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What 'Negative Temperature' Really Means
On Friday we discussed news of researchers getting a quantum gas to go below absolute zero. There was confusion about exactly what that meant, and several commenters pointed out that negative temperatures have been achieved before. Now, Rutgers physics grad student Aatish Bhatia has written a comprehensible post for the layman about how negative temperatures work, and why they're not actually "colder" than absolute zero. Quoting:
"...you first need to engineer a system that has an upper limit to its energy. This is a very rare thing – normal, everyday stuff that we interact with has kinetic energy of motion, and there is no upper bound to how much kinetic energy it can have. Systems with an upper bound in energy don’t want to be in that highest energy state. ...these systems have low entropy in (i.e. low probability of being in) their high energy state. You have to experimentally ‘trick’ the system into getting here. This was first done in an ingenious experiment by Purcell and Pound in 1951, where they managed to trick the spins of nuclei in a crystal of Lithium Fluoride into entering just such an unlikely high energy state. In that experiment, they maintained a negative temperature for a few minutes. Since then, negative temperatures have been realized in many experiments, and most recently established in a completely different realm, of ultracold atoms of a quantum gas trapped in a laser."
I do not think this word means what you think it means.
kudos souskill
At least nowadays. Plenty of lasers around.
that absolute zero isn't absolute anymore? don't we just move the bar of absolute zero downward?!?
This doesn't really help. I pondered this for a while the other day when I read that first and gave up trying to wrap my head around it. I was always under the impression that 0 kelvin (absolute 0) meant a state at which there was no movement at the atomic/subatomic level. It would seem as though to reach a negative temperature, one would have to slow a substances particles to less than 0 movement. Then I realized they were talking about a quantum state and I pretty much gave up trying to understand it at that point, because anything which has the word 'quantum' in it suddenly defies all the rules I'd ever been taught about anything at all. :o)
Systems with an upper bound in energy don’t want to be in that highest energy state.
Sigh...
It's called 'mod down' not 'downvote' you idiot. Go back to fucking Reddit where you belong.
So essentially they changed the definition of temperature to one which allows for negative values. Interesting but not quite as radical as achieving negative motion.
If 'nerds' had paid any attention to their thermodynamics/statistical mechanics class they would have already know all this and we would have been spared two frivolous posts in the front page.
Just change the definition and you have negative kelvin, even though it really isn't.
temperature = change in entropy /total system energy
This graph of a system with finite energy will look like the graph of y=-(x-2)^2 + 4 (go google it for visual). obviously the dimensions will be different, but energy is on x and entropy is on y. my p.chem professor told me that negative temperatures were achievable in our schools research lab. this was 2 years ago and at a very good research school.
...It'll have something to do with Australia.
Everything on Slashdot has something to do with Australia, now.
Of course it will. Australia is the centre of the universe. Even the name "Aatish Bhatia" is obviously Australian in origin, and Rutgers is a suburb of Sydney I think.
I'm still not getting the definition of "temperature" here. As I read this it says "some matter in some states will get colder without giving it energy." How does this not go directly against the laws of physics by reversing entropy?
If video games influenced behavior the Pac Man generation would be eating pills and running away from their problems.
In the USA, it means its really, really cold, you'll have to dress well, including good gloves and hat. If there is any wind you'll wand to cover your face too.
and the air is very dry, inside, getting a humidifier is a good idea.. If your car or truck has been parked outside for a while you would need to start it and have it warm up for 10 minutes before driving off.
In the rest of the world its cold but bearable, since its just below freezing sidewalks may be slippery.
It would have been nice for Aatish to go a bit into what Purcell and Pound did in their 1951 experiment, namely "inverting" the orientation of the fluorine nuclei in the presence of an applied magnetic field by application of a radio frequency magnetic pulse, where the frequency is the Larmor frequency of fluorine and the pulse amplitude and length was sufficient to cause a 180 degree nutation. The result is that the nuclei have the same order (entropy) as the rest state, but have higher energy. In NMR, this is referred to as applying a 180 degree or pi pulse.
Aatish's comment about reality being liberal is unconvincing.
A Shadeless room is a brighter room.
It just means the pressure pulls inwards rather than pushes outwards. Given given P=nRT, that would correspond to a negative temperature (since it means the pressure is negative (like a vacuum) and since n and R must be positive (being a count and a constant respectively), thus you can only get the negative sign from T (temperature). Never mind that baked into R (Rydberg Constant) there are assumptions that would exclude the current application and thus the "Negative Temperature" assertion, it's marketing, and marketing ignores the facts if they get in the way.
