Ice

From Feynman's book QED The Strange Theory of Light and Matter.

Because the theory of quantum mechanics could explain all of chemistry and the various properties of substances, it was a tremendous success. But still there was the problem of the interaction of light and matter. That is, Maxwell's theory of electricity and magnetism had to be changed to be in accord with the new principles of quantum mechanics that had been developed. So a new theory, the quantum theory of the interaction of light and matter, which is called by the horrible name of "quantum electrodynamics," was finally developed by a number of physicists in 1929.

But the theory was troubled. If you calculated something roughly, it would give a reasonable answer. But if you tried to compute it more accurately, you would find that the the correction you thought was going to be small (the next term in a series, for example) was in fact very large--in fact it was infinity! So it turned out that you couldn't really compute anything beyond a certain accuracy.

...

Well, this problem of how to calculate things in quantum electrodynamics was straightened out by Julian Schwinger, Sin-Itiro Tomonaga, and myself in 1948. Schwinger was the first to calculate this correction using a new "shell game"; his theoretical value [for the magnetic moment of the electron] was around 1.00116, which was close enough to the experimental number [of 1.00118] to show that we were on the right track. ...

The theory of quantum electrodynamics has now lasted for more than fifty years, and has been tested more and more accurately over a wider and wider range of conditions. At the present time I can proudly say that there is no significant difference between experiment and theory!

Just to give you an idea of how the theory has been put through the wringer, I'll give you some recent numbers: experiments have Dirac's number at 1.00115965221 (with an uncertainty of about 4 in the last digit); the theory puts it at 1.00115965246 with an uncertainty of about five times as much). To give you a feeling for the accuracy of these numbers, it comes out something like this: if you were to measure the distance from Los Angeles to New York to this accuracy, it would be exact to within the thickness of a human hair. That's how delicately quantum electrodynamics has, in the past fifty years, been checked -- both theoretically and experimentally.

So this part of my project is to get a framework for formally describing these different languages in a way that shows more clearly the meanings we are attributing to words like "speed" and to be able to do it in a way that allows us to produce models like this: https://github.com/mithuna-y/speed_of_light_in_a_medium/blob/main/multiple_layers/plane_wave_in_medium/main.py

See Mithuna's video I don't know why light slows down in water. (part 2)

Here's part 1:

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See David Dorran - The z-Transform and Beautiful Analogue of Quantum Mechanical Phenomena.