Relativity visualized
Space Time Travel 
Motion near the cosmic speed limit 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. 
The Ball is Round 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. 
Sights that Einstein could not yet see  visualization of relativistic effects 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. 
Rolling Wheels 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. 
Brightness and color of rapidly
moving objects: The visual appearance of a large sphere
revisited 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. 
Through the city at nearly the speed of light
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.

Visual observations in high speed flight 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. 
Accelerated motion 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. 
Relativistic Flight through a Lattice 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. 
Destination Black Hole
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. 
Step by Step into a Black Hole Computer simulated images show views of the night sky as seen from positions close to the horizon of a black hole. 
Flight through a Wormhole
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.

Light Deflection Near Neutron Stars 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 Xray pulsars, because the ratio of neutron star radius to Schwarzschild radius strongly affects the pulse profiles predicted from models of the pulsar's Xray emission regions. 
The Real Einstein Ring A little contribution to the general personal cult of Albert Einstein in the Einstein year 2005. 
Interactive Black Hole Simulation 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. 
Röntgenpulsare 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. 
Fourdimensional ray tracing in a curved spacetime 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. 
Sector models  A toolkit for teaching general relativity: I. Curved spaces and spacetimes Teaching the general theory of relativity to high school or undergraduate students must be based on an approach that is conceptual rather than mathematical. In this paper we present such an approach that requires no more than elementary mathematics. The central idea of this introduction to general relativity is the use of socalled sector models. Sector models describe curved space the Regge calculus way by subdivision into blocks with euclidean geometry. This procedure is similar to the approximation of a curved surface by flat triangles. We outline a workshop for high school and undergraduate students that introduces the notion of curved space by means of sector models of black holes. We further describe the extension to sector models of curved spacetimes. The spacetime models are suitable for learners with a basic knowledge of special relativity. 
Sector models  A toolkit for teaching general relativity: II. Geodesics Sector models are tools that make it possible to teach the basic principles of the general theory of relativity without going beyond elementary mathematics. This contribution shows how sector models can be used to determine geodesics. We outline a workshop for high school and undergraduate students that addresses gravitational light deflection by means of the construction of geodesics on sector models. Geodesics close to a black hole are used by way of example. The contribution also describes a simplified calculation of sector models that students can carry out on their own. The accuracy of the geodesics constructed on sector models is discussed in comparison with numerically computed solutions. 
Sector models  A toolkit for teaching general relativity: III. Spacetime geodesics Sector models permit a modelbased approach to the general theory of relativity. The approach has its focus on the geometric concepts and uses no more than elementary mathematics. This contribution shows how to construct the paths of light and free particles on a spacetime sector model. Radial paths close to a black hole are used by way of example. We outline two workshops on gravitational redshift and on vertical free fall, respectively, that we teach for undergraduate students. The workshop on redshift does not require knowledge of special relativity, the workshop on particles in free fall presumes familiarity with the Lorentz transformation. The contribution also describes a simplified calculation of the spacetime sector model that students can carry out on their own, if they are familiar with the Minkowski metric. 
Teaching gravitational light deflection:
A short path from the metric to the geodesic Gravitational light deflection was one of the early tests of the general theory of relativity and has by now attained a huge importance in astronomy. When teaching this topic in school, however, one is faced with the problem that the theoretical description of light paths as geodesics relies on advanced mathematics. In this contribution we describe a method that allows students to determine the geodesics for a given metric by means of a graphic construction. 
Firstperson visualizations of the special and general theory of relativity Visualizations that adopt a firstperson 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. 
Gravitational Waves:
Models and Experiments on Waveforms, Effects and Detection In this contribution we present models and experiments that are designed to convey an idea of the nature of gravitational waves to students. These teaching materials have been developed for the "Schülerlabor Raumzeitwerkstatt" (student lab on relativistic physics) at Hildesheim university, where they are used for teaching students in grades 9 to 13 (aged 15 to 19 years). 
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