This doesn't really help. I pondered this for a while the other day when I read that first and gave up trying to wrap my head around it. I was always under the impression that 0 kelvin (absolute 0) meant a state at which there was no movement at the atomic/subatomic level. It would seem as though to reach a negative temperature, one would have to slow a substances particles to less than 0 movement. Then I realized they were talking about a quantum state and I pretty much gave up trying to understand it at that point, because anything which has the word 'quantum' in it suddenly defies all the rules I'd ever been taught about anything at all. :o)
That was my first reaction when I learned about quantum mechanics - nothing fundamentally works the way I was taught it works, it only appears to work that way under certain conditions.
Though, for this article, my first reaction was And the relevance of this discovery (again) is what, exactly? I didn't understand it before, I don't understand it now, and I don't see how it makes any difference what-so-ever.
- Nec Impar Pluribus, or so I'm told.
In the USA, it means its really, really cold, you'll have to dress well, including good gloves and hat. If there is any wind you'll wand to cover your face too. and the air is very dry, inside, getting a humidifier is a good idea.. If your car or truck has been parked outside for a while you would need to start it and have it warm up for 10 minutes before driving off.
In the rest of the world its cold but bearable, since its just below freezing sidewalks may be slippery.
So, what you're saying is that the canadian climate has below 0 temperatures for two reasons: The system of measurement is fundamentally flawed, and it's colder than we get in this area, normally.
- Nec Impar Pluribus, or so I'm told.
...It'll have something to do with Australia.
Everything on Slashdot has something to do with Australia, now.
Of course it will. Australia is the centre of the universe. Even the name "Aatish Bhatia" is obviously Australian in origin, and Rutgers is a suburb of Sydney I think.
Considering how "new" australia is as a country, it's not surprising that these things may appear to belong to other parts of the world. It's called intertexuality, and it's a natural process of borrowing ideas from established works.
- Nec Impar Pluribus, or so I'm told.
Here!
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.
That a system at negative temperature is hotter than any system at positive temperature is paradoxical if absolute temperature is interpreted as an average internal energy of the system. The paradox is resolved by understanding temperature through its more rigorous definition as the tradeoff between energy and entropy, with the reciprocal of the temperature, thermodynamic beta, as the more fundamental quantity. Systems with positive temperature increase in entropy as one adds energy to the system. Systems with negative temperature decrease in entropy as one adds energy to the system.
You add more energy, but the entropy doesn't increase. Gods damn that moronic blogger and his useless "tricks" metaphor. You don't "trick" shit you stupid fuck. You wouldn't say gunpowder "tricks" a lead projectile to scurry from the gun barrel if you were explaining a gun. We're not idiots, we just need to have the terms defined because some of us hadn't heard the term before in relation to absolute zero.
Protip: Next time you want to submit or vote up a "follow-up" fucking read the damn thing, and compare it to the wiki. Unless it's significantly more useful than the damn wikipedia article, don't fucking submit or vote it up.
Literally 50 years old textbooks. This isn't news at all.
http://www.youtube.com/watch?v=xxa7Y1TLjas
Anthropocentric Neoteny will kill us all!
Inverse temperature is proportional to the rate of change of entropy with energy. So if you can make entropy drop with increasing energy in a system you get negative temperature. Entropy is a measure of the likelihood of a system state so you need unlikely high energy states.
footpaths
Australia was after all, the last nation to survive a global nuclear war On the Beach in 1959.
9/11 Eyewitnesses to Explosive WTC Demolition 1 of 2
http://en.wikipedia.org/wiki/Negative_frequency
I suppose you should call me a semi layman... er... mostly layman. I have a lot of physics knowledge that I've gotten 2nd hand if you will over the years. Huge gaps in my knowledge, so bear with me....
Isn't the article talking about a different way of thinking about temperature? It's not "negative" in terms of it being "less than zero", it's negative in terms of its ability to absorb energy. I find the comparison and the use of the word "temperature" kind of inappropriate.
negative temperature implies by adding energy, you could get back to zero and then keep adding and be positive again, but all of his example actually are entirely different processes...
He cites black holes, which of course is increasing the mass/gravitational force, not "getting colder". Those particles ( particle if you are going to call it a singularity I suppose )
He cites "cooling the sun" which similarly is adding mass and thereby gravitational force, which you might say is "cooling" but I would say is more akin to just adding matter to a "battery"... would the surface temperature of the sun actually go down if you added a meaningful amount of hydrogen or helium to it? I suppose. In the same way, adding logs to a fire, brings the average temperature down on the fire.
And he goes on to say that as the star loses energy its temperature rises... and of course this might be observationally true, but only to a point... once it has lost enough energy ( after a Nova ) , it will undoubtably cool. So that behavior is not simply by the definition of loss of energy. There's more to it.
