6 ms·

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 http://arxiv.org/abs/1

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 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.

balsam 14y ago
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 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.
- mistercow 14y ago
  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.
  - balsam 14y ago
    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.)
aphyr 14y ago
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!
- cygx 14y ago
  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-temperature-an-extensive-property-like-density/33752#33752 http://physics.stackexchange.com/questions/33750/is-temperat...
- frozenport 14y ago
  Does stimulated emission hold this property? We increase the energy until the system lases but the entropy decreases as the gain narrows?
  - jpdoctor 14y ago
    > 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.
ignostic 14y ago
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."
- Xcelerate 14y ago
  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.
  - boboblong 14y ago
    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?
- gus_massa 14y ago
  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.)
Xcelerate 14y ago
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.)
- aphyr 14y ago
  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. :)
  - pm90 14y ago
    I think the parent was criticizing the unfortunate naming of these discoveries (designed to capture the imagination of laymen) rather than the discoveries themselves.
    - mvaliente2001 14y ago
      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."
      - jessriedel 14y ago
        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)"
levlandau 14y ago
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.... :)
derleth 14y ago
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_temperature.html 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.
AnthonyMouse 14y ago
>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?
bfe 14y ago
PSA: the published form of the article at http://www.sciencemag.org/content/339/6115/52 http://www.sciencemag.org/content/339/6115/52 includes revisions from the arxiv.org draft copy.

balsam 14y ago

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 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.

mistercow 14y ago
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.
- balsam 14y ago
  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.)

aphyr 14y ago

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!

cygx 14y ago
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-temperature-an-extensive-property-like-density/33752#33752 http://physics.stackexchange.com/questions/33750/is-temperat...
frozenport 14y ago
Does stimulated emission hold this property? We increase the energy until the system lases but the entropy decreases as the gain narrows?
- jpdoctor 14y ago
  > 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.

ignostic 14y ago

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."

Xcelerate 14y ago
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.
- boboblong 14y ago
  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?
gus_massa 14y ago
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.)

Xcelerate 14y ago

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.)

aphyr 14y ago
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. :)
- pm90 14y ago
  I think the parent was criticizing the unfortunate naming of these discoveries (designed to capture the imagination of laymen) rather than the discoveries themselves.
  - mvaliente2001 14y ago
    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."
    - jessriedel 14y ago
      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)"

levlandau 14y ago

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.... :)

derleth 14y ago

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_temperature.html 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.

AnthonyMouse 14y ago

>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?

bfe 14y ago

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