Visualization of the Gödel universe
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| Number of Parts | 63 | |
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| License | CC Attribution 3.0 Unported: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. | |
| Identifiers | 10.5446/39056 (DOI) | |
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Transcript: English(auto-generated)
00:04
Welcome to our video clip introducing our paper on visualizations of the good universe. My name is Michael Busser. I'm Endo Kayari. And I'm Wolfgang Schleich. In July of 1949, the ingenious logician Kurt Gödel published a paper entitled
00:21
An Example of a New Type of Cosmological Solution of Einstein's Field Equation of Gravitation. He dedicated this article to his friend Albert Einstein on the occasion of his 70th birthday. The intriguing mystery of this new cosmological solution is the existence of closed time-like curves
00:41
which make it feasible to go on a mind-boggling journey into one's own past. The main goal of our article is to visualize this unusual space-time geometry. In general relativity, light cone diagrams are a useful tool to get a first idea about the structure of a space-time.
01:01
Here you can see the light cone diagram of Gödel's universe in which the future light cones point towards the time axis. As one increases the distance to the origin, the light cones keel over and reach the domain of negative coordinate time allowing the existence of closed time-like curves. To understand the visual perception in Gödel's universe, one has to know how light propagates.
01:24
The picture shows two light rays emitted at the origin. Common to all light rays is their helical structure stretched along the z-axis. The top view reveals that all light rays emanating from the origin are encompassed by a cylinder. This cylinder is indicated by the red circle whose radius we call the critical Gödel radius.
01:45
For the visualization of Gödel's universe, we use retracing, a simple but powerful method. The basic idea is to trace back light rays from the observer's eye to the scenery. In case a light ray hits an object, the corresponding pixel on the screen is colored accordingly.
02:04
As a first example, we visualize the view in a globe seen by an observer at the origin. There exist two possible ways, the orange and the blue ones, that light can take to reach the observer. These two possibilities lead to two mirror-inverted images of the globe in a visualization.
02:24
As one increases the distance of the globe from the origin, the two images come closer and finally merge near the Gödel radius. Beyond the critical Gödel radius, the globe is out of sight.
02:40
We are now ready to embark on our mind-boggling journey into the past. In order to go on such a mind-boggling journey, we have to find an appropriate closed timelike curve. By using isometries, we can transform the simplest closed timelike curve such that it passes through the origin.
03:00
For our visualization, we use exactly this curve to send a sphere on a trip back in time. The first phase of the journey of the sphere is at rest near the observer. At time t equals zero, the sphere starts to move along the closed timelike curve until it returns back to the origin at the end of phase two. After this round trip, the sphere remains at rest near the observer.
03:25
The visualization of this scenario shows the young red sphere and its copies due to the light rays that first take a detour to the Gödel horizon. Suddenly, the older blue version of the sphere approaches the younger sphere at rest. It reaches the origin at the same moment in time at which the red, younger sphere departs on its journey along the closed timelike curve.
03:47
While the red sphere disappears after it crossed the Gödel horizon, its blue older version remains at rest. In our work, we have employed the tracing to provide a new perspective on the structure of Gödel's universe
04:00
and we hope that it inspires further investigations of other curved spacetimes using this powerful technique.