# Is absolute zero possible in a complete vacuum? [duplicate]

Thermal energy is the energy an object due to the motion of it's molecules. This means as long as an objects molecules have kinetic energy, it will not reach absolute zero. Does that mean if there was a complete vacuum(no molecules or waves inside the vacuum at all), it would be at absolute zero inside the vacuum because there is no molecules, meaning they can't have kinetic energy, and theirs no radiation to heat the space. So I was thinking it would be absolute zero in a complete vacuum.

• What do you mean by "complete vacuum"? Is the cosmic microwave background allowed to exist in this vacuum? Are we considering the effect of vacuum fluctuations? – probably_someone Apr 6 '18 at 20:45
• By complete vacuum, I mean no molecules inside a given area. Yes, I now realize that radiation doesn't need particles to travel. – Daniel Turczynskyj Apr 6 '18 at 21:08
• I've asked the question, see What is the temperature INSIDE a black hole?. – John Duffield Apr 9 '18 at 11:45

## 2 Answers

This means as long as an objects molecules have kinetic energy, it will not reach absolute zero.

Classically, you would be correct. Quantum physics says that this isn't quite correct. Even at absolute zero, objects would still have a non-zero amount of kinetic energy. This would be the system's zero-point energy.

Does that mean if there was a complete vacuum, it would be at absolute zero inside the vacuum.

No. It would be more difficult to define a temperature at all. That wouldn't make it a temperature of "zero".

Even without any atoms inside the space, there would still be radiation. Only if all the radiation were eliminated could you describe the temperature in that region as consistent with a temperature of absolute zero.

• Can you explain the top part a little more, I'm in middle school and don't exactly understand it. – Daniel Turczynskyj Apr 6 '18 at 20:48
• This answer is pretty misleading and even incorrect. First of all, the zero point "motion" of matter does not mean that the matter is at nonzero temperature. Zero point energy/motion is not like classical motion at all, i.e. it does not indicate that the matter has nonzero temperature. Second, It is not difficult to define temperature in a vacuum. A vacuum supports electromagnetic modes, and if the surroundings (e.g. the walls of the vacuum chamber) are at some temperature, then the occupation of those modes can be described by a thermal distribution. – DanielSank Apr 7 '18 at 17:08
• @no_choice99 "Zero point energy" is not really energy at all. If an e.g. quantum harmonic oscillator of frequency $\omega$ is in its ground state, it has zero point energy of $\hbar \omega / 2$. However, there is no way to extract this "energy". There is no way to use that "energy" to produce a photon, a phonon, or to make any other system's energy increase in any way. The so-called "zero point energy" isn't really energy at all; it's certainly not kinetic energy. – DanielSank Apr 7 '18 at 22:48
• @no_choice99 : yes it does mean there's a non-zero kinetic energy. See the chart on the right on the [Wikipedia zero-point energy]( non zero kinetic energy) page. This answer looks good to me, +1. – John Duffield Apr 8 '18 at 17:08
• @no_choice99 The kinetic energy is nonzero. However, we could make the kinetic energy zero by simply subtracting a constant from the Hamiltonian. Just like in classical mechanics, changing the Hamiltonian by a constant would have no effect on the dynamics of the problem. Therefore, just like in classical physics, absolute values of energy are meaningless, while energy changes are what matter. For example, the so-called "ground state energy" cannot be transferred to anything else, so it's not usable energy and certainly does not represent a nonzero temperature. – DanielSank Apr 9 '18 at 4:22

Is Absolute Zero Possible?

Yes. In a black hole.

Thermal energy is the energy an object due to the motion of its molecules. This means as long as an objects molecules have kinetic energy, it will not reach absolute zero.

That's true.

Does that mean if there was a complete vacuum, it would be at absolute zero inside the vacuum because there is no molecules, meaning they can't have kinetic energy.

No, because "the vacuum" isn't something that's totally empty, it has vacuum fluctuations. Think of them as something like the little ripples on the surface of the ocean.

Or is it even possible at all for any object to reach absolute zero?

Yes, a black hole is a place where time dilation goes infinite, so there is no motion, so there is no heat or temperature. I know people talk about Hawking radiation, but that is said to emanate from near the black hole, not within it.

• What do you have to say about a particle in a quadratic potential? I don't remember exactly but I think that the momentum of the particle is non zero (if it is even possible to define it) in the ground state. This would mean the particle still has kinetic energy at 0K, assuming one can associate a temperature to a single particle. If not, then take a bunch of particles and ask the same question. – AccidentalBismuthTransform Apr 7 '18 at 13:25
• @no_choice99 : I'd say temperature is an emergent phenomena, and the temperature of a particle like a free electron is derived from the motion of the particle. If it's motionless, temperature doesn't apply. It doesn't apply to a photon either. It does apply to an ensemble of particles, but in a black hole the motion is time-dilated away, and so doesn't occur. Hence no temperature. – John Duffield Apr 7 '18 at 14:03
• "Vacuum fluctuations" do not preclude a thing from being at absolute zero. – DanielSank Apr 7 '18 at 17:10
• Note to readers: The statements about vacuum fluctuations in this answer are misleading, if not incorrect. So-called "vacuum fluctuations" in quantum mechnics refer to the fact that ground state wave functions have nonzero variance of position, moment (or whatever other conjugate pair of degrees of freedom you're looking at). The presence of vacuum fluctuations does not mean that a vacuum cannot be at absolute zero. The vacuum can be at absolute zero (at least theoretically) and in that case the vacuum fluctuations are still there. – DanielSank Apr 9 '18 at 4:10
• Even if Hawking radiation did not exist a black hole would only asymptotically approach absolute zero because the event horizon takes an infinite time to form. This is no different to any other chunk of matter taking in infinite time to approach absolute zero. So the first part of this answer is simply wrong. – John Rennie Apr 9 '18 at 5:34