Quantum gas goes below absolute zero | Hacker News Reader

Quantum gas goes below absolute zero

nature.com

175 pointsevgen64 comments

I don't really like the misleading headline, although it seems as though the actual paper does it as well (http://arxiv.org/abs/1211.0545). Temperature is conventionally defined as the average kinetic energy of a collection of particles.

However, in statistical mechanics, you derive thermodynamic relations from the principles of quantum mechanics. It turns out there is a term β which for most purposes seems to match up with 1/kT, where k is the Boltzmann constant and T is classical temperature. According to this article, there are some occasions where "conventional" T and quantum mechanical T do not match up.

The most famous relationship in statistical mechanics is:

S = k ln Ω

S is entropy. Ω is the partition function for the microcanonical ensemble, and it corresponds to the number of quantum states available to a system. (In English: Ω is the number of different configurations that a system of particles can possible have.)

Another relation that can be derived is:

1/kT = ∂ln(Ω)/ ∂E

Substituting the first equation into the second, we get

1/T = ∂S/∂E

So what would a negative temperature imply? That increasing energy leads to decreasing entropy. My guess is that these researchers have created some system that does exactly that.

Are any laws of thermodynamics violated here[1]? If not, why is this experiment interesting? As a physics student, let me check: 0. Probably not. 1. Not directly applicable 2. Nope. 3. Nope. [1] http://en.wikipedia.org/wiki/Laws_of_thermodynamics

(double post because I really would like an answer) BTW, I now check HN for physics news too, as a BTW.

So your baseline standard for whether an experimental result is interesting is "does this violate the laws of physics?" You must find science so disappointing.

On the other hand, I find engineering very undisappointing. That's why I'm a scientist, since science has a higher standard for being interesting. Call it hipsterism or whatever you will, I upvote thee. (This is an engineering result, not a science result.)

Temperature is conventionally defined as the average kinetic energy of a collection of particles.

Many thermo and statmech texts will use this phrase as an operational definition for temperature in idealized kinetic models, but the conventional thermodynamics definition is actually (as you note) T ~ ∂E/∂S.

Negative-temperature systems are perfectly possible in both theory and the lab; all you need is for an increase in energy to decrease the system's entropy. This is the first gas I've heard of with a negative temperature, but systems like electron spin in crystal lattices can have this property. :)

Amusingly, these systems don't transition from positive to negative temperatures by getting cooler and cooler, crossing through absolute zero. Instead their temperature increases towards positive infinity, flips to negative infinity, and rises asymptotically towards zero. Some folks like to think of temperature as the inverse (∂S/∂E) because this seems so unintuitive!

Temperature is conventionally defined as the average kinetic energy of a collection of particles.

More precisely, temperature is related to average energy per degree of freedom via the equipartition theorem.

This doesn't only break down in case of negative temperatures, but also if continuity is no longer a good approximation for quantized energy levels. See http://physics.stackexchange.com/questions/33750/is-temperat...

Does stimulated emission hold this property? We increase the energy until the system lases but the entropy decreases as the gain narrows?

> Does stimulated emission hold this property?

Yes.

> We increase the energy until the system lases but the entropy decreases as the gain narrows?

Typical model is the two level system. At abs 0+, all the electrons are in the lower state. at abs 0-, all the electrons are in the upper state.

So are the photons in a laser at a negative temperature.

No. The photon population is not in thermal equilibrium. (They are concentrated at one energy, rather than obeying the Bose-Einstein distribution vs energy.)

More generally: A negative absolute temperature is possible only when the distribution of energy states is bounded by some maximum.

Your guess? So to clarify, you're sure that the headline is misleading, or you're guessing that it is? Could someone explain in terms we non-physicists can understand?

I'm willing to bet most people (myself included) don't understand the equations you posted. Still, it's the top comment because every top comment on Hacker News is "that headline is misleading."

I was trying to write my post so that it comes across in a way that doesn't require stat. mech to understand (you just need to know how derivatives work). You don't have to understand how the equations are derived to understand what the result means.

