system
Given the following post, respond as if you're commenting on Reddit:
human
Are There Infinite Colors (Rather, Can Wavelengths Be Infinitely Fractioned)?

I was discussing with a friend if it was possible to find an infinite number of points between colors.  For instance, between red and yellow is orange, between red and orange is a darker orange, and so on.  Of course the human eyes can only perceive up to a certain level, but theoretically -- could these colors/wavelengths be infinitely fractioned?

My thought process is that the variables that determine wavelength have universal constraints on them, and so I would suspect the same is true of wavelengths.  Could anybody shed some light on this question?

edit: Thanks for the overwhelming response!  I'll be alt-tabbing to my dictionary a lot tonight.
gpt
We're going to drop "infinity" from this conversation, because it will only hinder us.

What you want to know, stated unambiguously, is whether the electromagnetic spectrum is continuous, or whether it's discrete. Is there, in other words, some fundamental quantum of electromagnetic energy, and all electromagnetic radiation is an integer multiple of this fundamental quantum.

The answer is no, it's a continuum, and here's why:

Imagine you have a lamp that puts out only one colour of light. You have an idealised detector, and pointing it toward the lamp tells you the wavelength of the light the lamp is emitting.

If both you and the lamp are at rest relative to each other, you point the detector at the lamp and read off the wavelength — call it *λ* units of length, because we really don't care. Wherever you stand, no matter how far from the lamp you are, you always get the same reading.

But if you're moving *toward* the lamp, you find your detector registers a shorter wavelength, and if you're moving *away* from the lamp, your detector registers a longer wavelength.

You play around for a while, and discover there's a simple relationship between your speed relative to the lamp — either toward or away from it — and the difference between the emitted wavelength and the detected wavelength.

Which means you can plug in *any wavelength you like* and compute the necessary speed at which to move either toward or away from the lamp in order to register that wavelength on your detector.

Of course, in the real world no detector can detect *all possible* wavelengths of light. But we can ignore that because the fact that we're imagining an impossible detector is irrelevant; what matters is that *there exists* some speed, call it *v*, at which you can in principle move relative to a light source to make the light from that source any wavelength you like.

We call this "boosting," and it's a maths thing. It's possible to boost a light-emitting system, mathematically, to get whatever wavelength of light out of that system you like. Since boosting a system only involves changing your velocity relative to it, and since velocity is definitely not quantized, the electromagnetic spectrum cannot be quantized either.