object
vmax=0.99c
| classical, moving camera
vmax=3.50c
| classical, moving object
vmax=7.02c
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without Doppler effect
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with Doppler- effect
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Such movies can be calculated by the program
EinsteinB.
... and, finally, the portraits of Einstein and Galileo at v=0.9c
| slowly
| relativistic, moving camera
| classical, moving camera
| classical, moving object
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x-motion
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y-motion
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Those movies can be generated using the program
Galstein.
The simulations of this project have been generated partly for R.
Thiel's paper during her examination at the Institut für Physik to become a
physics teacher for lower grade secondary schools, partly parallel to this
examination and during our following cooperation.
The essential results of R. Thiel's paper:
Der Einfluss der endlichen Lichtgeschwindigkeit auf das Aussehen
schnell bewegter Objekte (in German)
are contained in the short version of a speech (in German, too).
Prof. Dr. Udo Backhaus
last modification: March 28th, 2008