I have a feeling this is mostly a clash of terminology rather than a misunderstanding. Sort of like classical gravity vs general gravity maybe?
I would like someone to explain to me if negative temperature is indeed possible outside of intense gravitational situations, does this mean that Randall Mill's Hydrino theory on sub-ground state Hydrogen is right?
To get below zero K, y
So you give more energy to it to force it into a high energy state and that lowers its temperature even though it's more energy? Or you force the material to act like it's in a high energy state without giving it the energy so its amount of transmittable heat results in a math glitch? Either way, that's stupid and all it means is temperature isn't measured correctly. I'm in the minority who considers temperature to be total average speed that a group of atoms are moving at. Since that type of system can't drop below zero, I'd say it's superior.
nt.
It's called intertexuality, and it's a natural process of borrowing ideas from established works.
Until people start using copyrights and patents to suppress this process.
I thought about explaining it, and i will do so *without* mentioning the Dalai Lama.
The Situation is very simple: The definition of Temperature you learned in school, namely that it is only related to the average energy of many equal systems *is right*, but only for *classical systems*.
What does it mean?
If i have a classical gas, e.g. air at room temperature and i have to input to it, i can add this energy in whichever distribution i want. Easy to do that, no matter at which temperature we are.
No lets consider a quantum gas (to be complete: a quantum gas and not consiting of harmonic oscillators), e.g. electrons spins which are aligned to a magnetic field. Each of the electron can either have an Energy of -1/2E or +1/2E, where E depends on the electron spin and the magnetig field, but is constant. This means that if i have N electrons, we wont be able to input more energy than N * E into the system. Moreover if only a single electron in not in the high-energy state, we have to flip exactly this electron to get the system into its highest energy state. That may be pretty hard, statistically speaking.
So now imagine a quantum gas somehow statistically exchanging energy with a classical gas. That means, in our case, to bring the quantum gas to the state of Total energy = N*E (from the state of (N-1)*E) a high energy gas molecule would have the hit the very last of the low-ebergy electrons. If the high-energy molecules bounce from the electron in the excited state, then nothing will happen.
It is intuitive that, even if the two gases are in contact, the avergae energy between the systems will *not* be the same, just because its unlikely to flip *all* or *nearly all*.
The fromal version if this consideration is the textbook definition of the Temperature as a property in statistical physics, which is T=dE/dS, where E is the total energy and S is the Entropy (yes, the very same one as in computational science).
In the case of the two-level systems we find (let n be the numebr of systems in exited state)
S is proportional to -(n*log(n/N) + (N-n)*log((N-n)/n))
E is proprotioanl to n
That means that the sign of the temperature changes, as soon as more systems are excited than not.
Maxwell-Boltzmann statistics, and the field of statistical mechanics in general, work quite well with quantized systems. As an example, if you look at Boltzmann's definition of entropy: S = k ln W, where W is the possible number of microstates that can contribute to the system, you can see how statistical mechanics does a good job of handling quantized energy levels. Likewise, the Maxwell-Boltzman distribution does a fine job of describing the population distribution of an equilibrium ensemble of molecules / atoms / whatever with discrete quantized energy levels. The critical term here is equilibrium. If the system is not in equilibrium, such as a laser, then one can argue that it's temperature (at least for the degrees of freedom where there's a population inversion) is not well defined.
The thing that makes the Science paper really interesting is that the negative temperature is observed in the motional degrees of freedom where you normally think about a continuum of energies, and where you seldom have the necessary isolation from other degrees of freedom to prepare such exotic states. The key here is that Bose-Einstein condensate have coherent, quantized motional degrees of freedom that are highly decoupled from the rest of the universe.
For laymen laymens: A negative marklar can be reached by reducing the marklar to marklar.
Don't anthropomorphize systems. They hate it when you do that.
We get negative temperatures in Colorado, every year. It was -20 outside my house last year.
Temperature and other statistical mechanical properties work just fine in systems with discrete energies as a continuum of energy.
Actually, it's not to hard to intuitively understand negative temperature if you think of it as something hotter than the hottest possible temperature. Classically, that isn't possible, but then you need a bit of quantum weirdness.
In a typical system of normal temperature particles of occupy various quantum energy levels available to them. In thermal equilibrium, statistically, lower energy levels tend to get occupied first and higher energy levels have fewer particles. If somehow you can create a stable system where higher energy states are occupied, but by some quirk (of quantum mechanics), lower ones are not, it turns out that is what a negative temperature system is.
