Relativity visualized

# Overview visualization of special relativity

The speed of light, nearly 300 000 km/s or just over one billion km/h is very much larger than any speed that we know from everyday life. But the speed of light is not merely a high velocity. The special theory of relativity, formulated by Albert Einstein in 1905, describes it as a limiting velocity: The speed of light is the cosmic speed limit that no material object can reach or exceed. At velocities close to this speed limit, relativistic effects are important that are unmeasurably small at everyday velocities.
In the computer simulation we can "experience" high speed motion. We observe objects that move by at nearly the speed of light. Or from the other point of view: We travel at nearly the speed of light and take a look-around. Ultimately, these two points of view are equivalent. We may consider the observer to be moving or the object, the resulting movie is the same (principle of relativity). The explanations, however, are different for the two different points of view. For this reason, and also because it simply is more natural to consider houses as stationary and bikers as moving than the other way around, we discuss both points of view.

## Part I: The visual appearance of fast moving objects

In the main article Motion near the cosmic speed limit we observe various objects in motion at nearly the speed of light. We find, e. g., that moving rulers may sometimes look contracted, but mostly do not. Or, the side of a cube that is facing us and is unobstructed is not necessarily visible. These findings are effects of finite light travel times and are explained by animations. Other topics are the changes in apparent colour due to fast motion and real observations of high-speed motion in space.

The complexities of relativistic soccer are discussed in The ball is round.. Also features a movie on what a high-speed football would look like according to pre-Einstein physics. Animations explain the consequences of finite light travel times.

Sights that Einstein could not yet see shows more simulations of objects moving at nearly the speed of light. The most important effects (apparent change in length, apparent rotation and distortion) are explained in a non-mathematical way. Also contains two examples of observations by a moving observer: We fly by Saturn and the Sun.

The motion of Rolling wheels is more complex than a simple translation. All of the visual effects described in the articles above can be discovered here.

Brightness and color of rapidly moving objects: The visual appearance of a large sphere revisited provides a detailed explanation of the changes in color and brightness observed from a high-speed object. Includes the mathematical derivation of the formula for the searchlight effect. This formula also applies to the case of a moving observer (principle of relativity).

## Part II: Observations in high-speed flight

The main article Through the city at nearly the speed of light describes a virtual world with a speed of light so low that a biker can nearly reach it. In this world we ride a bike at nearly the speed of light through the old city centre of Tübingen. The striking images are caused by the phenomenon of aberration, explained in a non-mathematical way in this article.

Visual observations in high speed flight gives another example of observations while in high-speed motion: passing throught the Brandenburg Gate in Berlin. In this article you can find a simple mathematical derivation of the aberration formula. There are also suggestions for making your own computer simulations of high-speed flights.

Relativistic flight through a lattice is an interactive simulation in which you can choose the flight velocity. The Java code can be used as a starting point for your own computer simulations.
This may equally well be regarded as the simulation of a moving lattice seen by a stationary observer (principle of relativity).

There is additional information in the following articles that, based on their main topics, belong to other subject areas:
• The simplest approach to aberration, a qualitative argument making use of everyday experiences, is described in Destination Black Hole.

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Authors: Ute Kraus, Corvin Zahn, Date: 2022-06-16 17:50:44