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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.

Qmechanic
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Daniel Turczynskyj
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2 Answers2

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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.

BowlOfRed
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  • Can you explain the top part a little more, I'm in middle school and don't exactly understand it. – Daniel Turczynskyj Apr 06 '18 at 20:48
  • QM says that objects at absolute zero have all the extractable energy removed from them. But some (non-extractable) energy may remain. As an example, helium at atmospheric pressure would not solidify (stop moving/vibrating), even if it were to be cooled to absolute zero. – BowlOfRed Apr 06 '18 at 20:53
  • Does that mean if the helium or another object were to be pressurized to higher atmospheres, it would be possible to reach absolute zero? – Daniel Turczynskyj Apr 06 '18 at 21:07
  • Nope. (1) You can't reach absolute zero. (2) Even at (the unreachable) absolute zero, material still have a non-zero kinetic energy. – BowlOfRed Apr 06 '18 at 21:54
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    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 07 '18 at 17:08
  • @DanielSank I think he's right on the 1st point. He says that even at 0K, there is non zero kinetic energy involved. And you say that no motion does not imply non zero temperature. I do not see how this conflicts with his point. Am I missing something? – untreated_paramediensis_karnik Apr 07 '18 at 19:07
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    @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 07 '18 at 22:48
  • Thanks a lot @DanielSank . Do that mean that the expectation value of the momentum operator for the ground state vanishes? I.e. $\langle \psi_0 | \hat {\vec p} | \psi_0 \rangle =0$? – untreated_paramediensis_karnik Apr 08 '18 at 11:24
  • Edit: According to Wolfram Alpha, it is. Wow. So this answer deserves a downvote, unless it gets corrected. But as of now, it deserves a downvote for sure. Certainly not a +3. – untreated_paramediensis_karnik Apr 08 '18 at 11:30
  • Wait @DanielSank, but the expectation value of the momentum squared is non zero. Does that mean that there's a non zero kinetic energy after all? If so, then it's quite unfortunate that I can't undo my downvote. – untreated_paramediensis_karnik Apr 08 '18 at 11:53
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    @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 08 '18 at 17:08
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    @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 09 '18 at 04:22
  • @DanielSank : I suggest you re-read this answer too. It is correct. If you beg to differ, perhaps we could re-open the question and you could volunteer an answer of your own. – John Duffield Apr 09 '18 at 10:52
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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.

John Duffield
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  • 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. – untreated_paramediensis_karnik Apr 07 '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 07 '18 at 14:03
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    "Vacuum fluctuations" do not preclude a thing from being at absolute zero. – DanielSank Apr 07 '18 at 17:10
  • @DanielSank : I didn't say that. Read up on zero point energy. Note that "Liquid helium retains kinetic energy and does not freeze regardless of temperature due to zero-point energy" – John Duffield Apr 08 '18 at 13:01
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    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 09 '18 at 04:10
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    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 09 '18 at 05:34
  • You also can't ignore the Hawking radiation. If you hover a distance $\epsilon$ from an event horizon you will always observe Hawking radiation coming from the black hole no matter how small the value of $\epsilon$. In fact the radiation intensity goes to infinity as $\epsilon\to0$. – John Rennie Apr 09 '18 at 08:05
  • @DanielSank : you're misreading what I said. Read the question and answer again, and note Daniel's "no molecules" comment under the question. A vacuum containing no molecules is not necessarily at absolute zero temperature. Even when it is, it still contains kinetic energy. – John Duffield Apr 09 '18 at 10:37
  • @JohnRennie: we have good evidence that black holes exist, and no evidence that they take an infinite time to form and therefore do not exist. Your claim that the first part of this answer is wrong is based on an unwarranted assertion. – John Duffield Apr 09 '18 at 10:37