The Appearance of Fast Moving Objects

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This project has been presented at .

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

Galileo, classically retarded	Einstein, relativisticly retarded

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

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

  	slowly	relativistic, moving camera	classical, moving camera	classical, moving object
  x-motion without Doppler effect
  x-motion with Doppler effect
  y-motion without Doppler effect
  y-motion with Doppler effect
  xy-motion without Doppler effect
  xy-motion with Doppler effect
  y-motion without Doppler effect (traced)
  y-motion with Doppler effect (traced)

  Those movies can be calculated with the program Wuerfel.

• Moving names

  	slowly	relativistic, moving camera	classical, moving camera	classical, moving object
  x-motion without Doppler effect
  x-motion with Doppler effect
  y-motion without Doppler effect
  y-motion with Doppler effect
  xy-motion without Doppler effect
  xy-motion with Doppler effect
  y-motion without Doppler effect (traced)
  y-motion with Doppler effect (traced)

  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":
  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
  without energy flow
  with energy flow

• ... 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
  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.

  	relativistic, moving camera vmax=0.99c	relativistic, moving object vmax=0.99c	classical, moving camera vmax=3.50c	classical, moving object vmax=7.02c
  without Doppler effect
  with Doppler- effect

  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
  x-motion
  y-motion

  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).

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Prof. Dr. Udo Backhaus
last modification:  March 28th, 2008