# Can a cubic meter of space at absolute zero have any object with mass inside?

I ask this question because, I have seen many places where they say the average temperature of the universe is some 2 degrees K and this somehow relates to mass present within a given volume of space.

So if there is a relation between temperature and the mass present inside a volume, i want to know that if a cubic meter of space is said to be at absolute zero(no approximations) then can it be said that there is no mass bearing object inside this volume?

Also conversely, if in this cubic volume at absolute zero, if one were to introduce say an electron or any other mass carrying particle; could it be said that the system is no longer at absolute zero?

If so can we conclude that for any system with temperature above zero kelvin, there has to be something with mass inside the system?

• Temperature is a statistical measure of the kinetic energy of an ensemble of particles. How do you propose to define the "temperature" of a volume of space containing no mass? – The Photon Feb 6 '15 at 21:52
• 3 answers within a minute, here you go! – Jim Feb 6 '15 at 22:03
• I've seen all the answers,never expected such quick responses 😀. But from what I understand from the answers is that practically there cannot be any system at absolute zero? Any system with or without mass, automatically means it has some temperature however small that might be. Even if it had absolute zero temp, any attempt to study the temperature of such system automatically causes such system to have some temperature. Am I right? – rapidclock Feb 7 '15 at 2:22

A cubic metre void of anything cannot be described with a temperature. Spacetime itself does not have the property of temperature, so it would be incorrect to say such a void is at absolute zero.

However, it is not necessary that any volume not at absolute zero has mass. The property of temperature could be held by photons or other massless particles. For example, the photons from the Cosmic Microwave Background (CMB) - the 2.7K background you referred to - are described as having a temperature. These photons, when they are the only inhabitants of a given volume, would make the mean temperature of that volume the mean of their temperatures.

We can say, though, that any volume containing thermal particles (I mean particles describable as having a temperature and not specifically phonons or photons) is not at absolute zero. Thus sayeth the almighty Third Law of Thermodynamics.

• Regarding "temperature generated by photons"... Doesn't the generation of temperature require the photons to interact with something that actually has mass? Otherwise it wouldn't have a temperature? The answers on this question also seem to imply that... Now I'm intrigued. – tpg2114 Feb 6 '15 at 22:07
• @tpg2114 Aha! good catch, I meant "held by photons" not "generated" – Jim Feb 6 '15 at 22:11
• Peer review FTW! Not those pesky photons. – tpg2114 Feb 6 '15 at 22:11

As mentioned in the comment above, temperature is defined to be a measure of the average kinetic energy of the particles in a system. So with that definition, the answers to your questions should fall out naturally:

1. If there is no mass in a volume, you could say the temperature is absolute zero. I would say it isn't defined because you cannot take the ensemble average of zero things.

2. If there is a mass in the volume, it may or may not have a temperature of absolute zero. If all of the particles contained no kinetic energy, the temperature would be zero. But we can only asymptotically remove all energy which is why we can only asymptotically approach zero.

3. If any system has a temperature that can be defined, it must have some sort of mass within it. Without mass in a volume, we cannot define a temperature, zero or otherwise.

• Re point 3: Not with that attitude – Jim Feb 6 '15 at 22:02
• @Jim Those pesky photons... I was undecided on whether a volume containing only photons really had a temperature or not. I'm still not sure... I also like how we all answered within 10 seconds of each other. – tpg2114 Feb 6 '15 at 22:04
• Photons FTW! I was thinking "do photons count as having temperature?" And then I remembered that we talk about the temperature of photons from the CMB all the time, which has cooled over time but the temperature of the emitting source didn't cool (okay it did, but not when the photons were emitted), it's expansion that has cooled the photons themselves. So 2.7K really does refer to the temperature of the photons. But not all photons could have a temp, just ones from thermal emission – Jim Feb 6 '15 at 22:09
• @Jim, no. The moon is just the sun at night. – tpg2114 Feb 6 '15 at 22:21
• @tpg2114 they have an energy that equilibriates with matter at a certain temperature, which seems like a good enough reason to say that they have a temperature of their own. – hobbs Feb 7 '15 at 5:10

Temperature is a quantity that determines how heat flows into and out of a system of particles when it is placed in contact with other systems. By this definition, measuring the temperature of a system with no mass inside is nonsensical; it's not absolute zero, it's undefined.

Temperature can equivalently be defined as being proportional to the average kinetic energy of particles in a system. Quantum mechanically, if your cubic meter of space has a single particle in it, it cannot have zero kinetic energy. This is because this would imply that the magnitude of the momentum of the particle is known with 100% precision (to be zero), and by Heisenberg's uncertainty principle, this implies that the position of the particle cannot be pinned down with even the weakest precision. This means that a particle with zero kinetic energy cannot definitively be said to be in your cubic meter of space at all!

• But it also can't be definitively said to not be in the cubic meter. Therefore, it must be there. Science! – Jim Feb 6 '15 at 22:20
• In fact, if this cubic meter is a part of the infinitude of space, then the particle has a 0% chance to be inside of it. – Izzhov Feb 6 '15 at 22:25
• Not zero, infinitesimal. But that's greater than or equal to the probability of it being anywhere else. Again, therefore it's there – Jim Feb 6 '15 at 22:28
• Mathematically, the probability of it being outside of the box is the integral of its probability distribution across all of space except for the box, which comes out to 100%. Science does not care about infinitesimals when it is taking actual data. – Izzhov Feb 6 '15 at 22:30
• Just in case it's not obvious, I was being facetious – Jim Feb 10 '15 at 15:08