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

[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.

 

[lightarrow]

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.

 

[unusualname]

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.

 

[Meir Achuz]

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.

 

[unusualname]

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.

 

[A. Neumaier]

EM spectrum would be discrete if time is discrete.

Could you please provide some evidence for this claim?

 

[A. Neumaier]

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.

 

[unusualname]

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!)

 

[A. Neumaier]

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.

 

[unusualname]

?
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.

 

[A. Neumaier]

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.

 

[unusualname]

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.

 

[A. Neumaier]

But if time was found to be discrete then so would the the EM spectrum be discrete.

You assert this without any shred of evidence. The argument you gave for it is completely spurious, as I showed by applying it to a different situation.

 

[TheNutyProfesr]

''If light is quantized, and is given out in packets, why are the EM wave spectrum and the black body spectrum continuous? ''

1) Imagine a sine wave, via the Doppler shift we can stretch at and squish it. Therefore the spectrum will appear continuous.
2) There is also the matter of kinetic energy of particles, a single particle can be heated ie from 20 to 30 deg, now it can releases this energy. We don't heat the atom discretely, ie 20.1 20.2 ... therefore the blackbody radiation it will release will trace a continuous spectrum. :)

 

[cabrera]

the density of states( number of rasonators -EM ssources- per unit of space frequency) of black body radiator is a continuous function. However, to obtain the density of states Planck assumed that the distribution was quantised.

 

[vanhees71]

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.

 

[cabrera]

So the EM fiels, ω, is continuous but the exchange of energy between the field inside of the cavity and the wall of the cavity is discontinous, isn't it? It can only happened in a quantised way

 

[A. Neumaier]

If light is quantized, and is given out in packets, why are the EM wave spectrum and the black body spectrum continuous?

Well, this is a very old thread, and the original poster hasn't visited the site for years. Nevertheless, the question displays a widespread misunderstanding of the meaning of ''quantized''.

Everything in Nature is quantized, but this doesn't mean that it is discrete. A spectrum of a quantum system has a continuous part (contributed by the kinetic energy of a constituent) whenever some part of it can move over arbitrary distances. In particular, this holds for light.