How does an antenna behave when it is cooled so that its black-body radiation is emitting energy at its resonant frequency?

Edit: To clarify, its not how they're related in general, but how might thermal radiation and resonance interact with each other when their spectra are aligned well?

Edit: Also, I'm sure that the thermal radiation spectra that have a significant peaks are associated with incredibly high temperatures, and peak at incredibly small wavelengths, rendering such an antenna completely impractical to build. Still, I'm still interested in the theoretical concept.

  • $\begingroup$ I can't add the tag because my rep here isn't high enough. Would have liked to add 'black-body'... $\endgroup$ – somebody Apr 2 '11 at 3:45
  • $\begingroup$ we have the thermal-radiation tag for that. I added it for you. $\endgroup$ – David Z Apr 2 '11 at 3:47
  • $\begingroup$ I edited the question: "Resonance" cannot interact, resonance is a property of some arrangements able to oscillate. $\endgroup$ – Georg Apr 2 '11 at 10:26

OK, the simple answer: When there is a resonance in the antenna you have a coherent phenomenon. All the bands of electrons of the antenna are marching in tune.

The black body radiation is an incoherent phenomenon coming from the individual atoms of the antenna. Even if the peak of the black body radiation were sitting on the resonance of the antenna it is still an incoherent phenomenon that cannot couple to the coherent behavior of the electrons in the current that resonate.

Think of a single violin tune and a crowd of people talking. The noise of the people does not cover the clarity of the violin even in high volumes.

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  • $\begingroup$ Ah, so to go along with the violin analogy, the crowd, even if they were all chattering at the resonant frequency of the violin strings, won't cause the strings to resonate because the crowd is producing noise/static that isn't coherent. $\endgroup$ – somebody Apr 2 '11 at 8:04
  • $\begingroup$ Well, if the crowd managed to get a coherent voice, an opera singer, then the chord of the violin will resonate, if it is quiet. The crowd noise has a large distribution in frequencies which might peak at the tune of the violin and maybe a small hum might be induced, but it would not affect a played tune drawn on the chord, the chord will give the specific frequencies it resonates in, whatever the crowd does, even an opera singer in tune. The note in the air will not be changed by the crowd's noise. $\endgroup$ – anna v Apr 2 '11 at 9:19
  • $\begingroup$ Such a noise (which is called "white" if power is distributed uniformly over frequency, as opposed to "black" body radiation :=) has some power at the violin strings frequency, and will cause the latter to vibrate a little bit. $\endgroup$ – Georg Apr 2 '11 at 10:30
  • $\begingroup$ What does coherence to do with it? Antenna has some frequency and when an incident radiation of different frequencies fall upon it, the component of the radiation which match the frequency of the antenna make the circuit of the antenna to resonate. That's all. Your answer is incorrect in many ways. $\endgroup$ – user1355 Apr 3 '11 at 2:50

They're not related. The black-body radiation as well as the resonance curve may look like "bumps" but they are very different bumps mathematically. The black body radiation gets emitted at all frequencies, and the "uncertainty of the frequency" is maximized, in some sense. On the other hand, resonances are peaked around a particular frequency.

Resonance curves are about matrix elements between pure states; thermal curves are traces over the whole Hilbert spaces so they arise from mixed stated. That's why the exponentials only appear in the thermal curves.

So the only thing they share is that they produce intensities as a function of frequency - but many other things in physics do the same thing - and in both cases, complex numbers are useful ($E_0-i\Gamma/2$ for resonances and imaginary time $i\beta$ in the thermal case) - but complex numbers are useful across physics.

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  • 3
    $\begingroup$ Ok, maybe 'How are they related?' is not the right question. Maybe its better stated: if the resonant frequency is close to the maximum frequency in the black-body radiation spectrum, could these phenomenon interact somehow? $\endgroup$ – somebody Apr 2 '11 at 6:02
  • $\begingroup$ This question shows the problem of understanding You have! Black body radiation at any temperature contains that eg 500 Mhz Your Antenna is tuned to. The difference is: how much power is in the field at that frequency? If You take a black body of, lets say 6000 K (sun) the maximum is far in the UV, but nevertheless the radiaton at 500 MHz is much stronger than that of a radiator at 1 K (which might have its maximum smewhere around 500 MHz). $\endgroup$ – Georg Apr 2 '11 at 10:20

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