# If light is quantized, why are EM spectrum and Blackbody spectrum continuous?

 P: 17 If light is quantized, and is given out in packets, why are the EM wave spectrum and the black body spectrum continuous? I am very confused, can someone offer some explanation? Any input is greatly appreciated.
 P: 1,521 What is quantized is the energy that can be transferred from the electromagnetic field (= the light) to another system. This energy comes in packets h*f where f is the frequency. This doesn't imply that f is not continuous.
 P: 661 Transitions between bound states in atoms give an (almost) discrete spectrum, but a continuous spectrum can arise from processes such as Bremsstrahlung, Compton Scattering, bound-free transitions, Synchrotron radiation ... EM spectrum would be discrete if time is discrete, but it's assumed to be continuous unless compelling evidence to the contrary appears.
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If light is quantized, why are EM spectrum and Blackbody spectrum continuous?

 Quote by annms If light is quantized, and is given out in packets, why are the EM wave spectrum and the black body spectrum continuous?
in the same way that a liquid composed of individual molecules is continuous. N is so large and \Delta E so small that you don't notice the quantization.
P: 661
 Quote by Meir Achuz in the same way that a liquid composed of individual molecules is continuous. N is so large and \Delta E so small that you don't notice the quantization.
Maybe, but the interesting question is whether the spectrum has discreteness at ANY fundamental level.

In thermal radiation from real materials you have molecular radiation which adds all sorts of "random" (continuous) noise, especially in the solid state which may have unbound electrons drifting near the surface.

I highlighted some specific processes where an arbitrary continuous variable might be assumed for the photon frequencies, and these will only be discrete if time is discrete in nature, a hypothesis which has no experimental support.
P: 1,943
 Quote by unusualname EM spectrum would be discrete if time is discrete.
Could you please provide some evidence for this claim?
P: 1,943
 Quote by annms If light is quantized, and is given out in packets, why are the EM wave spectrum and the black body spectrum continuous? I am very confused, can someone offer some explanation? Any input is greatly appreciated.
Any emission spectrum is continuous when measured precisely - the energy distribution even of fairly sharp peaks is Lorentz-shaped about the maximum. This can be rigorously demonstrated: The emission of light is a typical decay process, described by a resonance with a line width inversely proportional to the life time.

''quantized'' is just a buzzword meaning that something can be explained by describing it through quantum mechanics, and that _somewhere_ some discrete features show up. Many interesting operators in quantum mechanics have both a discrete and a continuous spectrum.
P: 661
 Quote by A. Neumaier Could you please provide some evidence for this claim?
at the end of the nineteenth century Planck discovered the (constant) quantum of action which is energy * time, therefore if time is discrete so is energy and hence so is photon frequency (duh!)
P: 1,943
 Quote by unusualname at the end of the nineteenth century Planck discovered the (constant) quantum of action which is energy * time, therefore if time is discrete so is energy and hence so is photon frequency (duh!)
???
Units have nothing to do with discreteness.

The spectrum of the hydrogen atom has a discrete part and a continuous part. So energy is both discrete and continuous. According to your argument, since Plancks constant is constant, it follows that time is both discrete and continuous, too.
P: 661
 Quote by A. Neumaier ??? Units have nothing to do with discreteness. The spectrum of the hydrogen atom has a discrete part and a continuous part. So energy is both discrete and continuous. According to your argument, since Plancks constant is constant, it follows that time is both discrete and continuous, too.
I've said something very simple above. The continuous part of the hydrogen spectrum is a mathematical construction which assumes continuously varying time parameter, not an experimentally established fact down to 10^-43 secs resolution.

I know you're a very smart guy, so you're obviously having some "overthink" problem here, really, I haven't said anything complicated or controversial.
P: 1,943
 Quote by unusualname I've said something very simple above. The continuous part of the hydrogen spectrum is a mathematical construction which assumes continuously varying time parameter, not an experimentally established fact down to 10^-43 secs resolution. I know you're a very smart guy, so you're obviously having some "overthink" problem here, really, I haven't said anything complicated or controversial.
You talked and talk nonsense. I refuted your _argument_ by applying it to different assumptions. This is independent of whether or not the physics changes at short time scales.
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 Quote by A. Neumaier You talked and talk nonsense. I refuted your _argument_ by applying it to different assumptions. This is independent of whether or not the physics changes at short time scales.
I don't understand you and I doubt many people reading this do either. You are not explaining yourself in an understandable way and btw you should not resort to ad hominem. The thread simply asks if the EM spectrum is discrete. As far as we know it is continuous, and there are physical processes which we believe can generate arbitrary continuously varying photon frequencies. But if time was found to be discrete then so would the the EM spectrum be discrete.
 Sci Advisor Thanks P: 2,502 Of course, Planck has not derived the Black-Body Spectrum from this wrong assumption but from the right one that any electromagnetic field mode with frequency $\omega$ exchanges energy with the atoms in the walls of the cavity by portions of $\hbar \omega$. The spectrum itself is continuous (in the limit of cavity extensions large compared to the relevant wavelengths of the radiation, determined solely by the temperature of those walls), i.e., $\omega$ can take any real value.