Discreet Quanta versus the Continuous Electromagnetic Spectrum

[Mcellucci]

How can discreet quanta of photon energy make up a continuous electromagnetic spectrum, whose wavelengths are any arbitrary value? Is there overlap of quanta, temperature dependency, or so many finely divided energy levels that the spectrum just appears continuous? Electron energies are quantized as are the photons emitted, but wavelengths are any length whatsoever. Are there any wavelengths that have never been "seen"?
What am i missing?

 

[phinds]

How can discreet quanta of photon energy make up a continuous electromagnetic spectrum, whose wavelengths are any arbitrary value? Is there overlap of quanta, temperature dependency, or so many finely divided energy levels that the spectrum just appears continuous? Electron energies are quantized as are the photons emitted, but wavelengths are any length whatsoever. Are there any wavelengths that have never been "seen"?
What am i missing?

I think what you are missing is that photons are not waves and they are not particles, they are quantum objects. If you measure wave behavior, you GET wave behavior (with no quantization). If you measure particle behavior, you GET particle behavior (with quantization). Thinking of quantum objects as classical objects leads to this kind of confusion.

 

[Mcellucci]

Yet, isn't Planck's constant a quantum function which relates energy to wavelength?

 

[The_Duck]

* Photons are quantized in that they come in discrete units, but you can have a photon with any frequency. It's just that 500 nm light, say, always comes in packets (photons) with energy 6.23e-20 Joules.

* In general, the allowed energy levels of a particle get quantized if you confine the particle to a finite region. Electrons in atoms are bound by the electric field of a nucleus to orbit within a small region around the nucleus, and so the electrons only have a discrete set of allowed energy level. Photons propagate freely through space, and so their allowed energy levels are not quantized. Free electrons, which are not currently part of any atom, can also have any energy. Conversely, If you build a closed box with mirrors on the inside to contain photons, the photons you trap will only be able to occupy a discrete set of energy levels. (The spacing between the energy levels gets smaller as you increase the size of the box, so this goes over smoothly to the free space situation as you increase the size of the box.)

 

[Mcellucci]

Oh, I get it, now. The wavelength can be changed arbitrarily but the energy in it is in constant inverse porportion to it. And free photons are not quantized in free space. Hmm...but how would you know that? Free photons can't be measured, can they? Only after their wave function collapses? No?