system
Given the following post, respond as if you're commenting on Reddit:
human
Does a vacuum have a temperature?

I know that space is cold, but does that rule apply to all vacuums? Can something have a temperature whilst being empty of mass?
gpt
Vacuum has more than one temperature!  The notion of a single temperature depends on something called "local thermal equilibrium" (LTE), which depends on all the, well, stuff in a place being strongly coupled.  In very tenuous gases or plasmas (aka vacuums) individual particles don't interact with one another much, and you can have several systems with different temperatures co-existing in the same space(!)

For example, in the solar corona -- which is a far better vacuum than the "empty space" through which the Space Station flies -- we commonly deal with:

* ion kinetic temperature - the temperature you can derive from the average kinetic energy of free ions in the plasma
* electron kinetic temperature - the temperature you can derive from the average kinetic energy of free electrons in the plasma
* ionization temperature - the temperature you can derive from the average level of ionization (number of missing electrons) from each ion
* photon temperature - the temperature you can derive from the energy density of sunlight passing through the system
 
In some parts of the corona, the kinetic temperatures split again, into field-aligned and transverse kinetic temperatures, because those components of the average kinetic energy of ions and electrons are not well coupled:  a collection of ions that is whirling around the magnetic field lines may or may not also be zooming along the field lines at a similar average speed.  In places where wiggles in the magnetic field can excite particular species of ion more than others, there are separate transverse and field-aligned kinetic temperatures for every ion species -- for example, there might be a different "oxygen transverse kinetic temperature" than "helium transverse kinetic temperature", even though the oxygen ions are all strongly enough coupled to one another to form an LTE population, and the helium ions are too -- but there isn't a strong oxygen-helium coupling.
 
If you throw more material into a volume, the collision rate between particles increases.  With more collisions comes more coupling between the different energy reservoirs in the system.  If the coupling time between all the different relevant temperatures is short compared to times you care about, then the system is in local thermal equilibrium and it makes sense to talk about just one temperature.  LTE takes just a few typical collision times to achieve, which in air is order of tens of microseconds.  But in the corona, electron-ion collisions take anywhere from a few seconds (in the "dense" parts of the corona) to a few hours (in the transition to the solar wind), and a lot of other dynamics happens faster than that -- so the single thermal system breaks into multiple loosely coupled systems, each of which is in local thermal equilibrium with itself even though they aren't in equilibrium with each other.

Strictly speaking, even the terrestrial environment isn't in full LTE -- there are solar neutrinos passing through you, and their energy spectrum reflects a temperature of at least several million degrees Kelvin (the local temperature at the site where they were formed, deep in the core of the Sun).  But they couple too weakly to equilibrate with you and your surroundings, so you have a separate "main temperature" and "neutrino kinetic temperature".

Even in a hypothetical completely mass-free region of space, there would be at least a "photon temperature" reflective of the amount of electromagnetic waves passing through that system.  The photon temperature couples surprisingly quickly to other types of temperature, which is why spacecraft designers have to think carefully about thermal design, why toasters and industrial vacuum ovens work, and why the insides of thermos bottles are silvered (to reduce radiative coupling between the inside and outside of the thermos bottle).  Close to the surface of the Sun, the photon temperature is close to 6,000K, and that temperature falls as one proceeds into deep space (near Earth the photon temperature in space is close to 300K, which is one reason why it's pleasant to live here -- the temperature on the surface of the Earth is coupled to the local photon temperature).  The Universe as a whole has a photon temperature of 3K, which means (for example) that it's not possible to keep anything colder than that without a refrigerator of some sort.