To explain what I mean by states, consider a 3-bit string. How many states are there? 2^3 = 8 states. Similarly, if you have a collection of particles, there's only a finite number of "arrangements" (for lack of a better word) that these particles can be in. The more possible arrangements, the higher the entropy.

I added another post on why I think the headline is misleading. Basically, if the article's intent is to explain the subject to non-physicists, they're just going to confuse people by using that word "temperature". Instead, it's better to say what you normally think of as temperature (hot and cold) has a more precise, mathematical definition that doesn't really correspond to intuitive notions of hot and cold any more.

> Still, it's the top comment because every top comment on Hacker News is "that headline is misleading."

And for good reason. That's why the article gets so much attention and discussion. If it had been submitted as "Unique quantum gas has decreasing entropy for increasing energy" it would have no replies.

But isn't that just as fascinating (as long as you know what it means)? I just finished my first college-level physics course a few weeks ago and I'm already fuzzy on the thermodynamics stuff, but the entropy of this gas shouldn't decrease with increasing energy, should it?

A little late, but I hope this clarifies why the headline is misleading.

The natural interpretation of "Quantum gas goes below absolute zero" is that someone had a super-freezer that cooled a gas so much that it is passed the 0K and it's so cold that it has negative temperature.

The real thing is that it is so hot that the temperature "goes beyond" infinity and is negative. A better headline would have been "Quantum gas goes negative absolute temperature".

Usually "bellow zero" and "negative" mean the same thing. The problem with "absolute" temperature is that the natural order of the real numbers is not the same as the hot-cold order. (It's a topological problem :).) (It's explained in more detail in other comments.)

After thinking about the article's headline some more, I've come to the conclusion that to get a lot of attention and hype you need to:

    1. Take a word that has a commonly accepted meaning
    2. Redefine the word to a more general case using advanced physics or chemistry
    3. Find an obscure property that this new definition allows
    4. Shock and amaze!

(See "mass" for similar phenomena.)

I know you're being sarcastic, but this is a wonderful thing about science! Commonly held, intuitive, time-honored ideas about temperature, space, mass, time, turn out to break down in edge cases, and those breakdowns drive the development of new mathematics, physics, and chemistry. The universe is so much deeper, stranger, and more beautiful than we ever imagined.

If you aren't compelled by ideas alone it can feel like much ado about nothing (who cares about tiny variations in spacetime curvature?), but without general relativity, we couldn't have built the GPS. Without quantum mechanics we couldn't have lasers--and without lasers, no modern internet.

Pretty cool time to be a human being, I think. :)

I think the parent was criticizing the unfortunate naming of these discoveries (designed to capture the imagination of laymen) rather than the discoveries themselves.

But in this case, it seems to be correct. So, we, laymen, should update our concepts and throw away the idea that "0° is the lowest temperature."

No. If you don't know the abstract definition of temperature from statistical mechanics, you haven't learned anything from the headline "temp can actually be negative (properly defined)"

But 0K (notice there's no °) is the lowest temperature - it's just that it's also the hottest temperature, depending on which direction you're coming from.

Temperature has a nice interpretation as average energy for classical systems, but in a sense thermodynamic β = 1/kT is the more 'natural' quantity that has a pole at T = 0, corresponding to infinite hotness or coldness respectively.

"quantum teleportation" fits the bill

"Faster than light" stories in relation to phase velocities.

Thing is this is a Nature paper. I don't think it's really fair to expect scientists to rephrase this discovery differently. Negative temperature is a pretty long standing concept in physics and when a stable system is synthesized in the lab, scientists ought to be free to use the appropriate terminology. Scientists claiming to have found the harry potter invisibility cloak on the other hand.... :)

Here's a well-written piece specifically on the physical meaning of negative temperature, using the same definitions as the parent post:

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/neg...

It provides a specific example of a scenario where a temperature below absolute zero would actually make sense: A spin-system of spin-1/2 atoms confined to a wire. The atoms aren't free to leave the wire, but they can change their spin state from spin-down (lowest energy) to spin-up (highest energy); thus, there is one lowest possible energy state (all atoms spin-down) and one highest possible energy state (all atoms spin-up).

