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Yet again I feel the need to scold New Scientist for crappy reporting on physics. Ulrich Schneider and colleagues have gotten some atoms to have negative temperatures.  That's nothing new!  What's new is that they're doing it not using the atoms' spins, or other discrete quantities: they're doing it using the motion of the atoms.   But:

1) The article doesn't say that.

2) The blurb here says the existence of negative temperatures "could help us understand dark matter."  Well, anything is possible, but this is not at all what Schneider's new work is about!   The article says dark energy has negative pressure - true, according to our theories - "which suggests it might have negative temperature."  Oh yeah?  That seems very unlikely to me.   Clearly this aspect was emphasized just to catch our attention. 

3) They also say this new work "might allow us to build ultra-efficient heat engines."   But when New Scientist says something about physics "could" or "might" be true, they often mean "with probability 0.1%". 

4) They begin by saying "Nothing is colder than absolute zero..." This is a botched version of a commonly heard sloppy statement of the Third Law of thermodynamics, which goes "it's impossible to reach absolute zero."    But negative temperatures are possible, for systems that have a maximum allowed energy.  And Schneider's work is one of many examples of this.

5) In modern physics what's more fundamental than temperature is the reciprocal of temperature, which I call coolness.  Coolness can be positive, negative or zero.  When coolness goes from positive to zero to negative, the temperature gets big, then becomes infinite, and then becomes negative.   That sounds weird in terms of temperature!   But it's perfectly reasonable in terms of coolness.  The sloppy statement of the Third Law also becomes more reasonable: it just says infinite coolness is impossible.

The New Scientist article tries to explain this as follows: "The resulting thermometer is mind-bending with a scale that starts at zero, ramps up to plus infinity, then jumps to minus infinity before increasing through the negative numbers until it reaches negative absolute zero."   This emphasizes the weirdness rather than the reasonableness of what's going on.  It also suggests that a temperature of "negative zero" is different than zero, and allowed where zero is not.

For more on negative temperatures, try the FAQ:

I didn't write it - it's from the early days of the internet, when a few of us physics people got tired of answering the same questions over and over.

Harald Hanche-Olsen's profile photoKonstantin Kk's profile photoJacob Aron's profile photoJohn Baez's profile photo
All the articles describing this result as "breaking the absolute-zero barrier" have really been annoying me. You'd think that negative temperature was not a well-established phenomenon already. the first thing I usually do is to explain that negative temperatures are not colder than absolute zero, but, as P. W. Atkins put it, "hotter than infinity". And the next thing I do is to try to convey the somewhat esoteric definition of temperature in statistical mechanics that makes this kind of thing possible.

Most people who have been through high-school chemistry get the idea from ideal gases that temperature is basically a measure of energy density, and these situations are the ones where it's very much not that.
thank you, the old FAQ helped ! 
+Matt McIrvin - Everything you say is true.  Of course, you are another of those internet old-timers who "got tired of answering the same questions over and over".   We certainly learned all the most popular ways people get confused about physics!
Yes, yes, and yes!

But while it is annoying to see so much miscomphrension, I have to prefer ignorant but excited to ignorant and bored. 
If it were merely a choice between different kinds of ignorance, I too would prefer excited ignorance. 
+John Baez In point of fairness, you really ought not take NS to task about your point 2. This is suggested by the authors of the Science paper themselves, and supported in their supplemental material. (At least, in the supplemental material in the version of the paper.) It would be more constructive if you addressed the author's assertions and logic instead.
+Kam-Yung Soh - the Physics World post is certainly better!   But...

Like New Scientist, they don't say what's new about this work.  Negative temperatures are nothing new.  The theory behind them is old; I'm not sure when they were first produced, but it may be 1951:

• E. M. Purcell and R. V. Pound, A nuclear spin system at negative temperature, Phys. Rev. 81 (1951), 279 - 280.

