Yes, deep space has a temperature of about 3K. Or -270°C. It’s not a vacuum though. It’s filled with light, specifically light left around from the big bang called the cosmic microwave background. The light, the gas made of photons, has a temperature. It’s not like a temperature, it is a temperature. It’s not the occasional atom that has the temperature, the light itself has this temperature.
How can light have a temperature? Same way as anything else, it’s a bunch of particles with energy. Does it mean an object in deep space would reach this? Yes, if an object was send out there, it would give off its heat as light. Everything emitts thermal radiation off. The amount if gives off would rapidly decrease, but would never lose all its heat. At 3K, the amount of CMB light that it absorbs would match the amount an object gives off. That is the definition of being at the same temperature, two things exchange an equal amount of energy.
What temperature is it within the solar system? Poorly defined, it’s not in equilibrium. Facing the sun near earth will cause rapid heating, and the side away from the sun will cool. It’s like being in the sunshine on earth, it gives a poor temperature reading.
Temperature is the average kinetic energy of the particles. But in space, there are so few particles that it leads to wrong assumptions. Space might be cold, but with few particles taking the kinetic energy from your body, it would take a while to freeze. Also, the high energy in the solar exposed sides of the space station will damage, but, as m not an expert BTW, I think the radiation is more of a hazard. Maybe they should put a raw Christmas Turkey on a dark and light side of the station and see what happens?
Deep space contains hydrogen atoms, at an insanely low density – IIRC it’s like single-digit atoms per cubic centimeter. If you go by the average velocity of those atoms, the temperature of deep space is about 3 kelvin.
Now, because there are so few particles, the heat conductivity of space is very, very close to zero – and so when it comes to conduction, “vacuum has no temperature” – it just insulates.
If you “touched vacuum”, basically zero heat would conduct out of your hand and into the vacuum because it has essentially zero mass. However, you can still radiate heat out into vacuum, and it radiates almost nothing back, so in that sense vacuum is cold. Also, if you have any moisture on your skin like, say, sweat or oil, that will evaporate fairly quickly because there’s zero pressure holding it down, so you’d feel a chilling effect from the evaporation.
It’s the temperature that a perfect black body will heat up to if you left it in that spot. It has a temperature because light can heat up objects, but objects also emit light as they heat up. An area of space in our solar system will be receiving a certain amount of light from the sun, which will cause an object to heat up until it is hot enough that its own radiation balances with that its receiving from the sun. That temperature can be thought of as the temperature of that area of space.
Preface: I’m not a physicist. I just watch lectures and read books on this stuff to help me sleep. I’m pretty sure that what I’m saying is accurate, though the actual application of this stuff is way over my head. Take what I say with a grain of salt. Also, this will be a bit more complex than an ELI5, but it’s the best I can do.
At least one comment here (I haven’t read them all, so there might be more) referenced the Cosmic Microwave Background (CMB) as the source of the temperature of space. This is the best answer for what we usually measure as the background temperature of space, but if you were to perfectly shield a portion of space from the CMB and create a “perfect” vacuum inside, you’d still have a very small amount of energy no matter what you do. That energy isn’t useful, though. Work can only be done when there’s an energy differential, and all of space is filled with this tiny energy density.
Quantum Field Theory (QFT) can be summarized by saying that space is permeated by “layers” of energy fields with discrete components. Computer monitors are a great analogy. What looks like fluid movement across the screen when viewed from afar is actually the energization and de-energization of individual pixels. In QFT, a particle is nothing more than an excitation of a particular quantum field, and the percieved motion of the particle is just the transfer of that energy to a different, indivisible location in the field.
Now, this is where things get really weird. According to the Heisenberg Uncertainty Principle, there is a fundamental limit to the precision with which you can measure complimentary variables. In this case, we’ll be dealing with position and momentum. The more precisely you measure a particle’s position, the more uncertain its momentum becomes (and vise versa). This isn’t a limit imposed by our technological ability to measure, but instead by the nature of reality itself.
So, how does the background temperature of space emerge from these two principles? Well, temperature is a measurement of particle vibration. But particles themselves are nothing more than vibrations in the quantum fields. So, to reach absolute zero temperature, you would have to eliminate all vibration in the quantum fields. But if you do this, you have perfectly defined their momentum and position (the latter being due to the fields themselves being made of discrete components), which the Heisenberg Uncertainty Principle does not permit. So, as you approach a perfectly defined measurement of position, the momentum would reach infinity. This gives the quantum fields a non-zero minimum temperature.
Edit: forgot to specify that absolute zero means a perfectly defined position *and* momentum
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