As it turns temporarily creating a system where the higher energy levels are occupied before the lower ones is something that people do all the time to create a pumped laser. But lasers aren't designed to be a stable system (you eventually want the higher energy state to emit light/photons and fall to the lower energy state), so although the population of the energy states are inverted (more in the upper energy states), it's not stable, so it's generally not accurate to call this a negative temperature system.
The reason the "sign" of the temperature is negative is just a problem with the definition of temperature. For most defintions of temperature, if you add energy, you increase entropy, so temperature is a measure of how these relate to each other (the slope). If somehow when you add energy to your system, you decrease entropy of your system (e.g, you pack the upper energy states even tighter reducing entropy instead of just letting particles in all energy states into statistically higher energy states), the slope is negative.
There's a link in the article to Leprechauns and Laser Beams, which IMHO does a much better job of explaining things. As I understand it, negative temperatures don't just come from the entropy-based definition of temperature. You also need to be talking about a system whose energy content is capped. Normal materials don't do this -- you can keep adding energy (speeding up atoms) as long as you want. But if you have a group of atoms with exactly two energy states (high and low), once every atom is in the high-energy state you can't add more energy. Apparently, one example of this is a laser.
From an entropy point of view, the lowest energy and highest energy states have identical entropy (i.e. none -- one possible state). Entropy reaches a peak with half of the atoms in the high energy state, since this gives the largest number of possible atom state combinations.
Temperature is defined as the slope of the energy/entropy curve. The curve goes vertical at max entropy. If I understand right, at this point the temperature overflows like an integer variable, going from +inf to -inf and approaching zero from the negative end. (It's not really a continuous curve, but I don't know enough to guess at what difference that makes.)
So it sounds like the recent news about a negative-temperature gas was more about creating a new material with these sorts of quantum states. The negative temperature part caught the attention of the reporters (and the rest of us), but isn't the real scientific discovery. That's my reading of it, anyway.
Visit the
negative freeze lasers?!
monkey hive
How can you go below the absence of atomic/molecular motion? 'Solid' helium is as cold as matter can get. Anything less is a physical impossibility, unless there's no matter involved.
If we want to get our names in the news we play with the meanings of the words we use. I.E. Negative Kelvin Temperaturs. Technically correct but basically sensationalistic in nature.
...It'll have something to do with Australia.
Everything on Slashdot has something to do with Australia, now.
It has less than nothing to do with ...
While the quantum gas is in a negative temperature state...
...can you boot Linux on it? :D
Particles at "negative" temperature like to give up energy. Then there's this explanation: "Temperature measures the willingness of an object to give up energy". This is contradictory.
I think most of the confusion is caused by this horribly nonsensical naming
If you think the point of the analogy was to accurately portray the motivations and social nature of such people, especially considering how over the top cartoonist it is, you would have to be practically dense and have bigger issues than trying to understand the implications of a generalized temperature.definition. Just be thankful you are not an emotionally invested gearhead, otherwise you would be seeing every crappy car analogy as an attack on the proper use and operation of cars.
OK, in grasping for an explanation of "negative temperature" here's my shot. Let's say you have an ordinary glass of water, half full at room temperature. Now you pour boiling water in. The resulting glass is warmer.
Now let's re-run the experiment starting with the same glass of half-full, room temperature water. You calculate the result that you would get from putting in a drop of absolute zero water. Let's say that would drop the water to just above freezing.
You put in a drop of "negative temperature water", an exotic substance that isn't frozen and somehow magically exists. The room-temperature water immediately freezes rock hard.
Of course this scenario doesn't exist anywhere in the normal world; but perhaps it exists at the quantum level.
You can poke holes in this explanation by saying that the result of mixing isn't the same as a temperature. True. It's not a measurement of the magic substance. OTOH, if you measured the magic substance Schroedinger's polar cat would leap out of the beaker and bite your face off, so don't do that.
For all intensive purposes, "whom" is no longer a word. That begs the question, "who cares"?
Absolute temperature is a phony measurement - what we're really measuring is it's *inverse*. This would be a measurement of "motionlessness" and the rule for is is that it can't tend to infinity - but positive and negative values are allowed. Hence Newton was wrong, because an "object at rest" would have infinite motionlessness, and therefore can't exist. Everything MUST move, and has a small tendency also to "go with the flow", a.k.a gravity. The flipside to this is that it isn't a particularly useful measurement numerically - it's just the inverse of absolute temperature. But so far as the universe is concerned, it's the number that it wants to keep real, and bounded.
Do they have one for something less than a layman? Perhaps one written for a complete ignoramus like myself.
or else!
You keep using that word. I do not think it's spelled the way you think it's spelled. Try "Inconceivable."