# What is Absolute Zero?
**URL:** https://boards.straightdope.com/t/what-is-absolute-zero/47381
**Category:** Factual Questions
**Created:** [December 27, 2000, 4:05pm UTC](https://boards.straightdope.com/t/what-is-absolute-zero/47381 "2000-12-27T16:05:10Z")
**Posts on this page:** 5
**Page:** 2
### Author:  [@Polycarp](https://boards.straightdope.com/u/Polycarp)
#### Post date: [December 28, 2000, 1:31am UTC](https://boards.straightdope.com/t/what-is-absolute-zero/47381/21 "2000-12-28T01:31:35Z")
**Perderabo** , it lost me too, but I got the distinct impression that temperature is related to spin state, and that there is a point at which all spin states are down, and that is the lowest possible temperature. You can have “negative” temperatures relative to any given state, but they’re **relative** , not absolute.
I’d get the idea, from all this, that absolute zero is an asymptotic state which can be approached infinitely closely but never quite achieved. (IIRC, cryogenic labs have gotten to one millionth of a © degree above absolute zero, but of course have not achieved or gone below it.
The question of what temperature is below absolute zero can be phrased and sounds intelligent, but it’s of the nature of “What’s beyond the end of a circle?” or “If the universe is closed in a fourth dimension though limitless in three, what’s beyond the edge of the universe?” – it’s meaningless in real life.
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### Author:  [@Pasta](https://boards.straightdope.com/u/Pasta)
#### Post date: [December 28, 2000, 8:42am UTC](https://boards.straightdope.com/t/what-is-absolute-zero/47381/22 "2000-12-28T08:42:20Z")
**Regarding negative temperatures…**
Here are a couple of ways (neither very intuitive) to think about negative temperatures:
1. _Entropy/energy relation._ We’ll define some things:
_U_ = internal energy of the system. This is all the energy from particle motion, spin interactions, anywhere energy can hide.
_S_ = entropy of the system. Entropy is no more than a count of how many states are accessible to the system (given its energy, let’s say). That is, if I say the system has energy _U_, you can look at the various parameters describing the system and count how many ways you can make the system have energy _U_. Probably a lot of ways. Entropy is the logarithm (base _e_) of this (often huge) number.
_T_ = temperature. Since _S_ is often thought of as a function of _U_ (i.e., _S_(_U_) = logarithm of number of states with energy _U_), it might be useful to know how _S_ changes as we change _U_. Temperature, then, is defined as _T_=1/(d_S_/d_U_). It is the inverse of the slope of the _S_-_U_ curve. (Note: this derivative is a partial derivative, if you care.)
Whew. So, with this non-intuitive (but fundamental) definition of temperature, all we need in order to have negative temperature is to find some point on the _S_-_U_ curve where increasing the energy _lowers_ the number of possible states (i.e., where _S_(_U_) has negative slope). Does this occur? Not usually, but sort of, sometimes. More later.
2) _Boltzmann factor._ You have a system at temperature _T_. What state might it be in? The probability of it being in some particular state with energy _E_ given _T_ is given by the Boltzmann factor: _P_=_e_[sup]_E_/_kT_[/sup]/_Z_, where _Z_ and _k_ are constants. (The use of _E_ instead of _U_ is unimportant.) It could just so happen that you have a system whose probability distribution of states, in fact, follows the Boltzmann distribution, but only if you say the temperature is negative.
Most normal systems cannot have negative temperature. You can’t have a brick with negative temperature. The concept only comes up in systems that have a highest possible energy. A free particle can’t meet this requirement as you can always stuff more energy into a particle (by making it go faster). But, if you had some isolated contrived system like this:
You have 2 particles. Each can have either energy 0 or _E_. The possible energies, then, are 0, _E_, and 2_E_. That’s it. (Maybe these 2 particles are held still so we can’t add energy in the motion.) There are two ways to make the system have energy _E_ – particle one has energy _E_ and particle two has energy 0 or vice-versa. Thus, there is a peak in the entropy at _U_=_E_ since _S_(0)=log(1), _S_(_E_)=log(2), and _S_(2_E_)=log(1). Thus, the system can have negative temperature (since d_S_/d_U_ goes negative. (Doing derivatives on discrete values is clearly bad, but the concept holds.))
Physically realizable? Finding these sorts of systems is easy (atomic levels, spins in magnetic fields), but finding _isolated_ versions is not. If the spins (etc.) are coupled to a particle motion, for instance, then you can’t ingnore that motion in your description of the state. All of a sudden, you can’t have negative temperatures anymore. All is not lost, though. You can speak of the temperature of just those degrees of freedom that allow negative temperatures. And, if those degrees of freedom (like spin) don’t interact too much with the “bad” ones (like momentum), then you can actually do some physics with the concept. Particularly, if the time scale for energy transfer between “good” and “bad” degrees of freedom is much longer than the time scale for interaction within just the “good” degrees of freedom, then talking about the temperature of only those degrees can be useful. This approximation aspect, though, doesn’t take away from the reality of negative temperature.
_(Relatively) super-short summary of everything above:_ You can’t take a system and cool it down and get past absolute zero. You can, however, talk about certain parts of certain systems as having negative temperature since the way these sub-systems interact with each other follows familiar statistical mechanics (but only if you let temperature go negative.)
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### Author:  [@Perderabo](https://boards.straightdope.com/u/Perderabo)
#### Post date: [December 28, 2000, 2:38pm UTC](https://boards.straightdope.com/t/what-is-absolute-zero/47381/23 "2000-12-28T14:38:57Z")
Thanks, **Pasta**. That helped a lot. It hasn’t totally sunk in yet, but it was nice to read something on negative temperatures without getting lost.
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### Author:  [@Phobos](https://boards.straightdope.com/u/Phobos)
#### Post date: [December 28, 2000, 3:19pm UTC](https://boards.straightdope.com/t/what-is-absolute-zero/47381/24 "2000-12-28T15:19:18Z")
isn’t it amazing how a simple question can grow into a complex discussion?
only here at the SDMB! 🙂
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### Author:  [@don\_willard](https://boards.straightdope.com/u/don_willard)
#### Post date: [December 28, 2000, 8:21pm UTC](https://boards.straightdope.com/t/what-is-absolute-zero/47381/25 "2000-12-28T20:21:32Z")
Maybe absolute zero would be where for instance the electron doesn’t spin at all (but above it was said that it would have “down” spin…???) And absolute zero would be where the protons and other particles didn’t have any spin, plus the electrons would stop in their tracks and not move around in their orbits anymore (or on their sphere or dumbbell-shaped or other-shaped surfaces). Does the nucleus itself have its own spin besides all the protons and neutrons spinning around? If so the nucleus would stop spinning around. All motion would be frozen. If a neutrino spins, it would no longer spin, nor would it head toward the earth or anywhere else. On earth, the sun would seem to stand still, as at Jericho, and yet we wouldn’t know it, because eight minutes after everything reached absolute 0
we would see only a cinder. In any case, where would this energy go if everything was absolute 0? Maybe this is where the universe will be all stretched out to what we could call Absolute Expansion = Total Entropy,sometime in the future.
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