If you start with that system in the lowest possible energy state, adding energy takes the temperature from zero to approaching positive infinity (half of the atoms are spin-up), then approaches negative infinity, and climbs back to approaching zero, but still negative.

>So what would a negative temperature imply? That increasing energy leads to decreasing entropy.

This is not my field, but the first thing I thought about when I saw "negative temperature" is what it does to the equation for Carnot efficiency. Does this mean we can now theoretically have a heat engine which is more than 100% efficient? That seems... breaks the laws of physics-y, so I assume it's wrong. But can someone explain why?

PSA: the published form of the article at http://www.sciencemag.org/content/339/6115/52 includes revisions from the arxiv.org draft copy.

I'm not sure I understand this part:

"Normally, most particles have average or near-average energies, with only a few particles zipping around at higher energies. In theory, if the situation is reversed, with more particles having higher, rather than lower, energies, the plot would flip over and the sign of the temperature would change from a positive to a negative absolute temperature."

If more particles have higher energy, then wouldn't the average energy increase as well? And if the average energy increases, then shouldn't that still keep things in positive, rather than negative, territory?

Temperature is not really the average kinetic energy any more. The temperature of a system says something about how much the entropy increases as you add energy. Negative temperature simply means that the entropy decreases as you add energy.

This is possible if the number of high energy states is small, because then adding energy will result in the system being in one of a smaller number of high energy states, thus having lower entropy (the entropy of a system is basically the logarithm of the number of states we think the system could be in, so if the number of states is lower, then the entropy is lower). Another way of saying this is that is as follows. For positive temperatures our knowledge of the state of the system would decrease if we added energy (think about a box full of neatly arranged balls and giving it a kick). For negative temperatures our knowledge of the system would increase if we added energy. In the extreme case if the number of possible high energy states is 1, then adding energy can force the system into exactly that state, thus we would know all you can know about the system.

In particular in the experiment described in the article, if you removed energy from the system the particles would not be in the lattice arrangement and instead would go around randomly. Thus the entropy would increase if you removed energy.

Your first three sentences are worth more than that entire article. Thanks!

Are any laws of thermodynamics violated here[1]? If not, why is this experiment interesting? As a physics student, let me check: 0. Probably not. 1. Not directly applicable 2. Nope. 3. Nope.

[1] http://en.wikipedia.org/wiki/Laws_of_thermodynamics

BTW, I now check HN for physics news too, as a BTW.

> Are any laws of thermodynamics violated here[1]? If not, why is this experiment interesting?

That's a pretty tough criteria for judging an experiment to be interesting. Seems that must pretty much rule out all experiments in fact...

So I understand it conceptually:

A thought experiment where a cup of some substance manages to be observed at a stable negative temperature.

This substance is a liquid at its current temperature. But it is colder than the ambient temperature of the room. As the liquid warms up from the ambient room temperature, it freezes. But taken outside on a cold day, it will melt and then evaporate?

I know you're not going to get a cup of this stuff in reality, but am I at least understanding the idea? The "temperature" of the liquid would remain negative, it's not like it could ever "warm up" to the point it was positive? It could reach an equilibrium state with its environment, but it would still be negative?

Yes, that's the right idea (assuming it has lower entropy when it's frozen than when it's liquid). In the context of the liquid you describe, and assuming it has otherwise normal properties then yes you can't warm it up (= add energy) and make it positive again. And if you took it outside, the temperature would first become more and more negative and then flip to positive. However, as long as we are talking about exotic stuff it is conceivable that as you add energy, the entropy first decreases (i.e. negative temperature) but if you add more and more energy, the entropy starts to go up again. For example lets say that if you add a lot of energy to the frozen stuff, it becomes a gas. I'm not sure if a system like that where you go from positive to negative to positive is physically possible, but I don't currently see any reason why it wouldn't be.

