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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?

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  • $\begingroup$ Why do you think Planck units are any kind of rigorous limits? They aren’t. $\endgroup$
    – Jon Custer
    May 31 at 16:29
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    $\begingroup$ Possible duplicates: physics.stackexchange.com/q/169209/2451 and links therein. $\endgroup$
    – Qmechanic
    May 31 at 17:12
  • $\begingroup$ The energy and thus the frequency of a photon in an infinite space is not quantized into a discrete set. The allowed energies form a continuum. This is true of any free particle. Whether this continuum has a cutoff around the Planck energy, or doesn’t, is irrelevant. $\endgroup$
    – G. Smith
    May 31 at 22:09
  • $\begingroup$ You seem to be thinking that the Planck energy is some kind of minimum energy, so that all possible energies are multiples of the Planck energy. This is wrong, and basically backwards; it may (or may not) be some kind of maximum energy for elementary particles. $\endgroup$
    – G. Smith
    May 31 at 22:13
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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 ;)

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