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Jason:

The temperature of space has been bothering me. People always say it's 4K [erratum: I think I meant 3K?], because that's what NASA has to think, because that's what medium sized dry goods tend to equilibriate at (insofar as that means anything - since I'm always thinking about cosmology I see this as only a short-term apparent equilibrium, but I don't think there's anything interesting or deep in that thought).

BUT

the standard definition of temperature is mean kinetic energy. And the mean kinetic energy of the particles in a region of space is usually way higher than 4K (and often very high indeed, as I'm sure you know).

It seems to me that the way people use "temperature" doesn't fit the definition they think the term has.

So there.


Carl:

Hmmm.

The main functional role of temperature is, as you say, thermodynamics. So if you treat the universe as an environment, then you get 4K as the temperature of the environment. If you treat it as a black body then, again, you get 4K (i.e. looking at the radiation curve of an arbitrary patch of the sky which doesn't contain, say, the sun).

A couple of late night speculations then (along the lines of 'temperature of what?') about how the apparent discrepancy between this and the MKE definition might be resolved.
The MKE definition is not general, and is for matter, not space. Space can only be treated thermodynamically as an environment, the gas within it need not have the same temperature (seems wrong - they should end up averaging out the same?)
The definition is functional/pragmatic, and we're not used to counting photons. In human-familiar objects/environments we don't need to because baryonic matter dominates the energy transfer. In your average unit of space (most of which are located in voids), for every reasonable quantity of baryonic matter there's a metric fuckton of photons, the vast majority from the CMB and weighing in at 4K.
neither of these satisfy me as they are. Nite.


Jason:

A related problem is: in addition to whether you count photons, what about virtual particles? And I believe the number of virtual particles depends on which theory you use, and even in some theories on other things like your reference frame, right? I can't remember the details of this. Do you know?


Carl:

Yeah I'm completely confused by the way that virtual particles should be invoked. When in undergrad they taught us that the whole point of virtual particles was that you don't count them in any way unless you supply the energy required to split them off their annihilation path - i.e. make them real, like in Hawking radiation. But then they told us about the Casimir effect and rapidly moved on in a "nothing to see here" sort of way. Been bemused ever since, though have to say I've never really followed up on it. Any reading suggestions? Any good treaties out there about the history and philosophy of particle physics?


Jason:

You just asked me the same question as I asked you! We should ask a third person. I'll do that next time I bump into one.

I think what's going on is that in some theories you can ignore virtual particles most of the time in the way you say, but those theories are unsatisfactory. What I don't know is whether those theories are merely (!) oversimplifications or whether they're theories that are unsatisfactory on other grounds. Must find out.