And it's no secret; it's on Wikipedia:

The title and abstract of Schneider et al's paper clearly says what's new about their work:

Negative Absolute Temperature for Motional Degrees of Freedom

The key word is motional

Abstract.  Absolute temperature is usually bound to be positive. Under special conditions, however, negative temperatures—in which high-energy states are more occupied than low-energy states—are also possible. Such states have been demonstrated in localized systems with finite, discrete spectra. Here, we prepared a negative temperature state for motional degrees of freedom. By tailoring the Bose-Hubbard Hamiltonian, we created an attractively interacting ensemble of ultracold bosons at negative temperature that is stable against collapse for arbitrary atom numbers. The quasimomentum distribution develops sharp peaks at the upper band edge, revealing thermal equilibrium and bosonic coherence over several lattice sites. Negative temperatures imply negative pressures and open up new parameter regimes for cold atoms, enabling fundamentally new many-body states.
I suppose one of the things that makes this case confusing is that the system is, considered in the ordinary fashion, very cold, which makes it hard to see how it can have degrees of freedom that are "hotter than infinity".
+Brent Neal - Thanks for pointing out that a version of Schneider et al's article is on the arXiv (  This is all it says about dark energy:

"Via a stability analysis for thermodynamic equilibrium we showed that negative temperature states of motional degrees of freedom necessarily possess negative pressure [9] and are thus of fundamental interest to the description of dark energy in cosmology, where negative pressure is required to account for the accelerating expansion of the universe [10]."

It's typical of New Scientist to take the most speculative, least solid sentence in a physics paper and promote it to a headline or summary blurb, so people walk away completely confused.
The real issue, I think, is twofold. First, John is precisely correct that what he calls coolness and what I (in a codgerly fashion) will still call beta is the more fundamental value. Secondly, the statistical mechanical formulation of temperature is not well taught even to graduate physicists, so unless that's your area of study, you likely haven't internalized all the implications of the math.
+Brent Neal I even saw one explanation of negative temperature quoted secondhand on Facebook that came close to being correct, except that the author got confused between temperature and reciprocal-of-temperature, and claimed that the derivative of entropy with respect to energy was increasing in typical situations.
+John Baez Yes, but read the sentence footnoted [9] - which is a footnote to the supplemental material. The negative temperature states of motional degrees of freedom possess negative pressure, which is the point of the comment. You were skeptical of the link between the two, and thus I made the comment I did.
I think its accurate to refer to speculative statements like that one about dark energy as "citation bait." :)
Yes, I now see there's more to the connection between negative temperature and negative pressure than I first thought.  That's interesting!  I still think the possible connection to dark energy is about the least important part of the whole paper, for a whole bunch of reasons.

There are relatively few papers about physics in Science and Nature, as compared to say biology, and they often go for flamboyant claims - probably because it helps them get published.  Just making negative-temperature matter with motional degrees of freedom is not enough, apparently, so the authors throw in remarks about dark matter and heat engines with over-unity Carnot efficiency.  And then the New Scientist mentions those and forgets to describe what the paper actually did - that is, what was new about it. 
This was all new to me but I'm glad that you were all able to better clarify the article. I'm really loving Google+ it's reopened my mind to understanding the world of physics, a passion I had back in high school. I can't contribute anything to the conversation but just wanted to say thank you! 
Btw, the paper suggests that "absolute pressure and temperature necessarily have the same sign in equilibrium", but this is not true for a small portion of a chunk of rubber that's been stretched out a bit in all directions.  Such a thing has negative pressure - that's what 'tension' is - but it has positive temperature.  The paper argues that this is impossible because "the system could spontaneously contract and thereby increase its entropy".  But if you're stretching the rubber by pulling on it with little hooks in all directions, it can't contract. 
Also btw, it used to disturb me a lot that in general relativity, the negative pressure of the dark energy makes the universe expand, not contract. 
Well, that is pretty weird, because on a cosmological scale it effectively gets you energy from nowhere.

I figure that effect (run at super-strength during the inflationary era) probably created all the matter in the universe, though, so it's good for something.
Gyl Sky
it is the nature of the business now.

