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Does quantum theory and Planck's length of $1.6\times10^{-35}\ \mathrm{m}$ mean that the electromagnetic spectrum is not continuous as every photon can only carry a discrete amount of energy?

If so, wouldn't that mean that a light spectrum with an upper and lower limit such as the visible light to us humans has a finite number of colors?

I know that photons get their wavelengths from the particles they are emitted from, but couldn't we say for example that the spectrum of visible light between $380$ and $750\ \mathrm{nm}$ is $370\ \mathrm{nm}$ long and divide by the minimal length of causality that would be Planck's length there no more than roughly $2.3\times 10^{28}$ possible wavelengths and therefore colors in the visible spectrum?

Qmechanic
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Libelldrian
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1 Answers1

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Welcome to stackexchange. You totally can postulate that the Planck length is a quantized minimal element of light, and you might or might not be correct about that. Truth is, we have no validated theory to describe what happens at such tiny lengths as the Planck length. The same is true for spacetime: Is there a minimum length or volume? Is there a minimum time increment? Nobody knows. It is entirely plausible to think that this was indeed the case, and Planck lengths and Planck times are natural scales at which to expect such new physics to occur - after all, this is where our current theories (notably quantum theory) break down. But none of this is backed by any experiment. So the honest answer is an unsatisfying "we don't know".

Within standard quantum theory, one can use Heisenberg's uncertainty to set a fuzzy lower bound but I think it would be misleading to interpret that as a discreet wavelength.

Another question is how many colors can be perceived by the human eye. The stackexchanging photographers think that's some millions or tens of millions of colors. Still plenty ;)

rfl
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