It is not clear (not even for an ideal blackbody like a cavity) from where in the interior of a radiating body the radiation passing through its boundary, effectively originates: Somehow a coordinated wave motion or oscillation is formed inside the body, which is then transmitted through its boundary to the outside as radiation.
This may be similar to an idea somehow formed as a coordinated wave motion involving the whole brain, which is then transmitted to the exterior through the mouth.
What do you mean with coordinated wave motion? Why must there be coordinated wave motion?
SvaraRaderaIn order to send a signal as an infrared wave of wave length much longer than atomic dimension, a coordinated action of many atoms is required.
SvaraRaderaUsing a quantum mechanical a counterexample is trivial.
SvaraRaderaIf you wish to stick to classical models, an excited atom relaxes by oscillatory motion of electrons, creating a wave train pulse. Typically from empirical measurements this happens in less then t~10^-8 s. Hence there is the possibility, in principal, to create a wavelength of l~1 m. That's >> more then enough to create infrared light.
So this turns what you write in your response completely on it's head.
There is no need for coordinated waves if we consider atoms as the originator of the waves.
A single atom cannot generate IR radiation an so coordinated action of many atoms is needed.
SvaraRaderaThat's complete nonsense.
SvaraRaderaAs mentioned. The wavelength in a vacuum is
\lambda = \frac{c}{f}
where c is the speed of light in vacuum and f is the frequency of the light. So for a relaxation of t~10^-8 s there is a charge oscillation frequency f~10^8 Hz if seen as a dipole radiator. Which gives
\lambda ~ 1 m.
This is in the microwave region and more then well covers the infra red wavelengths of 800 nm - 1 mm.
This is in complete agreement with classical electromagnetic theory. Do you disagree?
You should know this, but just for bookkeeping, in the quantum case,
E = h f.
I don't know what your hangup is. I cannot see that blackbody radiation is explained by single atomic motion. What I try to say is that bolometric temperature and lapse rate may be independent of the specific radiative properties of an atmosphere, and thus that a proclaimed greenhouse gas effect may be fantasy. Agree?
SvaraRaderaNow you are just trying to remix the deal.
SvaraRaderaI simply wonder about this blog post and your claim that there must be a coordinated wave motion. It looks like complete nonsense.
What is your intention of writing this in the first place? What is it supposed to show?
And further, is there something false in what I wrote? Or do you withdraw your claim about coordinated wave motion?
I still can't understand why there must be some coordinated motion to produce waves.
SvaraRaderaIf one wiggle the end of a stretched string there will be pulses traveling over the string. These pulses travel with the characteristic velocity v depending on the string.
If the disturbance is of simple harmonic nature with frequency f, there will be waves of wavelength l=v/f traveling along the string.
Are you saying that the dimension of the hand wiggling the string sets a restriction on how long the wavelength can be so that several hands working in a coordinated fashion must produce longer waves?
Yes, something like that. More precisely, a single atom (hand) would no be powerful enough to generate an IR wave even if the frequency of the atomic oscillation would correspond to that of the IR wave. Many atoms oscillating in coordination would be required. A gas would then need to have a sufficient concentration/pressure to be able to radiate (more or less) like a blackbody.
SvaraRaderaBut you agree that a molecule of atomic size can produce an IR-wave, feeble or not?
SvaraRaderaThe thermal energy of the supposed blackbody produces random accelerations of the electrons. These accelerations then sends of light from the electron with no interference since there is negligible correlation between the different sources. Hence the resulting wave just have the intensity of sums of all the intensities from individual waves.
So no coordination should actually be more reliable and always produce IR-waves since there is no interference between wavelets.
Think of a musical instrument like a piano with a vibrating string in resonance with a soundboard generating sound as coordinated wave motion. Or the wave around a soccer stadium as a coordinated motion.
SvaraRaderaWhy should I consider that?
SvaraRaderaI think it's much better to discuss the behavior of electromagnetic waves, don't you agree?
Your analogies sounds more like something that is useful for discussing diffraction or some other highly coordinated event. What does that have to do with the chaotic uncorrelated blackbody?
One more thing is highly unclear, where is your IR-waves in the stadium analogy?
How do you know that blackbody radiation is chaotic and uncorrelated? The wave in the stadium is "the Mexican wave". Haven't you seen it?
SvaraRaderaIf the electromagnetic waves are generated from thermal motion, which is chaotic and uncorrelated, then the resulting electromagnetic waves should necessarily consist of short pulses in form of wave-packets with short correlation length and time, as also observed from empirical measurements on thermal sources.
SvaraRaderaI still don't understand why there must be correlation? Why can't there be incoherent waves leaving, as expected from both rationality and empirical measurements?
Of course I know what "vågen" is, I just don't see the connection with generated electromagnetic pulses leaving the arena. Or is the arena an analogue for "outside" the blackbody?
