[Flash warning] A Michelson interferometer
Channel: Nils Berglund
Date: 12/02/2024

I put a flash warning on this video, because of the pulsing behavior of the standing waves in the second half or so of the simulation.
The Michelson-Morley experiment, performed in Cleveland, Ohio, in 1887, famously tried, and failed, to show a difference in the speed of light in perpendicular directions, thereby providing evidence for Albert Einstein's 1905 special theory of relativity. See for instance https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment for details.
The set-up shown here uses non-relativistic physics. It consists in a source of coherent light at the left, a beam splitter, two mirrors at the right and top, and a monitor at the bottom. The beam splitter divides the beam into two parts that are reflected on the mirrors, and return to the beam splitter.The transmitted part of the top beam and the reflected part of the right-hand beam then produce an interference pattern, that depends on the difference of distances traveled by the two beams.
In the situation shown here, the path lengths are the same. The idea of the Michelson-Morley experiment is that if the speed of light were measured with respect to a hypothetical "luminiferous aether", with respect to which the Earth moves in different directions along its orbit around the Sun, it should be possible to detect different interference patterns for different directions of travel. For instance, if the interferometer were moving to the right with respect to the aether, the vertical distance traveled would be longer than the horizontal one, while the situation would be reversed if it were moving up or down. 
This being a non-relativistic simulation, it cannot show that the speed of light is constant. However, it should be possible to see how the interference pattern depends on the positions of the mirror. I will try this and post the simulation if the result is interesting. 
The color hue depends on the wave height (or electric field intensity). 
There are absorbing boundary conditions on the top, bottom and right boundaries, and a time-periodic signal is imposed on the left boundary. The display at the bottom shows a time-average of the square of the wave height.

Render time: 45 minutes 14 seconds
Compression: crf 20
Color scheme: Twilight by Bastian Bechtold
https://github.com/bastibe/twilight

Music:  Hot Salsa by Audionautix is licensed under a Creative Commons Attribution 4.0 licence. https://creativecommons.org/licenses/by/4.0/
Artist: http://audionautix.com/

See also https://images.math.cnrs.fr/Des-ondes-dans-mon-billard-partie-I.html for more explanations (in French) on  a few previous simulations of wave equations. 

The simulation solves the wave equation by discretization. The algorithm is adapted from the paper https://hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf 
C code: https://github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!

#wave #interferenceoflight #Michelson_interferometer