Why You Can Never Reach the Speed of Light: A Visualization of Special R...
Δημοσιεύτηκε στις 7 Οκτ 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...é-2.jpg
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.
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...é-2.jpg
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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