An object with negative temperature is hotter than an object with positive temperature. So it's not possible for the cup of negative temperature liquid to be "cooler" than the ambient temperature of the room. The liquid's temperature will get more and more negative until it flips from negative infinity to positive infinity, and then cool down from there until it equilibrates with the ambient environment.

I did not read the article (shame on me), but the story goes like this:

Normally, energy of a system is bounded from below (there's a lowest energy). Adding energy to the system increases the number of accessible microstates (individual particles may occupy energy levels from lowest to highest accessible one) and thus the entropy. Such a system is characterized by positive temperature.

Now, quantum systems may come with an energy bounded from above, and adding energy to the system will decrease the number of accessible microstates (individual particles are forced into the highest energy level and have nowhere else to go). Such a system is characterized by negative temperature.

A system with negative temperature is hotter than one with positive temperature in the sense that heat will flow from the system with negative temperature to the one with positive temperature.

Why was this something that needed to be 'created' then? Isn't it just a different way of thinking about the same thing?

Negative temperature is a quantum effect than can be tricky to produce experimentally.

There's nothing mysterious about negative temperature from the thermodynamical point of view, but there are no classical systems that exhibit this property.

But isn't the property, as described, simply a different way of reasoning about the same physical phenomenon? (Clearly it's not, I'm just not sure where the gap in my understanding is)

This is eq 7 here (scroll down) if I'm not mistaken: http://en.wikipedia.org/wiki/Temperature#Second_law_of_therm...

That is, temperature relates to the change of entropy in relation to the energy that enters the system

Correct. Equation (8) can be used as definition for thermodynamical Temperature whereas equation (7) tells us about the direction of heat flow.

>"Normally, most particles have average or near-average energies, with only a few particles zipping around at higher energies. In theory, if the situation is reversed, with more particles having higher, rather than lower, energies, the plot would flip over and the sign of the temperature would change from a positive to a negative absolute temperature."

Unless I'm missing something that is complete nonsense. If more particles have higher rather than lower energies the average shifts up and the most particles have average energy with just a few with much more energy. There is nothing to limit the maximum energy of particles like absolute zero on the high end.

I didn't read the actual research article, but this fragment reads as the usual disfigurement of actual information commited by a journalist attempting to explain a concept he/she doesn't understand at all.

No, it's not... really nonsense--it's just really confusing if you haven't worked with entropy and canonical ensembles before. See my comment above, or http://en.wikipedia.org/wiki/Thermodynamic_beta.

The usual explanation of such things: T is not so important as 1/T. So negative abs temp is achieved by going through +infinity temp and coming back via -infinity temp.

Note that this is only allowed in systems which have states that are bounded in energy. The usual example is a laser: When in inversion, its absolute temperature (of the electron population) is negative.

If you'll allow a car analogy - isn't this like saying backing up is slower than being parked?

Yes, it's a negative number in the context of a forward velocity vector, but it's a higher energy state.

No. The problem is that for historical reasons we choose the wrong scale and it's a little late to change all the books.

We choose to measure the temperature in this way

  (infinityK) ... ->- 10K ->- 1K ->- .1K ->- ... | 0K(impossible) | ... ->-.1K ->- -1K  ->- -10K ->- ... (infinityK)

Where ->- means hotter

In this scale 0K is impossible and impassable. But infinityK is possible (only one unsigned infinity) and some kind of systems when they get hotter they can pass from very "big" positive temperatures to very "big" negative temparatures.

And the negative values are hotter than the positive. For example: -.1 is hotter than -10K that is hotter than 10K that is hotter than .1K

It's (theoretically) better to measure beta=1/temperature (the usual notation is beta) In this way:

  (infinity/K) ... -<- 10/K -<- 1/K -<- .1/K -<- ... 0/K(possible) ... -<-.1/K -<- -1K  -<- -10K -<- ... (infinityK)

Where -<- means hotter

In this scale infinity/K is impossible as expected. But 0/K is possible. And the order is the correct order hotter=less_than. Using beta they are ordered more intuitively. Hotter means moving to the right in the line.

