I was trying to make sense of color combining and prime colors. I was trying to look at it from an electron orbit and photon perspective. Aside from having an organ that over simplifies things, it doesn't seem to make much sense that I'd be looking for an array of prime blue colored and prime yellow colored photons to band together and make green. Though I could imagine that a yellow photon and a blue photon interacting with an electron orbit could form green. The bigger question I am asking is, are photons not in some sort of whole numbered eigenstate? Like a guitar string? I never really thought of the light spectrum as truly being continuous, that all values were discrete regardless of how many. Everything having a quantum source like Sodium D-Lines. Seems like a simple question, but I can't find an answer and am just starting Ryder, which is a step for me.
2 Answers
Photons
Photons are not (so far as we are aware) fixed to distinct frequencies at fixed intervals like the notes of a guitar.* Indeed no photon exists at just once single frequency, the bandwidth theorem means that any signal with a finite duration in time has a finite spread of frequencies in it. Photons trapped in a cavity for instance will have Lorentzian frequency peaks that look (for a good cavity) allmost like perfect spikes, but in fact have a small width.
Eyes
However, the way the human eye works doesn't treat the photons as being a continuous spectrum. The eye has "buckets" and sorts the photons roughly into one of four categories, "red", "blue", "green" or "did not see it". Your brain then turns these three numbers (amount of red, amount of blue and green) into a sensation. So human colour perception is discretised. https://en.wikipedia.org/wiki/Color_vision
Paint
Blue paint looks blue because it is absorbing the red light, and reflecting the other frequencies. In (R,G,B) colour spectrum it is reflecting (0, some, lots). Yellow paint looks yellow because it absorbs all the blue light. (Red light and Green light together looks yellow. That is not a physics thing, its a biology thing. Just the circumstances under which the human brain produces the sensation of yellow). So the RGB of the yellow paint is (Lots, Lots, 0).
When you mix them together you now have a paint that absorbs all the Red (the blue paint's work) and absorbs all the Blue (the yellow paint's work). What is left is Green.
The important thing is that the paints do not in any way need to interact with eachother or notice one another's presence. They both cut away at the light spectrum and the gap they leave looks green.
Size of the Universe
Following on from that "so far as we are aware" caveat (*) at the beginning. Waves that are trapped in a container (like the guitar string waves of your example, trapped between the ends of the guitar) do have a, discrete, restricted set of allowed frequencies. However, like the cavity I proposed above (and a guitar in fact) these containers are not perfect: sound and light can escape. (This is why we can hear the guitar).
This escape broadens the allowed frequency, so that rather than some exact frequency being allowed some narrow spread (Lorentzian) is allowed near that exact value.
It follows that, if the universe were of a finite size (it wrapped around or had edges) then there would indeed be "pixelation": fixing all frequencies to certain tones. The bigger the universe the more closely packed those increments are, so the bigger it is the more and more it looks like it is just a smooth continuous scale.
So ultimately the answer to your question is: nobody really knows. It depends on whether the universe is infinite or not. However, the universe is pretty big, so it would make no difference to anything we are ever likely to be able to measure anyway.
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I believe this answer to be quite correct, and, in view of the fact that animals at least as intelligent as dogs see only in black & white, that it accounts for human survival and predominance to an extent compensating for our limited sense of smell: It's a result of evolution's "survival of the fittest", compensating for our rather small noses, and lets us distinguish, even thru many of a forest's leaves and branches, a racoon's tail from a bobcat's flank, so that we can decide whether to chase after it or run from it. – Edouard Jun 17 '20 at 11:18
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1"Buckets" is the wrong analogy. When you sort things into buckets, each thing goes in to just one bucket. But a single wavelength of light can stimulate all three cone types in a human eye to different degrees. – Solomon Slow Jun 17 '20 at 11:57
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2@Edouard, Dogs, and most other mammals, are dichromats. They are presumed to be able to distinguish yellow from blue, but unable to distinguish green from red. As for evolution, survival, and all that; Paleontologists believe that the main benefit to our ancestors from their ability to distinguish green from red, was that it helped them to distinguish ripe fruit from unripe fruit. – Solomon Slow Jun 17 '20 at 12:01
The other answer is very good however I now understand your confusion, so I will add something to it.
No. I'm asking if photons can have a non whole number standing wave frequency. It doesn't make sense in a quantum discrete physics that there should be non whole frequency photons.
Your confusion comes from the fact that quantum mechanics: 1- talks about orbitals and emission/absorption spectra and that all needs to be quantized; 2- photons are individual particles with individual energies.
Well, the model of quantum mechanics for the above properties serves to deal with bound electrons and their behaviour in matter. And they work together with light in special ways.
Now light, or electromagnetic radiation (EM) does not only come from electrons in their orbitals. EM fields can be excited in many different ways! For example, the color of the sun is continuous (no quantization) because the particles of the sun, in their frenetic hot movement can produce light. In general, any charged particle (electron, proton, muon, combination of those, whatever you want that has a charge) as it accelerates, will create EM radiation. And if the particles are free or quasi-free, then the light they produce can be perfectly continuous. There is no quantization of energy for free particles. That is why the other answer says
Photons trapped in a cavity for instance will have Lorentzian frequency peaks that look (for a good cavity) allmost like perfect spikes, but in fact have a small width
In this case we force light to not be free...in a simple analogy.
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In other words: it has to do with how human eye works, rather than the electron orbits.
– Roger V. Jun 17 '20 at 10:01