How do you know that thermal motion, in a lump of glowing iron for example, is chaotic uncorrelated?
SvaraRaderaI'm missing a comment here. Is it misplaced or didn't you approve of it?
SvaraRaderaPlease send again.
SvaraRaderaThe glowing lump of iron can be approximated by a blackbody. And as such it radiates as a diffuse emitter. All observers see the same amount of energy from a part of the surface independently of the viewing angle. Further there is no way to expect any polarization of the light. So it must necessarily be highly random in its nature.
SvaraRaderaI think I can give a much deeper reason connected with the nature of blackbody radiators, but I need to think a bit on how to formulate it first.
SvaraRaderaThe spectra of blackbody radiation in a closed cavity at constant temperature is independent of both constituents and shape. This is known from experiments. This is worth to emphasize, the materials or shape of the cavity has nothing to do with the resulting radiation.
SvaraRaderaSince the shape and material is arbitrary, it is most convenient to assume that the walls are perfect insulators shaped as a box of side L and then introduce periodic boundary conditions for the field in the cavity.
To satisfy the boundary conditions, the fields are expanded as Fourier frequency oscillators, hence integer multiples of the wave vector. Because of the standard dispersion the frequency is proportional to the wave vector and the energy of a frequency mode is therefore proportional to an integer multiple of the frequency.
Since the radiation is in thermal equilibrium, these Fourier modes are necessarily Boltzmann distributed, because they behave formally, precisely as material oscillators. The energy of an oscillating mode will then be random with a probability given by the Boltzmann distribution.
So, any object that enters the regime of being close to radiate pure blackbody radiation, the radiation field is closely approximated by a field of the same essence as described. Hence highly random.
So in the light of this, why must there be coordinated motion?
It makes completely no sense at all in the light of experimental data in connection with black radiation.
My view is that there is nothing random in radiation, because radiation is a wave phenomenon which is coordinated motion. When you resort to chaotic motion it is only black magic.
SvaraRaderaWhat does randomness mean in your view?
SvaraRaderaIt is not my cup of tea. Maybe, effect without cause?
SvaraRaderaWell, I'm talking about randomness as in unpredictability. As in no detectable coordination.
SvaraRaderaIf you take two different blackbody radiators and mix the light from them before measuring the intensity, what should be the expected outcome in your opinion?
Use stochastic process if you like. And then I mean stochastic in the functional sense, a stochastic process is a process;
SvaraRaderathat can be analysed in terms of probability theory.
Then there is no need for the messy and uninteresting discussion about determinism.
Go ahead. I stay with determinism.
SvaraRaderaLet me repeat the relevant questions. You're heading astray.
SvaraRaderaIf you take two different blackbody radiators and mix the light from them before measuring the intensity, what should be the expected outcome in your opinion?
You are asking many questions. I don't know if I can answer them all. Why not try to answer them yourself?
SvaraRaderaI'm trying to understand how you think.
SvaraRaderaSince the answers you given so far doesn't help me in doing that I thought that I'd try to ask more direct questions to see if you could explain in more detail how you think about how these kinds of systems function.
I still don't get your rational for why there must be a coordinated motion behind the emitted radiation.
The reason why I ask about the outcome of mixing black radiation from two different emitters is that the expected outcome is no interference at all. And I can't see how this can be consistent with coordinated wave motion. Remember that the blackbody radiations are independent of the shape and materials in the emitter. Where is the coordination??
I was really hoping that you could help me sort this out.
SvaraRaderaFrom what I've written there seems to be two possibilities.
If what I've written is true there is no need for any coordinated motion over the blackbody to form blackbody radiation. That is one possibility and it is opposite to what you claim.
The other possibility is that I've misunderstood the basic theory.
If you still think that there must be coordinated motion, please point out where I thought wrong.
Radiation is wave motion and wave motion is coordinated motion.
SvaraRaderaYes you have said so, many times.
SvaraRaderaI still don't see how this applies to electromagnetic waves.
Do you have any derivation or experimental result that support this?
I tried the other way around here, asking the question:
SvaraRaderaAt what amplitude would a test electron charge in an atom oscillate given a driving electromagnetic wave equivalent to the 1000 nm wavelength in black radiation at 300K?
I did a course estimation (keeping it on the safe side) on a test charge driven by the equivalent of the 1000 nm wave at 1 cm (subtending atomic dimensions) from a blackbody wall of 1 m^2.
The resulting amplitude of the oscillation is estimated to be below 10^-16 m.
I'm a bit tired now but should not this implicate that atomic dimensions more then well can handle infrared wavelengths? No need for coordination.
Do you have any derivation or empirical result that supports the claim of coordinated motion?
SvaraRaderaIf you have none, it would be nice to know. Is there some other reasoning then that you use then for the conclusion you suggest?