The Age of the Universe
This video explains, why we know that our universe is 14 billion years old. This question is used to show how Einstein's field equations of gravity are solved in the context of an expanding universe. In the second part of the video key concepts of relativity are illustrated.
0:00 - Intro
0:27 - Overview
0:55 - Bounds on the age of the universe
1:44 - An expanding universe
2:20 - Hubble's law
2:43 - Estimate from the expansion
4:06 - Time reversal
4:49 - Einstein's field equations of gravity
5:30 - The Friedmann equation
6:07 - The age of the universe
7:34 - Add ons: From Einstein to Friedmann - second outline
8:22 - The metric - the measurements of distances
9:24 - Coordinate transformations: translations
9:45 - Coordinate transformations: rotations
10:09 - In three dimensions
10:39 - In four dimensions - special relativity
10:55 - In the frame of the car
11:26 - In the frame of the platform
12:30 - Lorentz transformations and Minkowski space
13:06 - The metric of an expanding universe
13:31 - The Christoffel symbols
14:05 - The curvature quantities: The Ricci tensor
14:37 - The curvature quantities: The Einstein tensor
14:55 - The Friedmann equation
15:15 - The mathematica worksheet
15:30 - Concluding remarks
The mathematica notebook shown in the video can be downloaded from:
https://www.dropbox.com/s/awm879dlvyk...
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This video is produced with two libraries:
manim:
https://www.manim.community/
blender:
https://www.blender.org/download/
Besides these generic animation packages I made thankfully use of the incredible database of digital LEGO world:
https://www.mecabricks.com/
I'm also new to blender and I learnt a lot from blender tutorials like:
• Blender Tutorial: Text Transformation Anim... @tutor4u
• UPDATED Realistic Procedural Starfield Ble... @kaetsusstudio
• Procedural Galaxies in Blender 2.91! @CBaileyFilm
Images that were used:
black hole:
http://www.esa.int/var/esa/storage/im...
gravitational waves:
credits LIGO/T. Pyle
https://www.ligo.caltech.edu/image/li...
And the applet for the visualization of temperature as average kinetic energy was taken from:
https://phet.colorado.edu/en/simulati...
The video is dedicated to my advisors Lev Kofman
and Hans Stephani who convinced me with his lectures to take a chance on theoretical physics. The way of life is by in large directed by accident. It so often depends on people you meet, which direction you choose to take. I'm glad that these to physicists helped me finding my way.