You bluff (or exaggerate) more
You get more attention
You get shareholders/ investors attention
You get fund to continue your work

What they don't want
They reveal the progress (or real result)
Their shareholders/ investors feel uncomfortable and cut loss
They lose the fund
Project failed, they lose the job
Led Zeppelin reached infinite coolness.  What do you think about that Mr. Smartypants!
FWIW, it looks like the journal paper (which is obviously paywalled) is on the arxiv at

It does contain this paragraph, which while not justifying the language in 2 and 3, might explain why NS latched onto those ideas:

"As negative temperature systems can absorb entropy while
releasing energy, they give rise to several counterintuitive ef-
fects such as Carnot engines with an efficiency greater than
unity [4]. Via a stability analysis for thermodynamic equilib-
rium we showed that negative temperature states of motional
degrees of freedom necessarily possess negative pressure [9]
and are thus of fundamental interest to the description of
dark energy in cosmology, where negative pressure is required
to account for the accelerating expansion of the universe"
+David Tweed - if you read the earlier comments you'll see more about this....
+John Baez Sure, I'm actually not particularly interested in the topic, I just got a bit interested in the reportage angle from seeing that multiple news sources that all talked about the using it to understand dark matter that I got interested to see if this was something actually in the paper. I've seen a reasonable number of NS stories that wildly over-hype things, but it seems the criticism of it regarding points 2 and 3 is that it's taking very, very speculative connections in the paper and making them sound like they're "just ordinary possibilites"  than they are rather than bringing some completely off-the-wall ideas of their own into reporting on a new paper.
I was just trying to subtly point out that what you said had already been said here.  But that's okay, of course!
Good to see some intelligent discussion of this, and thanks +John Baez for your link to the old physics FAQ.

I have a special relationship with this phenomenon, I got the "negative temperature" question on my Ph.D. oral qualifying exam, and, having actually read a thing or two about it, handled it rather well, if I may say so.

Edited to add: The exam in question was in 1990, which reinforces that this is hardly a new idea.
Negative temperatures are really cool (!), and surprising at first, so I suppose it makes sense that ignorant journalists hearing about this new work would get excited about that aspect and not realize that it's something else that's the news here.
Yes I first came across it myself in about 4 pages in "statistical Physics" by Mandl written in 1971 (my copy is one of the reprints from 1978). To get more info I got "an introduction to statistical physics" by Rosser (1982) which has a small but entire chapter on negative temp. Prior to this post and all the links in it ( and their links), that was the best accessible treatment I had. I alway enjoy old books and the 1951 date explains why older yet excellent stat phys books don't mention it.
OK, not sure what happend: when looking at this story I only saw 1 coment, namely Matt McIrvin's first comment at the top of the set of comment when I wrote the comment two hours ago, and I'm sure after John's reply I still saw my comment originally after Matt's first comment. I thought John's talking about reading earlier comments referred to a separate post that must have come out when the arxiv paper was debuted. I just now tried to search G+ for "negative temperature Baez" and it refinds this post, only it now has the "31 comments" on it. Maybe I'm losing it and there really was a  "n comments" link there and I didn't see it when I looked; wouldn't be the first time I've not seen something starting me in the face.

(On a side-note, it is quite annoying G+ doesn't appear to have a manual "Refresh view" button, instead forcing you to trust that it is automatically up-to-date.)
+David Tweed wrote: "(On a side-note, it is quite annoying G+ doesn't appear to have a manual "Refresh view" button, instead forcing you to trust that it is automatically up-to-date.)"

Since I spend a lot of time reading comments on my own posts, I make heavy use of the "Notifications" area on the upper right of any G+ page, which shows how many new comments there are, and makes it easy to find them.  This also works for comments on other people's posts, as long as I've commented on their posts. 

Whenever I feel something ain't right, I just hit the refresh button on my browser.
Apparently, I am more ignorant of physics than I thought, for I certainly had never heard of negative temperatures before. The old FAQ is certainly appreciated – it explained a lot in such a short space!

+John Baez wrote “We certainly learned all the most popular ways people get confused about physics!”. I think a list of common misconceptions in physics would be instructive and fun (and possibly a little embarassing). Does anyobody know such a list?

Oh, and I do like the term “coolness” for inverse temperature.
+John Baez 
from the discussion seems, you understand the idea of negative temp for motional degree of freedom. May i ask a question? 
As i remember from ancient school times, there's no upper boundary for particle's possible energy. Even at a speed of light (having E(k)=mc^2) it still can oscillate. Then what is the physical sense of term "temperature higher than infinity"? 
I've read the faq before, actionally came here by the link from where it was already mentioned, and understanding it for spin temp - is ok. But for motional degree of freedom - the idea doesn't make friendship with my head. 

the abstract about bosons' coherence with peaks maybe could answer some questions, but i somewhy fail to translate it into more comprehensible form. 
+John Baez thanks for taking the time to critique our article - this was a difficult one to report and it's always good to be corrected when we've made mistakes.

