Relativity visualized

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Visualization of special relativity


Motion near the cosmic speed limit

Motion near the cosmic speed limit
Ute Kraus
July 14, 2005

The speed of light in vacuum – 299 792 458 meters per second or more than a billion kilometers per hour – is the ultimate speed limit, enforced by the laws of nature. Compared to light, motion in everyday life is extremely slow. But even though we never experience high velocities ourselves, in theory we understand them very well. Computer simulations based on the special theory of relativity make it possible to simply take a look at objects moving at nearly the speed of light.

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The Ball is Round

The Ball is Round
Ute Kraus
June 5, 2006

Our Contribution to the Football World Cup: In other sections of this website we show that objects moving at nearly the speed of light appear rotated, compressed, elongated or bent. A soccer ball is a remarkable exception: a freak of nature, it always appears to be round, no matter how fast it moves and in which direction: The Ball is Round.

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Sights that Einstein could not yet see - visualization of relativistic effects

Sights that Einstein could not yet see - visualization of relativistic effects
Ute Kraus, Hanns Ruderexterner Link, Daniel Weiskopfexterner Link, Corvin Zahn
May 25, 2002

Since we do not daily fly at 90% of the speed of light through a wormhole to our place of work near a black hole, but instead live in a part of the universe that is very well described by Newton's laws, we unfortunately never developed an intuitive understanding of special and general relativistic spacetimes. However, thanks to fast computers and modern computer graphics, we can today simulate and visualize the relativistic effects. This way, though we still may not "understand" them, we at least see them.

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Rolling Wheels

Rolling Wheels
Corvin Zahn
May 23, 2002

In his book "Mr. Tompkins in Wonderland" George Gamow describes the adventures of Mr. Tompkins in a fictitious world, in which the speed of light is only 30km/h. Motivated by the scene of Mr. Tompkins riding a bike along the street, the movies below show what a relativistically rolling wheel "really" looks like.

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Brightness and color of rapidly
moving objects: The visual appearance of a large sphere
revisited

Brightness and color of rapidly moving objects: The visual appearance of a large sphere revisited
Ute Kraus
January 1, 2000

An object at relativistic speed is seen as both rotated and distorted when it is large or close by so that it subtends a large solid angle. This is a consequence of the aberration effect and is obtained by purely geometric considerations. In this paper it is pointed out and illustrated that a photorealistic image of such an object would actually be dominated by the Doppler and searchlight effects, which would be so prominent as to render the geometric apparent shape effectively invisible.

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Through the city at nearly the speed of light

Through the city at nearly the speed of light
Ute Kraus, Marc Borchers
January 26, 2005

Driving at nearly the speed of light? Impossible in real life, but feasible in a computer simulation: A tour through the city centre of Tübingen illustrates what we should see when moving at such a high speed.

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Visual observations in high speed flight

Visual observations in high speed flight
Ute Kraus
January 28, 2005

High speed motion is the domain of the special theory of relativity. In this domain everyday experience fails us because we are simply too slow to ever personally experience relativistic effects. But high speed flights, i.e. flights at nearly the speed of light, can be simulated on a computer. The sights that travellers would see on such flights are amazing. Yet, they can be explained in an intuitive way and they illustrate important physical effects like aberration.

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Accelerated motion

Accelerated motion
Ute Kraus
July 17, 2008

On this relativistic trip we start from rest, accelerate to 90% of the speed of light, slow down again and then stop. While moving we look ahead and there see the Brandenburg Gate that we approach with this short sprint.

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Relativistic Flight through a Lattice

Relativistic Flight through a Lattice
Ute Kraus, Corvin Zahn
30.01.2003

As supplement to the "do it yourself" chapter of the paper Visual observations in high speed flight we have an online executable sample program. The Java program code can be used as template for own experiments.

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Visualization of general relativity


Destination Black Hole

Destination Black Hole
Ute Kraus
November 11, 2005

A journey nearly down to the horizon of a black hole - a computer simulation renders the trip possible and shows what we should see from there.

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Step by Step into a Black Hole

Step by Step into a Black Hole
Ute Kraus
December 16, 2004, March 20, 2005

Computer simulated images show views of the night sky as seen from positions close to the horizon of a black hole.

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Flight through a Wormhole

Flight through a Wormhole
Corvin Zahn
March 13, 2008

Wormholes are traversable connections between two universes or between two distant regions of the same universe. This contribution shows a flight through the wormhole that connects Tübingen University with Boulogne sur Mer in the north of France.

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Light Deflection Near Neutron Stars

Light Deflection Near Neutron Stars
Ute Kraus
1998

This contribution describes and illustrates light deflection near neutron stars as an example of the significance of general relativity for astrophysics. First, a summary is given of the properties of photon orbits in the Schwarzschild metric, the Schwarzschild metric being a good approximation to the exterior metric of slowly rotating neutron stars. Secondly, it is illustrated how light deflection affects the observation of sources on the surface or close to the surface of a neutron star. Thirdly, it is illustrated that it is imperative to take light deflection into account when interpreting the pulse profiles of accreting X-ray pulsars, because the ratio of neutron star radius to Schwarzschild radius strongly affects the pulse profiles predicted from models of the pulsar's X-ray emission regions.

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The Real Einstein Ring

The Real Einstein Ring
Corvin Zahn, Ute Kraus
February 24, 2005

A little contribution to the general personal cult of Albert Einstein in the Einstein year 2005.

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Interactive Black Hole Simulation

Interactive Black Hole Simulation
Corvin Zahn, Ute Kraus
April 01, 2006

You are looking out into space observing distant stars and galaxies. Imagine there was a black hole between you and the distant celestial bodies - what would you see?

Using the mouse you can place a black hole in front of the galaxy cluster Abell 2218 and experiment with the effects of relativistic light deflection.

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Röntgenpulsare

Röntgenpulsare
Ute Kraus
September 25, 2006

Röntgenpulsare gehören zu den hellsten Röntgenquellen des Milchstraßensystems. Der zeitliche Verlauf ihrer gepulsten Strahlung weist eine für den jeweiligen Pulsar charakteristische Form auf. Während gut verstanden ist, wie die Röntgenstrahlung entsteht, gibt die Interpretation der Pulsformen noch Rätsel auf.

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Four-dimensional ray tracing in a curved spacetime

Four-dimensional ray tracing in a curved spacetime
Corvin Zahn
October 14, 1990

A few movies show various objects (black holes, neutron stars, a gravitational collapse) in a Schwarzschild spacetime. This serves to illustrate the effect of gravitational light deflection on the visual appearance of these objects.

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Multi-focus contributions


First-person visualizations of the special and general theory of relativity

First-person visualizations of the special and general theory of relativity
Ute Kraus
August 24, 2007

Visualizations that adopt a first-person point of view allow observation and, in the case of interactive simulations, experimentation with relativistic scenes. I illustrate and explain the main aspects of the visual observations, outline their use in teaching relativity and report on teaching experiences. This paper assumes some basic knowledge about relativity on the part of the reader. It addresses instructors of physics at the undergraduate and advanced secondary school level as well as their students.

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Authors: Ute Kraus, Corvin Zahn, Date: 2013-10-23 23:45:51
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