Revisiting Thermal Radiation: A Note on Vibrations, Noble Gases, and the Quantum Field
Back in 2011, I posted a question on Physics StackExchange which still seems to me to get at something oddly under-discussed in undergraduate expositions of thermal radiation, like my OU course:
What are the quantum mechanisms behind the emission and absorption of thermal radiation at and below room temperature? If the relevant quantum state transitions are molecular (stretching, flexing and spin changes) how come the thermal spectrum is continuous?
What about substances (such as noble gases) which don't form molecules, how do they emit or absorb thermal radiation? Is there a semi-classical mechanism (with the EM field treated classically) and also a deeper explanation using the full apparatus of QFT?
I sketched some partial answers at the time, and complained how unhelpful Google search was. Fourteen years on, it seems worth revisiting the topic, not because the physics has changed, but because our pedagogical habits sometimes forget how subtle—and how rich—the story actually is. And, of course, now we have Gemini and ChatGPT to answer the question properly.
Molecular Motions at Room Temperature
At everyday temperatures - let’s say the range between ice and a really hot day - the thermal radiation emitted by most materials arises predominantly from molecular degrees of freedom: rotations and vibrations, not the grander electronic transitions we associate with chemical reactivity or flame colour.
-
Vibrational Modes: These are quantised oscillations of atoms within a molecule, typically involving the stretching or bending of chemical bonds. Photons emitted or absorbed in such transitions usually fall in the infrared region.
-
Rotational Modes: For gas-phase molecules, these quantised angular momenta yield spectral lines in the microwave and far-infrared regions.
-
Spin States: Nuclear or electronic spin flips do occur, but the energy scales involved are small—too small, generally, to contribute meaningfully to thermal radiation at room temperature.
All these transitions are discrete, in principle. So: why is the blackbody spectrum continuous?
Why the Spectrum Smears
Three interlocking reasons:
-
Broadening Mechanisms: In real matter, transitions are rarely perfectly isolated. Collisions, Doppler shifts due to thermal motion, and quantum uncertainties (spontaneous emission, finite lifetimes) all introduce line broadening. This ensures that even discrete transitions overlap.
-
Combinatorial Overload: Molecules—especially polyatomics—possess a bewildering number of vibrational and rotational modes, including overtones and combination bands. In condensed phases, the situation is even less tractable: individual molecular vibrations blend into collective modes, or phonons, that occupy quasi-continuous bands.
-
Macroscopic Statistics: Planck’s blackbody curve describes an idealised cavity in thermodynamic equilibrium with radiation. Its derivation involves summing over quantised oscillators at all frequencies. The result is continuous, not because the microphysics isn’t quantised, but because the density of accessible states is so high that discreteness gets washed out.
And What of Noble Gases?
Noble gases are monatomic and chemically inert. At room temperature, there are no vibrational or rotational transitions to speak of. And yet, even a flask of argon glows (in the infrared) if you warm it enough. What’s happening?
-
Electronic Transitions: At high temperatures, atoms can be thermally excited to higher electronic states and subsequently emit light. But these transitions require electron-volt energies—far above the thermal energy scale at room temperature (~25 meV).
-
Bremsstrahlung: Collisions between neutral atoms don’t normally generate radiation. But if those atoms are polarizable (as all are), then fleeting charge distortions during collisions can accelerate electrons ever so slightly—emitting weak, broadband radiation in the process.
-
Collision-Induced Emission/Absorption: A related but more specific mechanism involves transient “quasi-molecular” states during collisions. These states, however ephemeral, permit dipole transitions not allowed in the isolated atoms. The resulting spectrum is continuous, governed by collision dynamics rather than intrinsic atomic energy levels.
Semi-Classical and Quantum-Field Perspectives
One can explain a lot using semi-classical approximations—matter is quantised, fields are classical. Planck, after all, made sense of the blackbody curve by quantising the energy of the oscillators, not the electromagnetic field. This was enough to avoid the ultraviolet catastrophe.
But full fidelity requires the machinery of Quantum Field Theory:
-
Photons are not just handy bookkeeping devices; they’re quantised excitations of the electromagnetic field.
-
Atoms and molecules are excitations of matter fields.
-
Emission arises when a higher-energy excitation of the matter field drops to a lower energy state, accompanied by the creation of a photon excitation.
-
Absorption is the reverse: a photon excites the matter field into a higher state.
-
Spontaneous emission, long a mystery in semi-classical theories, emerges naturally in QFT as the atom interacts with vacuum fluctuations of the field.
Even in this framework, individual interactions are quantised. But the vast number of degrees of freedom in any macroscopic object ensures that radiation emerges as a smooth continuum.
The upshot is that thermal radiation, even at the scale of a warm hand or a ceramic mug of coffee, is an interplay of quantum transitions, statistical mechanics, and field theory. Each photon is the outcome of a microscopic quantum event, but their collective behaviour is a kind of spectral murmur—complex, continuous, and ubiquitous. The mystery is not that it occurs, but that the underlying processes are so subtle that it took a long time to understand why.
