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Blackbody radiation describes an electromagnetic field in thermal equilibrium. Typically, we associate this radiation with a particular source, or boundary; bu
by piannucci 6y ago
Blackbody radiation describes an electromagnetic field in thermal equilibrium. Typically, we associate this radiation with a particular source, or boundary; but the blackbody spectrum itself is a Maxwell fact, not a matter fact. Real systems have many degrees of freedom, some matter, some Maxwell. In this particular example, the Maxwell degrees of freedom have a temperature of 3K, while the matter degrees of freedom have a much higher temperature.
Clearly, then, the matter is not in equilibrium with the electromagnetic field. How can this be?
Equilibration is a process that proceeds through a large number of interactions that each exchange energy between two thermal systems (or subsystems). If energy transfer is prevented, for instance by the conservation of mass and momentum, or because no post- states of an appropriate energy are available for one subsystem to evolve into, then the systems may remain far from equilibrium relative to each other.
I’d have to do some homework to verify this, but I think a correct statement is that free massive charged particles don’t gain or lose energy in net from passing radiation; and conversely, they cannot radiate. This is guaranteed by Lorentz symmetry, btw: if you examine a million-kelvin electron in a frame of reference moving alongside it, you’d agree there’s no way it can be radiating: there’s a frame in which it is stationary, and stationary charges don’t radiate. If it isn’t radiating in one inertial frame, it isn’t radiating in any inertial frame.
Only during collisions between charged particles is there a possibility for the matter and Maxwell degrees of freedom to exchange energy: and these are very rare in tenuous plasma. (We would call these “three-body interactions” because the photon counts as one.)
[edit to add]
Now one might object that charged particles are always interacting, because their fields fall off like 1/r^2; they don’t just end. Indeed! But one of the effects of being in a plasma is that charges are “screened”. You can think of that as meaning the net effect of many-body interactions can be described as altering the “effective” field of each particle to fall off much faster, like e^-r.
- TeMPOraL 6y ago> If it isn’t radiating in one inertial frame, it isn’t radiating in any inertial frame. Maybe this is the answer to a question I've been harboring in the back of my head since high school: if moving charges radiate, they should lose energy, and thus eventually disappear. Almost nothing ever is stationary, so how come all the charges haven't radiated away? A quick googling now (I don't know why I never bothered to do that before) pointed me to https://physics.stackexchange.com/questions/65339/how-and-why-do-accelerating-charges-radiate-electromagnetic-radiation https://physics.stackexchange.com/questions/65339/how-and-wh..., which would suggest that it's not movement but acceleration that makes charges radiate. But again, almost nothing ever is stationary, nor is it ever in truly uniform motion, so how come all the charges haven't radiated away?
- throwaway2048 6y agoThe gas is so not-dense that it's particles effectively never collide, so its acceleration never really changes, so it never radiates.
- a1369209993 6y agoFor some reason this (along with piannucci's explaination) really helped it click for me - while the gas has a very high blackbody spectrum temperature, emitting hard radiation when it's particles collide at high speed, it effectively has very little surface area from which to emit that blackbody radiation.
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- ummwhat 6y agoYou ask a very good fundemental question. For things like planets in orbit (under constant acceleration) there really is radiating gravitational waves which carry energy and in principle the orbits must decay over time. Even in particle accelerators the electrons moving in a circle emit radiation which slows them down and must be compensated for. So why don't atoms give off a ton of radiation quickly while the electron decays and crashes into the nucleus? The answer is on that scale it no longer makes sense to think of an electron as a tiny planet orbiting another tiny planet. The rules of quantum mechanics apply, and quantum mechanics says the orbits are quantized and there are no tinier orbits to decay into. So the full answer is that there only seems to be a paradox because your notion of when things should and shouldn't radiate is an approximate truth which only holds for "normal" cases (neither microscopic nor cosmological).
- rhn_mk1 6y agoConsidering the particles are charged (plasma, right?), and that moving a charged particle through an electromagnetic field causes acceleration and emission of photons (bremsstrahlung), does that mean that WHIM is going to be more energetic where it didn't have a chance to encounter electromagnetic fields?