Jump to content

File:XYCoordinates.gif

Page contents not supported in other languages.
This is a file from the Wikimedia Commons
From Wikipedia, the free encyclopedia

XYCoordinates.gif (454 × 189 pixels, file size: 1.53 MB, MIME type: image/gif, looped, 49 frames, 6.7 s)

Summary

Description
English: Demonstration of Aberration of light and Relativistic Doppler effect. In this diagram, the blue point represents the observer. The x,y-plane is represented by yellow graph paper. As the observer accelerates, he sees the graph paper change colors. Also he sees the distortion of the x,y-grid due to the aberration of light. The black vertical line is the y-axis. The observer accelerates along the x-axis.
See below for additional description
Source
Author TxAlien at English Wikipedia

How these images were made

Diagram 1
Animation: Image:Lcprojection2m.gif

In this section we will use the Minkowski space 4-dimension vectors and units where speed of light c = 1. In this notation velocity vector is

where

is a 3D velocity vector and

The component is the timelike component of while the other three components are the spatial components and

In spacetime, any small object is the sequence of spacetime events or world lines. Hence a 3D object in space-time can be described as a set of world lines corresponding to all the points that make up that object. Consider a simple objects in the space such as a sphere:

Diagram 2. The grey ellipse is moving relativistic sphere, its oblate shape due to Lorentz contraction. Colored ellipse is visual image of the sphere. Background curves are a xy-coordinates grid which is rigidly linked to the sphere, it is shown only at one moment in time.

where a and b are parameters of the mapping and r is the radius of the sphere. To make the formulas easy to read we will leave out the parameters (a,b). In the frame where the object is at rest, the set of world lines can be represented as the world surface in Minkowski space

or

where is timelike history parameter. In a frame which moves relatively to the object with velocity after Lorentz transformations

it can be written as

At any given observer time

the surface in 3-d space after substitution

and

can be written as

However, observer can only see the object on light cone in the past when light is emitted by points on the object. Therefore, if observers coordinates are (t,0,0,0) he sees (Diagram 1) the surface points where they were in time

or in our notation

Solution to this equation is

Hence the observer will see the surface

where

On Diagram 2 surface is flattened (this effect is called Lorentz contraction) grey ellipse, while the visible sphere image is colored. Color change is due to the relativistic Doppler effect.


It's still not finished--TxAlien 05:04, 3 September 2006 (UTC)

Other images

Moving wave source..
Animation: Media:Waves01.gif
Relativistic Doppler effect in comparison with non-relativistic effect.
Animation: Media:Compare03s.gif


Next pictures show a model of movement through a subway tunnel at an increasing speed. Observer would not only see changes in colors but the outer walls will also appear convex. This convex appearance is due to seeing parts of the tunnel at different moments in time because of the finite speed of light. This effect is called aberration of light.

On this image observer (blue point) is inside the subway. Velocity is zero. It is the first frame in an animated model of movement.
Animation: Media:RelSubway2.gif
On this image observer (blue point) moves inside the same subway. Velocity is equal 0.7 speed of light
Animation: Media:RelSubway2.gif
The outside view of the subway. However, this is only a model, there does not exist an observer which can see the tunnel like this.


This images shows the view on a sphere moving at 0.7c relatively to a stationary observer, which is represented by blue point. Curved lines represent the xy grid coordinates of a moving system.

This sphere moves toward to observer.
Animation: Media:SphereAberration01.gif
On this picture an observer is inside the sphere.
Animation: Media:SphereAberration01.gif
This sphere moves away from observer.
Animation: Media:SphereAberration01.gif

Tachyon visualization. Since that object moves faster than speed of light we can not see it approaching. Only after a tachyon has passed nearby, we could see two images of the tachyon, appearing and departing in opposite directions.
Animation: Image:Tachyon03.gif
Animation: Media:Tachyon03.gif

All these images are graphical solutions of an accurate mathematical model which is based on the Lorentz transformation

Licensing

TxAlien at the English-language Wikipedia, the copyright holder of this work, hereby publishes it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. Subject to disclaimers.
Attribution: TxAlien at the English-language Wikipedia
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
This licensing tag was added to this file as part of the GFDL licensing update.
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. Subject to disclaimers.

Original upload log

The original description page was here. All following user names refer to en.wikipedia.
  • 2006-08-12 23:50 TxAlien 454×189× (1600354 bytes) Demonstration of light aberration and [[Relativistic Doppler effect]].

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current21:28, 15 January 2012Thumbnail for version as of 21:28, 15 January 2012454 × 189 (1.53 MB)Cantons-de-l'Est{{Information |Description={{en|Demonstration of en:Aberration of light and en:Relativistic Doppler effect. In this diagram, the blue point represents the observer. The x,y-plane is represented by yellow graph paper. As the observer accelerate
No pages on the English Wikipedia use this file (pages on other projects are not listed).

Global file usage

The following other wikis use this file: