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Kadi Runnels

**Shared October 7, 2015**

This video is an entry for the Breakthrough Junior Challenge 2015 which gives a unique visualization of Special Relativity using hyperbolic geometry.

This idea was inspired by the famous woodcut by M.C. Escher Circle Limit III. http://www.mcescher.com/gallery/recog...

I liked the idea of making a video on Special Relativity because I had already explored the use of M.C. Escher’s woodcut Circle Limit III as a teaching tool for explaining the hyperbolic geometry of Minkowski spacetime. The main intuition is that the principle of Relativity asserts that the manifold of frames of reference is homogeneous and isotropic, and there are exactly three geometries associated with this: Sphere (which exists as rotations through space), Plane (which represents Galilean Relativity) and the Hyperbolic Plane (which exists as rotations through spacetime).

I wanted to find a way to use this intuition without overwhelming the audience with technical terms. When the timelike unit vectors in 2+1 spacetime (which correspond to velocity four-vectors) are projected onto a disk (see Wikipedia: “Hyperboloid model”), the result is the Poincare Disk Model, which is (almost) the geometry portrayed in Circle Limit III. I had never seen anyone to use this as a visualization of Special Relativity, and so I decided to make the video.

Public Domain Image Sources (in order of appearance):

Einstein: https://commons.wikimedia.org/wiki/Ca...

pulse of light: https://pixabay.com/en/light-bokeh-ye...

stopwatches: https://pixabay.com/en/stopwatch-cloc...

crowd: https://pixabay.com/en/men-personal-m...

beakers: https://pixabay.com/en/beakers-experi...

map: https://pixabay.com/en/world-map-eart...

wall clock: https://pixabay.com/en/clock-analog-t...

starburst: http://www.cliparthut.com/starburst-c...

Electric Current: https://pixabay.com/en/current-electr...

mouth: https://pixabay.com/en/lips-sexy-mout...

water waves: https://pixabay.com/en/banner-header-...

cosmic lake: https://pixabay.com/en/graphics-virtu...

Galileo: http://fineartamerica.com/featured/1-...

flashlight: https://pixabay.com/en/light-torch-la...

Poincare: https://commons.wikimedia.org/wiki/Fi...

Einstein: https://commons.wikimedia.org/wiki/Ca...

Lorentz: :https://en.wikipedia.org/wiki/Hendrik...

Minkowski: :https://en.wikipedia.org/wiki/Oskar_M...

star cluster:https://pixabay.com/en/star-clusters-...

trash can: https://pixabay.com/en/trash-can-garb...

Einstein and Lorentz: https://en.wikipedia.org/wiki/Hendrik...

car: https://pixabay.com/en/car-red-vehicl...

bicycle: https://pixabay.com/en/vintage-bicycl...

jet: https://pixabay.com/en/jet-airplane-p...

spacetime: https://en.wikipedia.org/wiki/Minkows...

atomic cloud: https://pixabay.com/en/explosion-nucl...

stopwatch: https://pixabay.com/en/stopwatch-raci...

Software used to create this video includes iMovie, Keynote, Pixelmator, MathType, and Quicktime Player.

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