Thank you; this helped clarify things quite a bit.

isn't negative absolute temperature an oxymoron?

No. Temperature is just the relationship between entropy and energy: ∂S/∂E. This relationship can be negative.

Ok, this is at atomical level, it is possible to increase the energy of the system till you freeze the electrons? What would happen then if the particles are organized at subatomical levels?. And below that? Could it be a way to study matter properties?(in place of the cern way)

Ok, mind officially blown.

Still wrapping my head around the notion that you can flip the energy signature on atoms at near absolute zero and have that result in mirroring to the other side of the temperature number line.

Also intrigued by the notion that 'dark matter' is just 'regular matter' but flipped into the negative temperature side of the scale. Which really makes one wonder about the nature of heat.

From the article:

"Schneider and his colleagues reached such sub-absolute-zero temperatures with an ultracold quantum gas made up of potassium atoms. Using lasers and magnetic fields, they kept the individual atoms in a lattice arrangement. At positive temperatures, the atoms repel, making the configuration stable. The team then quickly adjusted the magnetic fields, causing the atoms to attract rather than repel each other. “This suddenly shifts the atoms from their most stable, lowest-energy state to the highest possible energy state, before they can react,” says Schneider. “It’s like walking through a valley, then instantly finding yourself on the mountain peak.”

At positive temperatures, such a reversal would be unstable and the atoms would collapse inwards. But the team also adjusted the trapping laser field to make it more energetically favourable for the atoms to stick in their positions. This result, described today in Science1, marks the gas’s transition from just above absolute zero to a few billionths of a Kelvin below absolute zero."

And this:

"Another peculiarity of the sub-absolute-zero gas is that it mimics 'dark energy', the mysterious force that pushes the Universe to expand at an ever-faster rate against the inward pull of gravity. Schneider notes that the attractive atoms in the gas produced by the team also want to collapse inwards, but do not because the negative absolute temperature stabilises them. “It’s interesting that this weird feature pops up in the Universe and also in the lab,” he says. “This may be something that cosmologists should look at more closely.”

Just sayin'

As others pointed out, there are two definitions of temprature, usually it is related to average energy per particle and formally it is T=dS/dE (S is the entropy, E the total emergy of the system). What I do not understand, is why is this news? A negative emergy is not very uncommen, for example lasers have negative temperature.

I think the new part is that this is very close to absolute zero from the negative side instead of the positive side. It also seems the other interesting part is that the system transitions from positive to negative temperatures very suddenly.

Assuming the second law is not violated, the system of lower (negative) temperature becomes a source of energy (as opposed to sink). If this is right, that is mighty interesting.

Not really - this has been done before and the textbook example are spin systems. The newsworthy part is that the negative temperature is realized via motional degrees of freedom.

Just checked wikipedia: "By contrast, a system with a truly negative temperature in absolute terms on the kelvin scale is hotter than any system with a positive temperature. If a negative-temperature system and a positive-temperature system come in contact, heat will flow from the negative- to the positive-temperature system."

Let's define wikipedia to be the absolute zero of information.

Once again I am reminded that half the facts I know are wrong.

Maybe the Universe somehow has a natural form of this effect in the intergalactic medium (or in spacetime) that causes negative pressure and is the mechanism of dark energy?

"Negative temperatures imply negative pressures and open up new parameter regimes for cold atoms, enabling fundamentally new many-body states."

Nature's article starting with completely anti-science statement like : "It may sound less likely than hell freezing over" is pretty disappointing.

To be fair, it's a news brief designed for the average layperson, not a research article. I think editorializing the content a bit is fine.

Besides, that particular phrase is commonly accepted as an idiom, not a serious reference to a Biblical Hell.

What you're saying is like "This TV channel is against sports because they aired a theatre show last night."

You're mixing metaphysical categories.

Yes, science must ignore the Siren call of religion! We welcome your efforts, for it is a truly Herculean task, nay, Sisyphean! You're like modern Prometheus, providing us fire on this Odyssey into the future.

Below absolute zero is an anti-concept.

cool.

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