@joefromchicago,
joefromchicago wrote: The only reason that physicists know that a certain light wavelength corresponds with a certain color is because they can already see the colors
That's not true. Here's another reason physicists know that: Together with biochemists, they have examined the photoreceptors in our eyes and measured which of those photoreceptors respond to which wavelength of light. (In different photoreceptors, different electrostatic environments surround the retinal molecules, shifting those molecules' absorption maximum in a distinct and predictable way.) In principle, then, even a team of color-blind physicists could have figured out that most other humans
can see colors, how many different colors they can distinguish, and which range of wavelength each color corresponds to. The physicists themselves didn't have to see colors to figure out the correspondence.
joefromchicago wrote:But that doesn't establish that everyone sees the same color blue.
That depends on what it means for you to "see" a color. If the sentence "I see blue" means, "incoming signal to my visual cortex from my retina's type-blue photoreceptors", then you're wrong: The biophysics of color and its reception by the eye
do tell us that my blue is the same as your blue.
Of course, if by "seeing" you mean a form of perception that happens on some neurological level further up in your brain's signal-processing stack, all bets are off. But then I don't see
anything that could establish whether my blue is your blue or not. The question, "is the `blue' I see the same as the `blue' you see?", simply becomes unintelligible under this definition of the term "see", and this lack of definition of the term "the same color".