Thanks for the Feynman notes. I didn’t know they were available legally, I hadn’t been able to get a copy.
I won’t say the Great Feynman is incorrect (audible gasps in the room) but he’s incomplete.
For the sake of his discussion there he has discounted damping. And the subject he’s talking about is very interesting though he doesn’t go into great detail. But without the damping what happens is the photon moves through a cloud of electrons (the air). The oscillating electric field of the photon causes the electron to move - all though the electric field moves at the speed of light, the electron cannot. This is where things get glitchy and funny, in we cross over into a classical electrodynamic interpretation - I would like to see a Quantum Electro Dynamic explanation. But in classical terms, when the electron moves in the electrical field of the photon, it takes its’ momentum - the electron has a different mass to the photon, so given Momentum = mv , the velocity of the electron must be much lower than the speed of light.
The direct path is not always the shortest path. With an angular cut prism, you will see light taking the shortest path. The light will split - but if you have a square cut block you will not see the light split. When Feynman discounts damping, then he’s effectively talking about a square cut block. The angle of the light will be different but it doesn’t change the distribution of frequencies - we’re getting the same amount of blue, just at different angles to the other colours. This effect would make the sky appear white, (the path of the sun light would be indistinct - it would appear to be coming from all directions).
Now. If we bring in damping, something else happens. Damping is when the photon loses energy. So if the electrons in their movement are losing some energy, then the photon will change frequency. Above the visible spectrum, we have the invisible ultra violets, etc. if they lose energy they will shift down into the visible spectrum. Hence the blueness of the sky. To tell you the truth I need to do more work on this to be absolutely rigorous. But it’s a small area of post grad physics that verges on near heresy. If the damping is also proportional to the fourth power of the frequency - then that further proves might point, as higher energy photons will lose a greater proportion of their energy, mean more will be shifted into the visible blue.
There’s a lot more to this. Where I am today there is a lovely blue sky. But from every angle the blue is consistent.
*Feynmann “This means that blue light, which has about twice the frequency of the reddish end of the spectrum, is scattered to a far greater extent than red light.”
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Without the dampening, if the angles of deflection were short, we might expect to see some strange (but wonderfully psychedelic) rainbow effect, the sky wouldn’t be consistently any colour. At a greater angles of deflection, the path to the source would be indistinct, and the sky would be whitish (that definitely does not happen - because the sky would appear white from outerspace, it doesn’t)
*"Thus when we look at the sky it looks that glorious blue that we see all the time! "
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Yes, Mr Feynman, but what about those glorious red skies and night, or red skies at morn.