I agree with your first point that we should have made it clearer that negative temperatures are not new and that the new aspect was using the motion of the atoms. This was present in my original draft of the story, along with an explanation of the discrete state experiments from the 1950s and beyond, but we decided to cut it from an already lengthy story. In hindsight I regret cutting it all together and not leaving a mention that this had been done before.

I make no apology however for highlighting the possibility that the work could have wider implications in terms of dark energy or heat engines, even if these are unlikely. As others have pointed out, these were not my own idle speculations, but mentioned in the paper and also by Schneider and Mosk when I interviewed them.

I like your idea of "coolness" (a catchier name than "thermodynamic beta", which was my understanding of the concept) and agree it is much more reasonable. Unfortunately we are stuck with the historical definition of temperature, which most people understand, and I think it's far more useful and interesting to explain the concept in those terms. I don't see how the statement "nothing is colder than absolute zero" is wrong in these terms, but am happy to be corrected.

We're currently putting together a slightly different version of the story for the print edition, out on Tuesday, so look out for that.
+Konstantin Kk - The trick in this experiment is to set up a situation where a bunch of atoms effectively have an upper bound to their energy.   These are atoms 'in the lowest band of an optical lattice', if that helps.  It's not really really true that there's an upper bound on their energy; there are things they could do that would give them more energy, but the experimenters carefully set up a situation where these things hardly ever happen. 

So, the system is not truly in thermodynamic equilibrium at negative temperatures, but it acts like it to a good approximation.  This may seem like 'cheating', but there are many situations like this.  For example, diamond at room temperature and pressure is not in thermodynamic equilibrium; if you wait long enough it will eventually turn into graphite.  However, eventually is a very very very long time.  We say it's 'metastable':

However, for many practical purposes we can act as if it's in thermodynamic equilibrium.
+Jacob Aron - Thanks for your response to my grumpy complaints. 

"As others have pointed out, these were not my own idle speculations, but mentioned in the paper and also by Schneider and Mosk when I interviewed them."

This reminds me a little bit of how on its blog, the New York Times asked its readers if it should "fact-check" some of Mitt Romney's absurd claims during the election, and the readers exploded "Of course! What is journalism for?"  I can't find the webpage now, but it was quite amusing, and the Times seems to have taken it to heart. 

It would be great to have science journalism that didn't simply transmit and amplify idle claims, but focused on the most substantial aspects of scientific work.  I don't quite understand how the new content of Schneider et al's work got completely cut, while the speculation about dark energy is the main thing we see when people link to your article - see above:

"The existence of negative temperatures on the Kelvin scale could help us understand dark energy as well as revise the thinking about what temperature"

The result is a wholly misleading impression.  I suspect there's some mechanism where editors work to make stories as shocking and eye-catching as possible.

The main lesson of negative temperatures is that temperature is weird and confusing compared to inverse temperature.  What you call a "mind-bending" process that "starts at zero, ramps up to plus infinity, then jumps to minus infinity before increasing through the negative numbers until it reaches negative absolute zero" is actually a perfectly reasonable process where something positive goes down through zero and becomes negative. 

For this reason, physicists switched to working mainly with inverse temperatures many decades ago, maybe even in the late 1800s.

Is it possible to explain this in a short article?  Sure!

The fun lesson for ordinary folks would be that a familiar concept - temperature - turned out to be the wrong way to think about things.  Revolutions like this change our picture of the world: for example, people once thought the Sun went around Earth, but the other way around is more enlightening.  We used to think time and space were separate things, now we know they're not.  This is why physics is fun: when we change our outlook, suddenly everything makes more sense!
+Jacob Aron wrote: "I don't see how the statement "nothing is colder than absolute zero" is wrong in these terms, but am happy to be corrected."

I guess "colder than absolute zero" is so ambiguous that I misunderstood what you meant.  I thought you meant "having a temperature less than absolute zero."  That's probably what most ordinary folks would think, too.  But okay: if we call temperatures less than absolute zero "hotter than infinity", then you're right.
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